Finite Group Databasebeta

← C3×#82714 #11836015

Subgroups — C3×#82714 #11836015

Order 1152.

2077 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic, complemented
4C2×C3×#937C211yesmaximal, characteristic, complemented
5C2×C3×#930C211yesmaximal, characteristic, complemented
6C2×C3×#882C211yesmaximal, characteristic, complemented
7C3×#5223C211yesmaximal, characteristic, complemented
8C3×#5223C211yesmaximal, characteristic, complemented
9C3×#5223C211yesmaximal, characteristic, complemented
10C3×#5213C211yesmaximal, characteristic, complemented
11C3×#4991C211yesmaximal, characteristic, complemented
12C3×#4990C211yesmaximal, characteristic, complemented
13C3×#4961C211yesmaximal, characteristic, complemented
14C3×#4960C211yesmaximal, characteristic, complemented
15C3×#4951C211yesmaximal, characteristic, complemented
16C3×#2669—31nomaximal
17#82714C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic, complemented
22C23×C32×C4C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic
28C22×C3×#67C2211yescharacteristic, complemented
29C22×C3×#67C2211yescharacteristic, complemented
30C22×C3×D12C2211yescharacteristic
31C22×C3×D12C2211yescharacteristic
32C32×#121—24no—
33C2×C32×C4⋊C4C2211yescharacteristic, complemented
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×C32×C22⋊C4C2211yescharacteristic, complemented
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic, complemented
39C2×C3×#217C2211yescharacteristic, complemented
40C3×#940—24no—
41C3×#937—24no—
42C3×#937—24no—
43C3×#930—24no—
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
53C2×C3×C4×Dic3C2211yescharacteristic, complemented
54C3×#882—24no—
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57C3×C3⋊#95C2211yescharacteristic, complemented
58C3×C3⋊#95C2211yescharacteristic, complemented
59C2×C3×#127—31no—
60C2×C3×#121—21no—
61C2×C3×#121—31no—
62C2×C3×#121D311yescharacteristic, complemented
63C2×C3×#121C2×C311yescharacteristic, complemented
64C2×C3×#120—31no—
65C2×C3×#120—31no—
66C2×C3×#120—31no—
67C2×#940C2×C311yescharacteristic, complemented
68C2×#937C2×C311yescharacteristic, complemented
69C2×#937C2×C311yescharacteristic, complemented
70C2×#930C2×C311yescharacteristic, complemented
71C2×#882C2×C311yescharacteristic, complemented
72C3×#394—31no—
73C3×#394—31no—
74C3×#392—31no—
75C3×#392—31no—
76C3×#392—31no—
77C3×#392—31no—
78C3×#388—31no—
79C3×#388—31no—
80C3×#386—31no—
81#5223C2×C311yescharacteristic, complemented
82#5223C2×C311yescharacteristic, complemented
83#5223C2×C311yescharacteristic, complemented
84#5213C2×C311yescharacteristic, complemented
85#4991C2×C311yescharacteristic, complemented
86#4990C2×C311yescharacteristic, complemented
87#4961C2×C311yescharacteristic, complemented
88#4960C2×C311yescharacteristic, complemented
89#4951C2×C311yescharacteristic, complemented
90C24×C32C2311yescharacteristic
91C24×C32C2311yescharacteristic
92C24×C32C2311yescharacteristic
93C23×C3×D3—22no—
94C23×C3×D3—22no—
95C23×C3×D3—22no—
96C23×C3×D3—41no—
97C23×C3×D3—41no—
98C23×C3×D3—41no—
99C23×C3×D3—41no—
100C23×C3×D3C2311yescharacteristic
101C23×C3×D3C2311yescharacteristic
102C23×C3×D3C2311yescharacteristic
103C2×C32×D4—22no—
104C2×C32×D4—22no—
105C2×C32×D4—22no—
106C2×C32×D4—22no—
107C2×C32×D4—22no—
108C2×C32×D4—22no—
109C2×C32×D4—41no—
110C2×C32×D4—41no—
111C2×C32×D4—41no—
112C22×C32×C4—22no—
113C22×C32×C4—22no—
114C22×C32×C4—41no—
115C22×C32×C4C2311yescharacteristic
116C22×C32×C4C2311yescharacteristic
117C22×C32×C4C2311yescharacteristic
118C22×C32×C4C2311yescharacteristic
119C2×C3×#67—22no—
120C2×C3×#67—22no—
121C2×C3×#67—22no—
122C2×C3×#67—22no—
123C2×C3×#67—22no—
124C2×C3×#67—22no—
125C2×C3×#67—22no—
126C2×C3×#67—22no—
127C2×C3×#67—22no—
128C2×C3×#67—41no—
129C2×C3×#67—41no—
130C2×C3×#67—41no—
131C2×C3×#67—41no—
132C2×C3×#67—41no—
133C2×C3×#67—41no—
134C2×C3×#67—41no—
135C2×C3×#67—41no—
136C2×C3×#67—41no—
137C2×C3×#67—41no—
138C2×C3×#67—41no—
139C2×C3×#67D414yescomplemented
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2311yescharacteristic
145C2×C3×D12—22no—
146C2×C3×D12—22no—
147C2×C3×D12—22no—
148C2×C3×D12—22no—
149C2×C3×D12—41no—
150C2×C3×D12—41no—
151C32×C4⋊C4—22no—
152C32×C22⋊C4—22no—
153C32×C22⋊C4D414yescomplemented
154C3×#217—22no—
155C3×#217—22no—
156C3×#217—41no—
157C3×#217—41no—
158C3×(C2×D3)⋊C4—22no—
159C3×(C2×D3)⋊C4—22no—
160C3×(C2×D3)⋊C4—22no—
161C3×(C2×D3)⋊C4—22no—
162C3×(C2×D3)⋊C4—22no—
163C3×(C2×D3)⋊C4—22no—
164C3×(C2×D3)⋊C4—41no—
165C3×(C2×D3)⋊C4D414yescomplemented
166C3×C4⋊Dic3—22no—
167C3×C4×Dic3—22no—
168#2669—31noSylow
169C25×C3—31no—
170C24×D3C22×C311yescharacteristic
171C22×C3×D4—21no—
172C22×C3×D4—21no—
173C22×C3×D4—21no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4—31no—
183C22×C3×D4C2×D311yescharacteristic
184C22×C3×D4C2×D311yescharacteristic
185C22×C3×D4C2×D311yescharacteristic, complemented
186C22×C3×D4C22×C311yescharacteristic
187C22×C3×D4C22×C311yescharacteristic
188C22×C3×D4C22×C311yescharacteristic, complemented
189C23×C3×C4—21no—
190C23×C3×C4C2×D311yescharacteristic, complemented
191C23×C3×C4C22×C311yescharacteristic, complemented
192C22×#67C22×C311yescharacteristic
193C22×#67C22×C311yescharacteristic
194C22×#67C22×C311yescharacteristic
195C22×#67C22×C311yescharacteristic
196C22×#67C22×C311yescharacteristic
197C22×#67C22×C311yescharacteristic, complemented
198C22×#67C22×C311yescharacteristic, complemented
199C22×D12C22×C311yescharacteristic
200C22×D12C22×C311yescharacteristic
201C3×#127—64no—
202C3×#121—28no—
203C3×#121—24no—
204C3×#121—24no—
205C3×#121—64no—
206C3×#120—64no—
207C3×#120—64no—
208C3×#120—64no—
209C2×C3×C4⋊C4—21no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
212C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
213C2×C3×C22⋊C4—21no—
214C2×C3×C22⋊C4—21no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4—31no—
217C2×C3×C22⋊C4—31no—
218C2×C3×C22⋊C4—31no—
219C2×C3×C22⋊C4—31no—
220C2×C3×C22⋊C4—31no—
221C2×C3×C22⋊C4—31no—
222C2×C3×C22⋊C4—31no—
223C2×C3×C22⋊C4—31no—
224C2×C3×C22⋊C4—31no—
225C2×C3×C22⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4C2×D311yescharacteristic
228C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
229C2×C3×C22⋊C4C22×C311yescharacteristic
230C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
231C2×C3×C42—31no—
232C2×#217C22×C311yescharacteristic
233C2×#217C22×C311yescharacteristic
234C2×#217C22×C311yescharacteristic, complemented
235C2×#217C22×C311yescharacteristic, complemented
236#940—24no—
237#937—24no—
238#937—24no—
239#930—24no—
240C2×(C2×D3)⋊C4C22×C311yescharacteristic
241C2×(C2×D3)⋊C4C22×C311yescharacteristic
242C2×(C2×D3)⋊C4C22×C311yescharacteristic
243C2×(C2×D3)⋊C4C22×C311yescharacteristic
244C2×(C2×D3)⋊C4C22×C311yescharacteristic
245C2×(C2×D3)⋊C4C22×C311yescharacteristic
246C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
247C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
248C2×C4⋊Dic3C22×C311yescharacteristic, complemented
249C2×C4×Dic3C22×C311yescharacteristic, complemented
250#882—24no—
251C3×#95—31no—
252C3×#95—31no—
253C3×#95—31no—
254C3×#95—31no—
255C3⋊#95C22×C311yescharacteristic, complemented
256C3⋊#95C22×C311yescharacteristic, complemented
257C3⋊#95C22×C311yescharacteristic, complemented
258C3⋊#95C22×C311yescharacteristic, complemented
259C23×C32—21no—
260C23×C32—21no—
261C23×C32—21no—
262C23×C32—21no—
263C23×C32—21no—
264C23×C32—21no—
265C23×C32—21no—
266C23×C32—21no—
267C23×C32—21no—
268C23×C32—21no—
269C23×C32—21no—
270C23×C32—21no—
271C23×C32—21no—
272C23×C32—21no—
273C23×C32—21no—
274C23×C32—21no—
275C23×C32—21no—
276C23×C32—21no—
277C23×C32—21no—
278C23×C32C2×D412yes—
279C23×C32C2×D412yes—
280C23×C32C2411yescharacteristic
281C22×C3×D3—21no—
282C22×C3×D3—21no—
283C22×C3×D3—21no—
284C22×C3×D3—21no—
285C22×C3×D3—21no—
286C22×C3×D3—21no—
287C22×C3×D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3—21no—
291C22×C3×D3—21no—
292C22×C3×D3—21no—
293C22×C3×D3—21no—
294C22×C3×D3—21no—
295C22×C3×D3—21no—
296C22×C3×D3—21no—
297C22×C3×D3—21no—
298C22×C3×D3—21no—
299C22×C3×D3—21no—
300C22×C3×D3—44no—
301C22×C3×D3—44no—
302C22×C3×D3—44no—
303C22×C3×D3—44no—
304C22×C3×D3—44no—
305C22×C3×D3—44no—
306C22×C3×D3—44no—
307C22×C3×D3C2×D412yes—
308C22×C3×D3C2×D412yes—
309C32×D4—44no—
310C32×D4—44no—
311C32×D4—44no—
312C2×C32×C4—21no—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4—21no—
317C2×C32×C4—21no—
318C2×C32×C4—21no—
319C2×C32×C4—21no—
320C2×C32×C4—21no—
321C2×C32×C4—44no—
322C2×C32×C4C2×D412yes—
323C2×C32×C4C2×D412yes—
324C2×C32×C4C2×D412yes—
325C3×#67—44no—
326C3×#67—44no—
327C3×#67—44no—
328C3×#67—44no—
329C3×#67—44no—
330C3×#67—44no—
331C3×#67—44no—
332C2×C3×Dic3—21no—
333C2×C3×Dic3—21no—
334C2×C3×Dic3—21no—
335C2×C3×Dic3—21no—
336C2×C3×Dic3—21no—
337C2×C3×Dic3—21no—
338C2×C3×Dic3—21no—
339C2×C3×Dic3—21no—
340C2×C3×Dic3—21no—
341C2×C3×Dic3—21no—
342C2×C3×Dic3—21no—
343C2×C3×Dic3—21no—
344C2×C3×Dic3—21no—
345C2×C3×Dic3C2×D412yes—
346C2×C3×Dic3C2×D412yes—
347C3×D12—44no—
348C3×D12—44no—
349C2×#127—31no—
350C2×#121—31no—
351C2×#121C3×D311yescharacteristic, complemented
352C2×#120—31no—
353C2×#120—31no—
354C2×#120—31no—
355#394—31no—
356#394—31no—
357#392—31no—
358#392—31no—
359#392—31no—
360#392—31no—
361#388—31no—
362#388—31no—
363#386—31no—
364C24×C3—21no—
365C24×C3—21no—
366C24×C3—21no—
367C24×C3—31no—
368C24×C3—31no—
369C24×C3—31no—
370C24×C3—62no—
371C24×C3—62no—
372C24×C3—62no—
373C24×C3—121no—
374C24×C3—121no—
375C24×C3—121no—
376C24×C3—121no—
377C24×C3C22×D311yescharacteristic
378C24×C3C22×D311yescharacteristic
379C24×C3C22×D311yescharacteristic
380C24×C3C23×C311yescharacteristic
381C24×C3C23×C311yescharacteristic
382C24×C3C23×C311yescharacteristic
383C23×D3—22no—
384C23×D3—22no—
385C23×D3—22no—
386C23×D3—41no—
387C23×D3—41no—
388C23×D3—41no—
389C23×D3—41no—
390C23×D3C23×C311yescharacteristic
391C23×D3C23×C311yescharacteristic
392C23×D3C23×C311yescharacteristic
393C2×C3×D4—24no—
394C2×C3×D4—24no—
395C2×C3×D4—24no—
396C2×C3×D4—22no—
397C2×C3×D4—22no—
398C2×C3×D4—22no—
399C2×C3×D4—22no—
400C2×C3×D4—22no—
401C2×C3×D4—22no—
402C2×C3×D4—22no—
403C2×C3×D4—22no—
404C2×C3×D4—22no—
405C2×C3×D4—22no—
406C2×C3×D4—22no—
407C2×C3×D4—22no—
408C2×C3×D4—34no—
409C2×C3×D4—42no—
410C2×C3×D4—42no—
411C2×C3×D4—42no—
412C2×C3×D4—41no—
413C2×C3×D4—41no—
414C2×C3×D4—41no—
415C2×C3×D4—41no—
416C2×C3×D4—41no—
417C2×C3×D4—41no—
418C2×C3×D4—42no—
419C2×C3×D4—42no—
420C2×C3×D4—42no—
421C2×C3×D4—62no—
422C2×C3×D4—62no—
423C2×C3×D4—62no—
424C2×C3×D4—62no—
425C2×C3×D4—62no—
426C2×C3×D4—62no—
427C2×C3×D4—62no—
428C2×C3×D4—62no—
429C2×C3×D4—62no—
430C2×C3×D4—62no—
431C2×C3×D4—62no—
432C2×C3×D4—62no—
433C2×C3×D4—62no—
434C2×C3×D4—121no—
435C2×C3×D4—121no—
436C2×C3×D4—121no—
437C2×C3×D4—121no—
438C2×C3×D4—121no—
439C2×C3×D4—121no—
440C2×C3×D4—121no—
441C2×C3×D4—121no—
442C2×C3×D4—121no—
443C2×C3×D4—121no—
444C2×C3×D4—121no—
445C2×C3×D4—121no—
446C2×C3×D4—121no—
447C22×C3×C4—24no—
448C22×C3×C4—22no—
449C22×C3×C4—22no—
450C22×C3×C4—22no—
451C22×C3×C4—22no—
452C22×C3×C4—21no—
453C22×C3×C4—21no—
454C22×C3×C4—21no—
455C22×C3×C4—21no—
456C22×C3×C4—31no—
457C22×C3×C4—31no—
458C22×C3×C4—31no—
459C22×C3×C4—31no—
460C22×C3×C4—31no—
461C22×C3×C4—42no—
462C22×C3×C4—41no—
463C22×C3×C4—41no—
464C22×C3×C4—42no—
465C22×C3×C4C22×D311yescharacteristic
466C22×C3×C4C22×D311yescharacteristic
467C22×C3×C4C22×D311yescharacteristic
468C22×C3×C4C22×D311yescharacteristic
469C22×C3×C4C23×C311yescharacteristic
470C22×C3×C4C23×C311yescharacteristic
471C22×C3×C4C23×C311yescharacteristic
472C22×C3×C4C23×C311yescharacteristic
473C2×#67—22no—
474C2×#67—22no—
475C2×#67—22no—
476C2×#67—22no—
477C2×#67—22no—
478C2×#67—22no—
479C2×#67—22no—
480C2×#67—22no—
481C2×#67—22no—
482C2×#67—41no—
483C2×#67—41no—
484C2×#67—41no—
485C2×#67—41no—
486C2×#67—41no—
487C2×#67—41no—
488C2×#67—41no—
489C2×#67—41no—
490C2×#67—41no—
491C2×#67—41no—
492C2×#67—41no—
493C2×#67C3×D414yescomplemented
494C22×Dic3C23×C311yescharacteristic
495C22×Dic3C23×C311yescharacteristic
496C22×Dic3C23×C311yescharacteristic
497C22×Dic3C23×C311yescharacteristic
498C22×Dic3C23×C311yescharacteristic
499C2×D12—22no—
500C2×D12—22no—
501C2×D12—22no—
502C2×D12—22no—
503C2×D12—41no—
504C2×D12—41no—
505C3×C4⋊C4—24no—
506C3×C4⋊C4—22no—
507C3×C4⋊C4—22no—
508C3×C4⋊C4—62no—
509C3×C22⋊C4—24no—
510C3×C22⋊C4—22no—
511C3×C22⋊C4—22no—
512C3×C22⋊C4—24no—
513C3×C22⋊C4—34no—
514C3×C22⋊C4—62no—
515C3×C22⋊C4—62no—
516C3×C22⋊C4—62no—
517C3×C22⋊C4—62no—
518C3×C22⋊C4—62no—
519C3×C22⋊C4—62no—
520C3×C22⋊C4—62no—
521C3×C22⋊C4—62no—
522C3×C22⋊C4—121no—
523C3×C22⋊C4—121no—
524C3×C22⋊C4—121no—
525C3×C22⋊C4#6714yescomplemented
526C3×C22⋊C4C3×D414yescomplemented
527C3×C42—62no—
528#217—22no—
529#217—22no—
530#217—41no—
531#217—41no—
532(C2×D3)⋊C4—22no—
533(C2×D3)⋊C4—22no—
534(C2×D3)⋊C4—22no—
535(C2×D3)⋊C4—22no—
536(C2×D3)⋊C4—22no—
537(C2×D3)⋊C4—22no—
538(C2×D3)⋊C4—41no—
539(C2×D3)⋊C4C3×D414yescomplemented
540C4⋊Dic3—22no—
541C4×Dic3—22no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32—22no—
546C22×C32—22no—
547C22×C32—22no—
548C22×C32—41no—
549C22×C32—41no—
550C22×C32—41no—
551C22×C32—41no—
552C22×C32—41no—
553C22×C32—41no—
554C22×C32—41no—
555C22×C32—41no—
556C22×C32—41no—
557C22×C32—41no—
558C22×C32—41no—
559C22×C32—41no—
560C22×C32—41no—
561C22×C32—41no—
562C22×C32—41no—
563C22×C32C22×D411yescharacteristic
564C22×C32C22×D411yescharacteristic
565C22×C32C22×D411yescharacteristic
566C22×C32H(5,𝔽2)11yescharacteristic
567C22×C32H(5,𝔽2)11yescharacteristic
568C22×C32H(5,𝔽2)11yescharacteristic
569C22×C32H(5,𝔽2)11yescharacteristic
570C2×C3×D3—22no—
571C2×C3×D3—22no—
572C2×C3×D3—22no—
573C2×C3×D3—22no—
574C2×C3×D3—22no—
575C2×C3×D3—22no—
576C2×C3×D3—416no—
577C2×C3×D3—41no—
578C2×C3×D3—41no—
579C2×C3×D3—41no—
580C2×C3×D3—41no—
581C2×C3×D3—41no—
582C2×C3×D3—41no—
583C2×C3×D3—41no—
584C2×C3×D3—41no—
585C2×C3×D3—41no—
586C2×C3×D3—41no—
587C2×C3×D3—41no—
588C2×C3×D3—41no—
589C2×C3×D3—41no—
590C2×C3×D3—41no—
591C2×C3×D3—41no—
592C32×C4—22no—
593C32×C4—22no—
594C32×C4—22no—
595C32×C4—41no—
596C3×Dic3—22no—
597C3×Dic3—22no—
598C3×Dic3—41no—
599C3×Dic3—41no—
600C3×Dic3—41no—
601C25—31no—
602C22×D4—31no—
603C22×D4—31no—
604C22×D4—31no—
605C22×D4—31no—
606C22×D4—31no—
607C22×D4—31no—
608C22×D4—31no—
609C22×D4—31no—
610C22×D4—31no—
611C22×D4C2×C3×D311yescharacteristic
612C22×D4C2×C3×D311yescharacteristic
613C22×D4C2×C3×D311yescharacteristic, complemented
614C23×C4C2×C3×D311yescharacteristic, complemented
615#127—64no—
616#121—24no—
617#121—64no—
618#120—64no—
619#120—64no—
620#120—64no—
621C2×C4⋊C4—31no—
622C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
623C2×C22⋊C4—31no—
624C2×C22⋊C4—31no—
625C2×C22⋊C4—31no—
626C2×C22⋊C4—31no—
627C2×C22⋊C4—31no—
628C2×C22⋊C4—31no—
629C2×C22⋊C4—31no—
630C2×C22⋊C4—31no—
631C2×C22⋊C4—31no—
632C2×C22⋊C4—31no—
633C2×C22⋊C4—31no—
634C2×C22⋊C4—31no—
635C2×C22⋊C4C2×C3×D311yescharacteristic
636C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
637C2×C42—31no—
638#95—31no—
639#95—31no—
640#95—31no—
641#95—31no—
642C23×C3—22no—
643C23×C3—22no—
644C23×C3—21no—
645C23×C3—21no—
646C23×C3—21no—
647C23×C3—21no—
648C23×C3—21no—
649C23×C3—21no—
650C23×C3—21no—
651C23×C3—21no—
652C23×C3—21no—
653C23×C3—21no—
654C23×C3—21no—
655C23×C3—21no—
656C23×C3—21no—
657C23×C3—21no—
658C23×C3—21no—
659C23×C3—21no—
660C23×C3—21no—
661C23×C3—21no—
662C23×C3—21no—
663C23×C3—21no—
664C23×C3—21no—
665C23×C3—21no—
666C23×C3—21no—
667C23×C3—21no—
668C23×C3—22no—
669C23×C3—21no—
670C23×C3—21no—
671C23×C3—21no—
672C23×C3—21no—
673C23×C3—21no—
674C23×C3—21no—
675C23×C3—21no—
676C23×C3—21no—
677C23×C3—21no—
678C23×C3—21no—
679C23×C3—21no—
680C23×C3—21no—
681C23×C3—21no—
682C23×C3—21no—
683C23×C3—21no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3—32no—
687C23×C3—32no—
688C23×C3—41no—
689C23×C3—41no—
690C23×C3—41no—
691C23×C3—41no—
692C23×C3—41no—
693C23×C3—41no—
694C23×C3—41no—
695C23×C3—41no—
696C23×C3—41no—
697C23×C3—41no—
698C23×C3—41no—
699C23×C3—41no—
700C23×C3—41no—
701C23×C3—41no—
702C23×C3—41no—
703C23×C3—41no—
704C23×C3—61no—
705C23×C3—61no—
706C23×C3—61no—
707C23×C3—61no—
708C23×C3—61no—
709C23×C3—61no—
710C23×C3—61no—
711C23×C3—61no—
712C23×C3—61no—
713C23×C3—61no—
714C23×C3—61no—
715C23×C3—61no—
716C23×C3—61no—
717C23×C3—61no—
718C23×C3—61no—
719C23×C3—61no—
720C23×C3—61no—
721C23×C3—61no—
722C23×C3—61no—
723C23×C3—124no—
724C23×C3—124no—
725C23×C3—124no—
726C23×C3—124no—
727C23×C3—124no—
728C23×C3—124no—
729C23×C3—124no—
730C23×C3D3×D412yes—
731C23×C3C2×#6712yes—
732C23×C3C2×C3×D412yes—
733C23×C3C2×C3×D412yes—
734C23×C3C23×D311yescharacteristic
735C23×C3C24×C311yescharacteristic
736C22×D3—21no—
737C22×D3—21no—
738C22×D3—21no—
739C22×D3—21no—
740C22×D3—21no—
741C22×D3—21no—
742C22×D3—21no—
743C22×D3—21no—
744C22×D3—21no—
745C22×D3—21no—
746C22×D3—21no—
747C22×D3—21no—
748C22×D3—21no—
749C22×D3—21no—
750C22×D3—21no—
751C22×D3—21no—
752C22×D3—21no—
753C22×D3—21no—
754C22×D3—21no—
755C22×D3—44no—
756C22×D3—44no—
757C22×D3—44no—
758C22×D3—44no—
759C22×D3—44no—
760C22×D3—44no—
761C22×D3—44no—
762C22×D3C2×C3×D412yes—
763C22×D3C2×C3×D412yes—
764C3×D4—44no—
765C3×D4—44no—
766C3×D4—44no—
767C3×D4—44no—
768C3×D4—48no—
769C3×D4—44no—
770C3×D4—44no—
771C3×D4—48no—
772C3×D4—48no—
773C3×D4—124no—
774C3×D4—124no—
775C3×D4—124no—
776C3×D4—124no—
777C3×D4—124no—
778C3×D4—124no—
779C3×D4—124no—
780C3×D4—124no—
781C3×D4—124no—
782C2×C3×C4—22no—
783C2×C3×C4—22no—
784C2×C3×C4—21no—
785C2×C3×C4—21no—
786C2×C3×C4—21no—
787C2×C3×C4—21no—
788C2×C3×C4—21no—
789C2×C3×C4—21no—
790C2×C3×C4—21no—
791C2×C3×C4—21no—
792C2×C3×C4—21no—
793C2×C3×C4—21no—
794C2×C3×C4—21no—
795C2×C3×C4—21no—
796C2×C3×C4—22no—
797C2×C3×C4—21no—
798C2×C3×C4—21no—
799C2×C3×C4—21no—
800C2×C3×C4—21no—
801C2×C3×C4—21no—
802C2×C3×C4—21no—
803C2×C3×C4—22no—
804C2×C3×C4—22no—
805C2×C3×C4—22no—
806C2×C3×C4—32no—
807C2×C3×C4—32no—
808C2×C3×C4—41no—
809C2×C3×C4—41no—
810C2×C3×C4—41no—
811C2×C3×C4—41no—
812C2×C3×C4—41no—
813C2×C3×C4—41no—
814C2×C3×C4—44no—
815C2×C3×C4—44no—
816C2×C3×C4—48no—
817C2×C3×C4—61no—
818C2×C3×C4—61no—
819C2×C3×C4—61no—
820C2×C3×C4—61no—
821C2×C3×C4—61no—
822C2×C3×C4—61no—
823C2×C3×C4—61no—
824C2×C3×C4—61no—
825C2×C3×C4—61no—
826C2×C3×C4—61no—
827C2×C3×C4—61no—
828C2×C3×C4—61no—
829C2×C3×C4—61no—
830C2×C3×C4D3×D412yes—
831C2×C3×C4C2×#6712yes—
832C2×C3×C4C2×#6712yes—
833C2×C3×C4C2×C3×D412yes—
834C2×C3×C4C2×C3×D412yes—
835C2×C3×C4C2×C3×D412yes—
836#67—44no—
837#67—44no—
838#67—44no—
839#67—44no—
840#67—44no—
841#67—44no—
842#67—44no—
843C2×Dic3—21no—
844C2×Dic3—21no—
845C2×Dic3—21no—
846C2×Dic3—21no—
847C2×Dic3—21no—
848C2×Dic3—21no—
849C2×Dic3—21no—
850C2×Dic3—21no—
851C2×Dic3—21no—
852C2×Dic3—21no—
853C2×Dic3—21no—
854C2×Dic3—21no—
855C2×Dic3—21no—
856C2×Dic3C2×C3×D412yes—
857C2×Dic3C2×C3×D412yes—
858D12—44no—
859D12—44no—
860C2×C32—42no—
861C2×C32—42no—
862C2×C32—81no—
863C2×C32#53411yescharacteristic
864C2×C32#53511yescharacteristic
865C2×C32#53511yescharacteristic
866C2×C32D4211yescharacteristic
867C2×C32D4211yescharacteristic
868C2×C32D4211yescharacteristic
869C2×C32#56011yescharacteristic
870C3×D3—42no—
871C3×D3—42no—
872C3×D3—81no—
873C24—31no—
874C24—31no—
875C24—31no—
876C24—62no—
877C24—62no—
878C24—62no—
879C24—121no—
880C24—121no—
881C24—121no—
882C24—121no—
883C24C22×C3×D311yescharacteristic
884C24C22×C3×D311yescharacteristic
885C24C22×C3×D311yescharacteristic
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—34no—
893C2×D4—41no—
894C2×D4—41no—
895C2×D4—41no—
896C2×D4—62no—
897C2×D4—62no—
898C2×D4—62no—
899C2×D4—62no—
900C2×D4—62no—
901C2×D4—62no—
902C2×D4—62no—
903C2×D4—62no—
904C2×D4—62no—
905C2×D4—62no—
906C2×D4—62no—
907C2×D4—62no—
908C2×D4—62no—
909C2×D4—121no—
910C2×D4—121no—
911C2×D4—121no—
912C2×D4—121no—
913C2×D4—121no—
914C2×D4—121no—
915C2×D4—121no—
916C2×D4—121no—
917C2×D4—121no—
918C2×D4—121no—
919C2×D4—121no—
920C2×D4—121no—
921C2×D4—121no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—31no—
925C22×C4—31no—
926C22×C4—31no—
927C22×C4—31no—
928C22×C4—31no—
929C22×C4—41no—
930C22×C4C22×C3×D311yescharacteristic
931C22×C4C22×C3×D311yescharacteristic
932C22×C4C22×C3×D311yescharacteristic
933C22×C4C22×C3×D311yescharacteristic
934C4⋊C4—22no—
935C4⋊C4—62no—
936C22⋊C4—22no—
937C22⋊C4—34no—
938C22⋊C4—62no—
939C22⋊C4—62no—
940C22⋊C4—62no—
941C22⋊C4—62no—
942C22⋊C4—62no—
943C22⋊C4—62no—
944C22⋊C4—62no—
945C22⋊C4—62no—
946C22⋊C4—121no—
947C22⋊C4—121no—
948C22⋊C4—121no—
949C22⋊C4C3×#6714yescomplemented
950C42—62no—
951C22×C3—24no—
952C22×C3—22no—
953C22×C3—22no—
954C22×C3—22no—
955C22×C3—22no—
956C22×C3—22no—
957C22×C3—22no—
958C22×C3—22no—
959C22×C3—22no—
960C22×C3—22no—
961C22×C3—22no—
962C22×C3—22no—
963C22×C3—22no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—21no—
971C22×C3—42no—
972C22×C3—42no—
973C22×C3—42no—
974C22×C3—42no—
975C22×C3—42no—
976C22×C3—42no—
977C22×C3—42no—
978C22×C3—42no—
979C22×C3—42no—
980C22×C3—42no—
981C22×C3—42no—
982C22×C3—42no—
983C22×C3—41no—
984C22×C3—41no—
985C22×C3—41no—
986C22×C3—41no—
987C22×C3—41no—
988C22×C3—41no—
989C22×C3—41no—
990C22×C3—41no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—41no—
1001C22×C3—41no—
1002C22×C3—41no—
1003C22×C3—41no—
1004C22×C3—41no—
1005C22×C3—41no—
1006C22×C3—41no—
1007C22×C3—41no—
1008C22×C3—41no—
1009C22×C3—41no—
1010C22×C3—41no—
1011C22×C3—41no—
1012C22×C3—41no—
1013C22×C3—62no—
1014C22×C3—62no—
1015C22×C3—62no—
1016C22×C3—62no—
1017C22×C3—62no—
1018C22×C3—62no—
1019C22×C3—81no—
1020C22×C3—81no—
1021C22×C3—81no—
1022C22×C3—81no—
1023C22×C3—81no—
1024C22×C3—81no—
1025C22×C3—81no—
1026C22×C3—81no—
1027C22×C3—1216no—
1028C22×C3—121no—
1029C22×C3—121no—
1030C22×C3—121no—
1031C22×C3—121no—
1032C22×C3—121no—
1033C22×C3—121no—
1034C22×C3—121no—
1035C22×C3—121no—
1036C22×C3—121no—
1037C22×C3—121no—
1038C22×C3—121no—
1039C22×C3—121no—
1040C22×C3—121no—
1041C22×C3—121no—
1042C22×C3—121no—
1043C22×C3C2×D3×D411yescharacteristic
1044C22×C3C2×D3×D411yescharacteristic
1045C22×C3#100411yescharacteristic
1046C22×C3#100411yescharacteristic
1047C22×C3#100911yescharacteristic
1048C22×C3#100911yescharacteristic
1049C22×C3C22×#6711yescharacteristic
1050C22×C3C22×C3×D411yescharacteristic
1051C22×C3C22×C3×D411yescharacteristic
1052C22×C3C22×C3×D411yescharacteristic
1053C22×C3C3×H(5,𝔽2)11yescharacteristic
1054C22×C3C3×H(5,𝔽2)11yescharacteristic
1055C22×C3C3×H(5,𝔽2)11yescharacteristic
1056C22×C3C3×H(5,𝔽2)11yescharacteristic
1057C2×D3—22no—
1058C2×D3—22no—
1059C2×D3—22no—
1060C2×D3—22no—
1061C2×D3—22no—
1062C2×D3—22no—
1063C2×D3—416no—
1064C2×D3—41no—
1065C2×D3—41no—
1066C2×D3—41no—
1067C2×D3—41no—
1068C2×D3—41no—
1069C2×D3—41no—
1070C2×D3—41no—
1071C2×D3—41no—
1072C2×D3—41no—
1073C2×D3—41no—
1074C2×D3—41no—
1075C2×D3—41no—
1076C2×D3—41no—
1077C2×D3—41no—
1078C2×D3—41no—
1079C3×C4—24no—
1080C3×C4—22no—
1081C3×C4—22no—
1082C3×C4—22no—
1083C3×C4—22no—
1084C3×C4—22no—
1085C3×C4—22no—
1086C3×C4—42no—
1087C3×C4—42no—
1088C3×C4—42no—
1089C3×C4—41no—
1090C3×C4—41no—
1091C3×C4—62no—
1092C3×C4—62no—
1093C3×C4—121no—
1094C3×C4—121no—
1095C3×C4—121no—
1096Dic3—22no—
1097Dic3—22no—
1098Dic3—41no—
1099Dic3—41no—
1100Dic3—41no—
1101C32#266911yescharacteristic, complemented, Sylow
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—32no—
1122C23—32no—
1123C23—61no—
1124C23—61no—
1125C23—61no—
1126C23—61no—
1127C23—61no—
1128C23—61no—
1129C23—61no—
1130C23—61no—
1131C23—61no—
1132C23—61no—
1133C23—61no—
1134C23—61no—
1135C23—61no—
1136C23—61no—
1137C23—61no—
1138C23—61no—
1139C23—61no—
1140C23—61no—
1141C23—61no—
1142C23—124no—
1143C23—124no—
1144C23—124no—
1145C23—124no—
1146C23—124no—
1147C23—124no—
1148C23—124no—
1149C23C3×D3×D412yes—
1150C23C2×C3×#6712yes—
1151C23C23×C3×D311yescharacteristic
1152D4—44no—
1153D4—44no—
1154D4—44no—
1155D4—124no—
1156D4—124no—
1157D4—124no—
1158D4—124no—
1159D4—124no—
1160D4—124no—
1161D4—124no—
1162D4—124no—
1163D4—124no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—32no—
1174C2×C4—32no—
1175C2×C4—44no—
1176C2×C4—61no—
1177C2×C4—61no—
1178C2×C4—61no—
1179C2×C4—61no—
1180C2×C4—61no—
1181C2×C4—61no—
1182C2×C4—61no—
1183C2×C4—61no—
1184C2×C4—61no—
1185C2×C4—61no—
1186C2×C4—61no—
1187C2×C4—61no—
1188C2×C4—61no—
1189C2×C4C3×D3×D412yes—
1190C2×C4C2×C3×#6712yes—
1191C2×C4C2×C3×#6712yes—
1192C2×C3—21no—
1193C2×C3—21no—
1194C2×C3—21no—
1195C2×C3—21no—
1196C2×C3—21no—
1197C2×C3—21no—
1198C2×C3—21no—
1199C2×C3—44no—
1200C2×C3—42no—
1201C2×C3—42no—
1202C2×C3—42no—
1203C2×C3—42no—
1204C2×C3—82no—
1205C2×C3—82no—
1206C2×C3—81no—
1207C2×C3—81no—
1208C2×C3—122no—
1209C2×C3—122no—
1210C2×C3—241no—
1211C2×C3#560511yescharacteristic
1212C2×C3#560711yescharacteristic
1213C2×C3#560911yescharacteristic
1214C2×C3#562011yescharacteristic
1215C2×C3D4×#6711yescharacteristic
1216C2×C3D4×#6711yescharacteristic
1217C2×C3#583011yescharacteristic
1218C2×C3C3×#53411yescharacteristic
1219C2×C3C3×#53511yescharacteristic
1220C2×C3C3×#53511yescharacteristic
1221C2×C3C3×D4211yescharacteristic
1222C2×C3C3×D4211yescharacteristic
1223C2×C3C3×D4211yescharacteristic
1224C2×C3C3×#56011yescharacteristic
1225D3—42no—
1226D3—42no—
1227D3—81no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—62no—
1250C22—62no—
1251C22—62no—
1252C22—62no—
1253C22—62no—
1254C22—62no—
1255C22—1216no—
1256C22—121no—
1257C22—121no—
1258C22—121no—
1259C22—121no—
1260C22—121no—
1261C22—121no—
1262C22—121no—
1263C22—121no—
1264C22—121no—
1265C22—121no—
1266C22—121no—
1267C22—121no—
1268C22—121no—
1269C22—121no—
1270C22—121no—
1271C22C2×C3×D3×D411yescharacteristic
1272C22C2×C3×D3×D411yescharacteristic
1273C22C3×#100411yescharacteristic
1274C22C3×#100411yescharacteristic
1275C22C3×#100911yescharacteristic
1276C22C3×#100911yescharacteristic
1277C22C22×C3×#6711yescharacteristic
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—41no—
1282C4—62no—
1283C4—62no—
1284C4—121no—
1285C4—121no—
1286C4—121no—
1287C3—21no—
1288C3#8271411yescharacteristic, direct product factor
1289C3C3×#266911yescharacteristic, complemented
1290C2—42no—
1291C2—42no—
1292C2—81no—
1293C2—122no—
1294C2—122no—
1295C2—241no—
1296C2C3×#560511yescharacteristic
1297C2C3×#560711yescharacteristic
1298C2C3×#560911yescharacteristic
1299C2C3×#562011yescharacteristic
1300C2C3×D4×#6711yescharacteristic
1301C2C3×D4×#6711yescharacteristic
1302C2C3×#583011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C3×#2669
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C32×#121C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#937C2semidirect
4. C2×C3×#937C2semidirect
5. C2×C3×#930C2semidirect
6. C2×C3×#882C2semidirect
7. C3×#5223C2semidirect
8. C3×#5223C2semidirect
9. C3×#5223C2semidirect
10. C3×#5213C2semidirect
11. C3×#4991C2semidirect
12. C3×#4990C2semidirect
13. C3×#4961C2semidirect
14. C3×#4960C2semidirect
15. C3×#4951C2semidirect
17. #82714C3direct (N × H)
21. C22×C32×D4C22semidirect
22. C23×C32×C4C22semidirect
28. C22×C3×#67C22semidirect
29. C22×C3×#67C22semidirect
33. C2×C32×C4⋊C4C22semidirect
35. C2×C32×C22⋊C4C22semidirect
38. C2×C3×#217C22semidirect
39. C2×C3×#217C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C2×C3×C4⋊Dic3C22semidirect
53. C2×C3×C4×Dic3C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
57. C3×C3⋊#95C22semidirect
58. C3×C3⋊#95C22semidirect
62. C2×C3×#121D3semidirect
63. C2×C3×#121C2×C3semidirect
67. C2×#940C2×C3semidirect
68. C2×#937C2×C3semidirect
69. C2×#937C2×C3semidirect
70. C2×#930C2×C3semidirect
71. C2×#882C2×C3semidirect
81. #5223C2×C3semidirect
82. #5223C2×C3semidirect
83. #5223C2×C3semidirect
84. #5213C2×C3semidirect
85. #4991C2×C3semidirect
86. #4990C2×C3semidirect
87. #4961C2×C3semidirect
88. #4960C2×C3semidirect
89. #4951C2×C3semidirect
139. C2×C3×#67D4semidirect
153. C32×C22⋊C4D4semidirect
165. C3×(C2×D3)⋊C4D4semidirect
185. C22×C3×D4C2×D3semidirect
188. C22×C3×D4C22×C3semidirect
190. C23×C3×C4C2×D3semidirect
191. C23×C3×C4C22×C3semidirect
197. C22×#67C22×C3semidirect
198. C22×#67C22×C3semidirect
211. C2×C3×C4⋊C4C2×D3semidirect
212. C2×C3×C4⋊C4C22×C3semidirect
228. C2×C3×C22⋊C4C2×D3semidirect
230. C2×C3×C22⋊C4C22×C3semidirect
234. C2×#217C22×C3semidirect
235. C2×#217C22×C3semidirect
246. C2×(C2×D3)⋊C4C22×C3semidirect
247. C2×(C2×D3)⋊C4C22×C3semidirect
248. C2×C4⋊Dic3C22×C3semidirect
249. C2×C4×Dic3C22×C3semidirect
255. C3⋊#95C22×C3semidirect
256. C3⋊#95C22×C3semidirect
257. C3⋊#95C22×C3semidirect
258. C3⋊#95C22×C3semidirect
351. C2×#121C3×D3semidirect
493. C2×#67C3×D4semidirect
525. C3×C22⋊C4#67semidirect
526. C3×C22⋊C4C3×D4semidirect
539. (C2×D3)⋊C4C3×D4semidirect
613. C22×D4C2×C3×D3semidirect
614. C23×C4C2×C3×D3semidirect
622. C2×C4⋊C4C2×C3×D3semidirect
636. C2×C22⋊C4C2×C3×D3semidirect
949. C22⋊C4C3×#67semidirect
1101. C32#2669semidirect
1288. C3#82714direct (N × H)
1289. C3C3×#2669semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C32×#1212
C2×C3×#9402
C2×C3×#9372
C2×C3×#9302
C2×C3×#8822
C3×#52232
C3×#52132
C3×#49912
C3×#49902
C3×#49612
C3×#49602
C3×#49512
C3×#26693
#827143