Finite Group Databasebeta

← C3×#77128 #11836027

Subgroups — C3×#77128 #11836027

Order 1152.

1983 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic, complemented
3C2×C3×#895C211yesmaximal, characteristic, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C2×C3×#882C211yesmaximal, characteristic, complemented
6C2×C3×#882C211yesmaximal, characteristic, complemented
7C32×#394C211yesmaximal, characteristic, complemented
8C3×#4990C211yesmaximal, characteristic, complemented
9C3×#4960C211yesmaximal, characteristic, complemented
10C3×#4960C211yesmaximal, characteristic, complemented
11C3×#4960C211yesmaximal, characteristic, complemented
12C3×#4959C211yesmaximal, characteristic, complemented
13C3×#4956C211yesmaximal, characteristic, complemented
14C3×#4671C211yesmaximal, characteristic, complemented
15C3×#4669C211yesmaximal, characteristic, complemented
16C3×#2669—31nomaximal
17#77128C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic, complemented
25C22×C3×#67C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic
27C22×C3×D12C2211yescharacteristic
28C22×C3×D12C2211yescharacteristic
29C22×C3×D12C2211yescharacteristic
30C22×C3×D12C2211yescharacteristic, complemented
31C22×C3×C4×D3C2211yescharacteristic, complemented
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×C32×C22⋊C4C2211yescharacteristic, complemented
36C2×C32×C22⋊C4C2211yescharacteristic, complemented
37C2×C3×#217C2211yescharacteristic
38C3×#940—24no—
39C3×#937—24no—
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
50C2×C3×C4×Dic3C2211yescharacteristic, complemented
51C3×#895—24no—
52C3×#884—24no—
53C3×#882—24no—
54C3×#882—24no—
55C32×#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57C3×C3⋊#95C2211yescharacteristic, complemented
58C3×C3⋊#95C2211yescharacteristic, complemented
59C2×C3×#127—31no—
60C2×C3×#121—31no—
61C2×C3×#121—31no—
62C2×C3×#120—31no—
63C2×C3×#120—31no—
64C2×C3×#120—31no—
65C2×#940C2×C311yescharacteristic, complemented
66C2×#937C2×C311yescharacteristic, complemented
67C2×#895C2×C311yescharacteristic, complemented
68C2×#884C2×C311yescharacteristic, complemented
69C2×#882C2×C311yescharacteristic, complemented
70C2×#882C2×C311yescharacteristic, complemented
71C3×#394—21no—
72C3×#394—31no—
73C3×#394D311yescharacteristic, complemented
74C3×#394C2×C311yescharacteristic, complemented
75C3×#392—31no—
76C3×#392—31no—
77C3×#392—31no—
78C3×#392—31no—
79C3×#388—31no—
80C3×#388—31no—
81C3×#386—31no—
82#4990C2×C311yescharacteristic, complemented
83#4960C2×C311yescharacteristic, complemented
84#4960C2×C311yescharacteristic, complemented
85#4960C2×C311yescharacteristic, complemented
86#4959C2×C311yescharacteristic, complemented
87#4956C2×C311yescharacteristic, complemented
88#4671C2×C311yescharacteristic, complemented
89#4669C2×C311yescharacteristic, complemented
90C24×C32C2311yescharacteristic
91C24×C32C2311yescharacteristic
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—22no—
95C23×C3×D3—41no—
96C23×C3×D3—41no—
97C23×C3×D3—41no—
98C23×C3×D3—41no—
99C23×C3×D3C2311yescharacteristic
100C23×C3×D3C2311yescharacteristic
101C23×C3×D3C2311yescharacteristic
102C23×C3×D3C2311yescharacteristic
103C2×C32×D4—22no—
104C2×C32×D4—22no—
105C2×C32×D4—41no—
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C2×C3×#67—22no—
112C2×C3×#67—22no—
113C2×C3×#67—22no—
114C2×C3×#67—22no—
115C2×C3×#67—22no—
116C2×C3×#67—22no—
117C2×C3×#67—22no—
118C2×C3×#67—22no—
119C2×C3×#67—41no—
120C2×C3×#67—41no—
121C2×C3×#67—41no—
122C2×C3×#67—41no—
123C2×C3×#67—41no—
124C2×C3×#67—41no—
125C2×C3×#67—41no—
126C2×C3×#67—41no—
127C2×C3×#67—41no—
128C2×C3×#67D414yescomplemented
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C2×C3×D12—22no—
134C2×C3×D12—22no—
135C2×C3×D12—22no—
136C2×C3×D12—22no—
137C2×C3×D12—22no—
138C2×C3×D12—22no—
139C2×C3×D12—22no—
140C2×C3×D12—22no—
141C2×C3×D12—22no—
142C2×C3×D12—41no—
143C2×C3×D12—41no—
144C2×C3×D12—41no—
145C2×C3×D12—41no—
146C2×C3×D12—41no—
147C2×C3×D12—41no—
148C2×C3×C4×D3—22no—
149C2×C3×C4×D3—22no—
150C2×C3×C4×D3—41no—
151C32×C4⋊C4—22no—
152C32×C22⋊C4—22no—
153C32×C22⋊C4—22no—
154C32×C22⋊C4—22no—
155C32×C22⋊C4—41no—
156C3×#217—22no—
157C3×(C2×D3)⋊C4—22no—
158C3×(C2×D3)⋊C4—22no—
159C3×(C2×D3)⋊C4—22no—
160C3×(C2×D3)⋊C4—22no—
161C3×(C2×D3)⋊C4—22no—
162C3×(C2×D3)⋊C4—41no—
163C3×(C2×D3)⋊C4—41no—
164C3×(C2×D3)⋊C4D414yescomplemented
165C3×(C2×D3)⋊C4D414yescomplemented
166C3×Dic3⋊C4—22no—
167C3×C4×Dic3—22no—
168#2669—31noSylow
169C25×C3—31no—
170C24×D3C22×C311yescharacteristic
171C22×C3×D4—21no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
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×D4C22×C311yescharacteristic
185C23×C3×C4—31no—
186C22×#67C22×C311yescharacteristic
187C22×#67C22×C311yescharacteristic
188C22×#67C22×C311yescharacteristic
189C22×#67C22×C311yescharacteristic
190C22×#67C22×C311yescharacteristic, complemented
191C22×#67C22×C311yescharacteristic, complemented
192C22×D12C22×C311yescharacteristic
193C22×D12C22×C311yescharacteristic
194C22×D12C22×C311yescharacteristic
195C22×D12C22×C311yescharacteristic
196C22×D12C22×C311yescharacteristic, complemented
197C22×C4×D3C22×C311yescharacteristic, complemented
198C3×#127—64no—
199C3×#121—64no—
200C3×#121—64no—
201C3×#120—64no—
202C3×#120—64no—
203C3×#120—64no—
204C2×C3×C4⋊C4—21no—
205C2×C3×C4⋊C4—31no—
206C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
207C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
208C2×C3×C22⋊C4—21no—
209C2×C3×C22⋊C4—21no—
210C2×C3×C22⋊C4—21no—
211C2×C3×C22⋊C4—21no—
212C2×C3×C22⋊C4—31no—
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
223C2×C3×C22⋊C4C2×D311yescharacteristic
224C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
225C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
226C2×C3×C22⋊C4C22×C311yescharacteristic
227C2×C3×C22⋊C4C22×C311yescharacteristic
228C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
229C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
230C2×C3×C42—31no—
231C2×#217C22×C311yescharacteristic
232#940—24no—
233#937—24no—
234C2×(C2×D3)⋊C4C22×C311yescharacteristic
235C2×(C2×D3)⋊C4C22×C311yescharacteristic
236C2×(C2×D3)⋊C4C22×C311yescharacteristic
237C2×(C2×D3)⋊C4C22×C311yescharacteristic
238C2×(C2×D3)⋊C4C22×C311yescharacteristic
239C2×(C2×D3)⋊C4C22×C311yescharacteristic
240C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
241C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
242C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
243C2×Dic3⋊C4C22×C311yescharacteristic, complemented
244C2×C4×Dic3C22×C311yescharacteristic, complemented
245#895—24no—
246#884—24no—
247#882—24no—
248#882—24no—
249C3×#95—21no—
250C3×#95—31no—
251C3×#95—31no—
252C3×#95—31no—
253C3×#95C2×D311yescharacteristic, complemented
254C3×#95C22×C311yescharacteristic, complemented
255C3⋊#95C22×C311yescharacteristic, complemented
256C3⋊#95C22×C311yescharacteristic, complemented
257C3⋊#95C22×C311yescharacteristic, complemented
258C23×C32—21no—
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×C32C2×D412yes—
272C23×C32C2411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3—21no—
278C22×C3×D3—21no—
279C22×C3×D3—21no—
280C22×C3×D3—21no—
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—44no—
299C22×C3×D3—44no—
300C22×C3×D3—44no—
301C22×C3×D3—44no—
302C22×C3×D3—44no—
303C22×C3×D3—44no—
304C22×C3×D3—44no—
305C22×C3×D3C2×D412yes—
306C22×C3×D3C2×D412yes—
307C22×C3×D3C2×D412yes—
308C32×D4—44no—
309C2×C32×C4—21no—
310C2×C32×C4—21no—
311C2×C32×C4—21no—
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—21no—
322C2×C32×C4C2×D412yes—
323C2×C32×C4C2×D412yes—
324C3×#67—44no—
325C3×#67—44no—
326C3×#67—44no—
327C3×#67—44no—
328C3×#67—44no—
329C3×#67—44no—
330C2×C3×Dic3—21no—
331C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
340C2×C3×Dic3C2×D412yes—
341C2×C3×Dic3C2×D412yes—
342C3×D12—44no—
343C3×D12—44no—
344C3×D12—44no—
345C3×D12—44no—
346C3×D12—44no—
347C3×C4×D3—44no—
348C2×#127—31no—
349C2×#121—31no—
350C2×#121—31no—
351C2×#120—31no—
352C2×#120—31no—
353C2×#120—31no—
354#394—31no—
355#394C3×D311yescharacteristic, complemented
356#392—31no—
357#392—31no—
358#392—31no—
359#392—31no—
360#388—31no—
361#388—31no—
362#386—31no—
363C24×C3—21no—
364C24×C3—21no—
365C24×C3—31no—
366C24×C3—31no—
367C24×C3—31no—
368C24×C3—31no—
369C24×C3—62no—
370C24×C3—62no—
371C24×C3—62no—
372C24×C3—121no—
373C24×C3—121no—
374C24×C3—121no—
375C24×C3—121no—
376C24×C3C22×D311yescharacteristic
377C24×C3C22×D311yescharacteristic
378C24×C3C23×C311yescharacteristic
379C24×C3C23×C311yescharacteristic
380C23×D3—22no—
381C23×D3—22no—
382C23×D3—22no—
383C23×D3—41no—
384C23×D3—41no—
385C23×D3—41no—
386C23×D3—41no—
387C23×D3C23×C311yescharacteristic
388C23×D3C23×C311yescharacteristic
389C23×D3C23×C311yescharacteristic
390C23×D3C23×C311yescharacteristic
391C2×C3×D4—22no—
392C2×C3×D4—22no—
393C2×C3×D4—22no—
394C2×C3×D4—22no—
395C2×C3×D4—34no—
396C2×C3×D4—42no—
397C2×C3×D4—42no—
398C2×C3×D4—41no—
399C2×C3×D4—41no—
400C2×C3×D4—42no—
401C2×C3×D4—62no—
402C2×C3×D4—62no—
403C2×C3×D4—62no—
404C2×C3×D4—62no—
405C2×C3×D4—62no—
406C2×C3×D4—62no—
407C2×C3×D4—62no—
408C2×C3×D4—62no—
409C2×C3×D4—62no—
410C2×C3×D4—62no—
411C2×C3×D4—62no—
412C2×C3×D4—62no—
413C2×C3×D4—62no—
414C2×C3×D4—62no—
415C2×C3×D4—62no—
416C2×C3×D4—62no—
417C2×C3×D4—62no—
418C2×C3×D4—121no—
419C2×C3×D4—121no—
420C2×C3×D4—121no—
421C2×C3×D4—121no—
422C2×C3×D4—121no—
423C2×C3×D4—121no—
424C2×C3×D4—121no—
425C2×C3×D4—121no—
426C2×C3×D4—121no—
427C2×C3×D4—121no—
428C2×C3×D4—121no—
429C2×C3×D4—121no—
430C2×C3×D4—121no—
431C2×C3×D4—121no—
432C2×C3×D4—121no—
433C22×C3×C4—21no—
434C22×C3×C4—21no—
435C22×C3×C4—21no—
436C22×C3×C4—21no—
437C22×C3×C4—21no—
438C22×C3×C4—31no—
439C22×C3×C4—31no—
440C22×C3×C4—31no—
441C22×C3×C4—31no—
442C22×C3×C4—62no—
443C22×C3×C4—62no—
444C22×C3×C4—121no—
445C22×C3×C4C22×D311yescharacteristic
446C22×C3×C4C22×D311yescharacteristic
447C22×C3×C4C22×D311yescharacteristic
448C22×C3×C4C22×D311yescharacteristic
449C22×C3×C4C22×D311yescharacteristic
450C22×C3×C4C23×C311yescharacteristic
451C22×C3×C4C23×C311yescharacteristic
452C22×C3×C4C23×C311yescharacteristic
453C22×C3×C4C23×C311yescharacteristic
454C22×C3×C4C23×C311yescharacteristic
455C2×#67—22no—
456C2×#67—22no—
457C2×#67—22no—
458C2×#67—22no—
459C2×#67—22no—
460C2×#67—22no—
461C2×#67—22no—
462C2×#67—22no—
463C2×#67—41no—
464C2×#67—41no—
465C2×#67—41no—
466C2×#67—41no—
467C2×#67—41no—
468C2×#67—41no—
469C2×#67—41no—
470C2×#67—41no—
471C2×#67—41no—
472C2×#67C3×D414yescomplemented
473C22×Dic3C23×C311yescharacteristic
474C22×Dic3C23×C311yescharacteristic
475C22×Dic3C23×C311yescharacteristic
476C22×Dic3C23×C311yescharacteristic
477C2×D12—22no—
478C2×D12—22no—
479C2×D12—22no—
480C2×D12—22no—
481C2×D12—22no—
482C2×D12—22no—
483C2×D12—22no—
484C2×D12—22no—
485C2×D12—22no—
486C2×D12—41no—
487C2×D12—41no—
488C2×D12—41no—
489C2×D12—41no—
490C2×D12—41no—
491C2×D12—41no—
492C2×C4×D3—22no—
493C2×C4×D3—22no—
494C2×C4×D3—41no—
495C3×C4⋊C4—22no—
496C3×C4⋊C4—22no—
497C3×C4⋊C4—42no—
498C3×C4⋊C4—62no—
499C3×C22⋊C4—22no—
500C3×C22⋊C4—22no—
501C3×C22⋊C4—22no—
502C3×C22⋊C4—22no—
503C3×C22⋊C4—22no—
504C3×C22⋊C4—22no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—42no—
508C3×C22⋊C4—42no—
509C3×C22⋊C4—42no—
510C3×C22⋊C4—41no—
511C3×C22⋊C4—41no—
512C3×C22⋊C4—42no—
513C3×C22⋊C4—62no—
514C3×C22⋊C4—62no—
515C3×C22⋊C4—62no—
516C3×C22⋊C4—62no—
517C3×C22⋊C4—62no—
518C3×C22⋊C4—62no—
519C3×C22⋊C4—121no—
520C3×C22⋊C4—121no—
521C3×C42—62no—
522#217—22no—
523(C2×D3)⋊C4—22no—
524(C2×D3)⋊C4—22no—
525(C2×D3)⋊C4—22no—
526(C2×D3)⋊C4—22no—
527(C2×D3)⋊C4—22no—
528(C2×D3)⋊C4—41no—
529(C2×D3)⋊C4—41no—
530(C2×D3)⋊C4C3×D414yescomplemented
531(C2×D3)⋊C4C3×D414yescomplemented
532Dic3⋊C4—22no—
533C4×Dic3—22no—
534C22×C32—22no—
535C22×C32—22no—
536C22×C32—22no—
537C22×C32—41no—
538C22×C32—41no—
539C22×C32—41no—
540C22×C32—41no—
541C22×C32—41no—
542C22×C32—41no—
543C22×C32—41no—
544C22×C32—41no—
545C22×C32—41no—
546C22×C32—41no—
547C22×C32—41no—
548C22×C32C22×D411yescharacteristic
549C22×C32C22×D411yescharacteristic
550C22×C32C22×D411yescharacteristic
551C22×C32H(5,𝔽2)11yescharacteristic
552C22×C32H(5,𝔽2)11yescharacteristic
553C22×C32H(5,𝔽2)11yescharacteristic
554C22×C32H(5,𝔽2)11yescharacteristic
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—416no—
565C2×C3×D3—41no—
566C2×C3×D3—41no—
567C2×C3×D3—41no—
568C2×C3×D3—41no—
569C2×C3×D3—41no—
570C2×C3×D3—41no—
571C2×C3×D3—41no—
572C2×C3×D3—41no—
573C2×C3×D3—41no—
574C2×C3×D3—41no—
575C2×C3×D3—41no—
576C2×C3×D3—41no—
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—
584C32×C4—22no—
585C32×C4—22no—
586C32×C4—41no—
587C32×C4—41no—
588C32×C4—41no—
589C3×Dic3—22no—
590C3×Dic3—22no—
591C3×Dic3—22no—
592C3×Dic3—41no—
593C25—31no—
594C22×D4—31no—
595C22×D4—31no—
596C22×D4—31no—
597C22×D4—31no—
598C22×D4—31no—
599C22×D4—31no—
600C22×D4—31no—
601C22×D4—31no—
602C22×D4—31no—
603C22×D4—31no—
604C22×D4—31no—
605C22×D4C2×C3×D311yescharacteristic
606C23×C4—31no—
607#127—64no—
608#121—64no—
609#121—64no—
610#120—64no—
611#120—64no—
612#120—64no—
613C2×C4⋊C4—31no—
614C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
615C2×C22⋊C4—31no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—31no—
624C2×C22⋊C4—31no—
625C2×C22⋊C4C2×C3×D311yescharacteristic
626C2×C22⋊C4C2×C3×D311yescharacteristic
627C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
628C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
629C2×C42—31no—
630#95—31no—
631#95—31no—
632#95—31no—
633#95C2×C3×D311yescharacteristic, complemented
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—21no—
639C23×C3—21no—
640C23×C3—21no—
641C23×C3—21no—
642C23×C3—21no—
643C23×C3—21no—
644C23×C3—21no—
645C23×C3—21no—
646C23×C3—22no—
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—22no—
663C23×C3—32no—
664C23×C3—32no—
665C23×C3—32no—
666C23×C3—41no—
667C23×C3—41no—
668C23×C3—41no—
669C23×C3—41no—
670C23×C3—41no—
671C23×C3—41no—
672C23×C3—41no—
673C23×C3—41no—
674C23×C3—41no—
675C23×C3—41no—
676C23×C3—41no—
677C23×C3—41no—
678C23×C3—61no—
679C23×C3—61no—
680C23×C3—61no—
681C23×C3—61no—
682C23×C3—61no—
683C23×C3—61no—
684C23×C3—61no—
685C23×C3—61no—
686C23×C3—61no—
687C23×C3—61no—
688C23×C3—61no—
689C23×C3—61no—
690C23×C3—61no—
691C23×C3—61no—
692C23×C3—61no—
693C23×C3—61no—
694C23×C3—61no—
695C23×C3—61no—
696C23×C3—61no—
697C23×C3—61no—
698C23×C3—61no—
699C23×C3—61no—
700C23×C3—61no—
701C23×C3—61no—
702C23×C3—61no—
703C23×C3—124no—
704C23×C3—124no—
705C23×C3—124no—
706C23×C3—124no—
707C23×C3—124no—
708C23×C3—124no—
709C23×C3—124no—
710C23×C3D3×D412yes—
711C23×C3C2×C3×D412yes—
712C23×C3C23×D311yescharacteristic
713C23×C3C24×C311yescharacteristic
714C22×D3—21no—
715C22×D3—21no—
716C22×D3—21no—
717C22×D3—21no—
718C22×D3—21no—
719C22×D3—21no—
720C22×D3—21no—
721C22×D3—21no—
722C22×D3—21no—
723C22×D3—21no—
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—21no—
728C22×D3—21no—
729C22×D3—21no—
730C22×D3—21no—
731C22×D3—21no—
732C22×D3—21no—
733C22×D3—21no—
734C22×D3—21no—
735C22×D3—21no—
736C22×D3—21no—
737C22×D3—21no—
738C22×D3—21no—
739C22×D3—44no—
740C22×D3—44no—
741C22×D3—44no—
742C22×D3—44no—
743C22×D3—44no—
744C22×D3—44no—
745C22×D3—44no—
746C22×D3C2×C3×D412yes—
747C22×D3C2×C3×D412yes—
748C22×D3C2×C3×D412yes—
749C3×D4—44no—
750C3×D4—44no—
751C3×D4—48no—
752C3×D4—124no—
753C3×D4—124no—
754C3×D4—124no—
755C3×D4—124no—
756C3×D4—124no—
757C3×D4—124no—
758C3×D4—124no—
759C3×D4—124no—
760C3×D4—124no—
761C3×D4—124no—
762C3×D4—124no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—21no—
767C2×C3×C4—21no—
768C2×C3×C4—21no—
769C2×C3×C4—21no—
770C2×C3×C4—21no—
771C2×C3×C4—21no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—21no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—21no—
781C2×C3×C4—21no—
782C2×C3×C4—21no—
783C2×C3×C4—21no—
784C2×C3×C4—21no—
785C2×C3×C4—21no—
786C2×C3×C4—21no—
787C2×C3×C4—21no—
788C2×C3×C4—21no—
789C2×C3×C4—22no—
790C2×C3×C4—22no—
791C2×C3×C4—32no—
792C2×C3×C4—32no—
793C2×C3×C4—32no—
794C2×C3×C4—41no—
795C2×C3×C4—41no—
796C2×C3×C4—41no—
797C2×C3×C4—41no—
798C2×C3×C4—41no—
799C2×C3×C4—41no—
800C2×C3×C4—41no—
801C2×C3×C4—41no—
802C2×C3×C4—41no—
803C2×C3×C4—41no—
804C2×C3×C4—41no—
805C2×C3×C4—41no—
806C2×C3×C4—41no—
807C2×C3×C4—61no—
808C2×C3×C4—61no—
809C2×C3×C4—61no—
810C2×C3×C4—61no—
811C2×C3×C4—61no—
812C2×C3×C4—61no—
813C2×C3×C4—61no—
814C2×C3×C4—61no—
815C2×C3×C4—61no—
816C2×C3×C4—124no—
817C2×C3×C4D3×D412yes—
818C2×C3×C4D3×D412yes—
819C2×C3×C4C2×C3×D412yes—
820C2×C3×C4C2×C3×D412yes—
821#67—44no—
822#67—44no—
823#67—44no—
824#67—44no—
825#67—44no—
826#67—44no—
827C2×Dic3—21no—
828C2×Dic3—21no—
829C2×Dic3—21no—
830C2×Dic3—21no—
831C2×Dic3—21no—
832C2×Dic3—21no—
833C2×Dic3—21no—
834C2×Dic3—21no—
835C2×Dic3—21no—
836C2×Dic3C2×C3×D412yes—
837C2×Dic3C2×C3×D412yes—
838C2×Dic3C2×C3×D412yes—
839D12—44no—
840D12—44no—
841D12—44no—
842D12—44no—
843D12—44no—
844C4×D3—44no—
845C2×C32—42no—
846C2×C32—81no—
847C2×C32#53411yescharacteristic
848C2×C32#53511yescharacteristic
849C2×C32#53511yescharacteristic
850C2×C32D4211yescharacteristic
851C2×C32D4211yescharacteristic
852C2×C32D4211yescharacteristic
853C2×C32#56011yescharacteristic
854C3×D3—42no—
855C3×D3—42no—
856C3×D3—42no—
857C3×D3—81no—
858C24—31no—
859C24—31no—
860C24—31no—
861C24—31no—
862C24—62no—
863C24—62no—
864C24—62no—
865C24—121no—
866C24—121no—
867C24—121no—
868C24—121no—
869C24C22×C3×D311yescharacteristic
870C24C22×C3×D311yescharacteristic
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—34no—
874C2×D4—41no—
875C2×D4—62no—
876C2×D4—62no—
877C2×D4—62no—
878C2×D4—62no—
879C2×D4—62no—
880C2×D4—62no—
881C2×D4—62no—
882C2×D4—62no—
883C2×D4—62no—
884C2×D4—62no—
885C2×D4—62no—
886C2×D4—62no—
887C2×D4—62no—
888C2×D4—62no—
889C2×D4—62no—
890C2×D4—62no—
891C2×D4—62no—
892C2×D4—121no—
893C2×D4—121no—
894C2×D4—121no—
895C2×D4—121no—
896C2×D4—121no—
897C2×D4—121no—
898C2×D4—121no—
899C2×D4—121no—
900C2×D4—121no—
901C2×D4—121no—
902C2×D4—121no—
903C2×D4—121no—
904C2×D4—121no—
905C2×D4—121no—
906C2×D4—121no—
907C22×C4—31no—
908C22×C4—31no—
909C22×C4—31no—
910C22×C4—31no—
911C22×C4—62no—
912C22×C4—62no—
913C22×C4—121no—
914C22×C4C22×C3×D311yescharacteristic
915C22×C4C22×C3×D311yescharacteristic
916C22×C4C22×C3×D311yescharacteristic
917C22×C4C22×C3×D311yescharacteristic
918C22×C4C22×C3×D311yescharacteristic
919C4⋊C4—22no—
920C4⋊C4—62no—
921C22⋊C4—22no—
922C22⋊C4—22no—
923C22⋊C4—22no—
924C22⋊C4—34no—
925C22⋊C4—34no—
926C22⋊C4—41no—
927C22⋊C4—62no—
928C22⋊C4—62no—
929C22⋊C4—62no—
930C22⋊C4—62no—
931C22⋊C4—62no—
932C22⋊C4—62no—
933C22⋊C4—121no—
934C22⋊C4—121no—
935C42—62no—
936C22×C3—22no—
937C22×C3—22no—
938C22×C3—22no—
939C22×C3—22no—
940C22×C3—22no—
941C22×C3—22no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—42no—
950C22×C3—42no—
951C22×C3—42no—
952C22×C3—42no—
953C22×C3—42no—
954C22×C3—42no—
955C22×C3—41no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3—41no—
961C22×C3—41no—
962C22×C3—41no—
963C22×C3—41no—
964C22×C3—41no—
965C22×C3—41no—
966C22×C3—41no—
967C22×C3—41no—
968C22×C3—41no—
969C22×C3—41no—
970C22×C3—41no—
971C22×C3—41no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—62no—
978C22×C3—62no—
979C22×C3—62no—
980C22×C3—62no—
981C22×C3—62no—
982C22×C3—62no—
983C22×C3—62no—
984C22×C3—62no—
985C22×C3—62no—
986C22×C3—81no—
987C22×C3—81no—
988C22×C3—81no—
989C22×C3—81no—
990C22×C3—81no—
991C22×C3—81no—
992C22×C3—81no—
993C22×C3—81no—
994C22×C3—1216no—
995C22×C3—121no—
996C22×C3—121no—
997C22×C3—121no—
998C22×C3—121no—
999C22×C3—121no—
1000C22×C3—121no—
1001C22×C3—121no—
1002C22×C3—121no—
1003C22×C3—121no—
1004C22×C3—121no—
1005C22×C3—121no—
1006C22×C3—121no—
1007C22×C3—121no—
1008C22×C3—121no—
1009C22×C3—121no—
1010C22×C3—121no—
1011C22×C3—121no—
1012C22×C3—121no—
1013C22×C3—121no—
1014C22×C3C2×D3×D411yescharacteristic
1015C22×C3C2×D3×D411yescharacteristic
1016C22×C3C2×D3×D411yescharacteristic
1017C22×C3#100411yescharacteristic
1018C22×C3#100911yescharacteristic
1019C22×C3#100911yescharacteristic
1020C22×C3#100911yescharacteristic
1021C22×C3C22×C3×D411yescharacteristic
1022C22×C3C22×C3×D411yescharacteristic
1023C22×C3C22×C3×D411yescharacteristic
1024C22×C3C3×H(5,𝔽2)11yescharacteristic
1025C22×C3C3×H(5,𝔽2)11yescharacteristic
1026C22×C3C3×H(5,𝔽2)11yescharacteristic
1027C22×C3C3×H(5,𝔽2)11yescharacteristic
1028C2×D3—22no—
1029C2×D3—22no—
1030C2×D3—22no—
1031C2×D3—22no—
1032C2×D3—22no—
1033C2×D3—22no—
1034C2×D3—22no—
1035C2×D3—22no—
1036C2×D3—22no—
1037C2×D3—416no—
1038C2×D3—41no—
1039C2×D3—41no—
1040C2×D3—41no—
1041C2×D3—41no—
1042C2×D3—41no—
1043C2×D3—41no—
1044C2×D3—41no—
1045C2×D3—41no—
1046C2×D3—41no—
1047C2×D3—41no—
1048C2×D3—41no—
1049C2×D3—41no—
1050C2×D3—41no—
1051C2×D3—41no—
1052C2×D3—41no—
1053C2×D3—41no—
1054C2×D3—41no—
1055C2×D3—41no—
1056C2×D3—41no—
1057C3×C4—22no—
1058C3×C4—22no—
1059C3×C4—22no—
1060C3×C4—22no—
1061C3×C4—42no—
1062C3×C4—42no—
1063C3×C4—41no—
1064C3×C4—41no—
1065C3×C4—41no—
1066C3×C4—41no—
1067C3×C4—41no—
1068C3×C4—41no—
1069C3×C4—62no—
1070C3×C4—62no—
1071C3×C4—62no—
1072C3×C4—81no—
1073C3×C4—81no—
1074C3×C4—81no—
1075C3×C4—121no—
1076Dic3—22no—
1077Dic3—22no—
1078Dic3—22no—
1079Dic3—41no—
1080C32#266911yescharacteristic, complemented, Sylow
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—32no—
1095C23—32no—
1096C23—32no—
1097C23—61no—
1098C23—61no—
1099C23—61no—
1100C23—61no—
1101C23—61no—
1102C23—61no—
1103C23—61no—
1104C23—61no—
1105C23—61no—
1106C23—61no—
1107C23—61no—
1108C23—61no—
1109C23—61no—
1110C23—61no—
1111C23—61no—
1112C23—61no—
1113C23—61no—
1114C23—61no—
1115C23—61no—
1116C23—61no—
1117C23—61no—
1118C23—61no—
1119C23—61no—
1120C23—61no—
1121C23—61no—
1122C23—124no—
1123C23—124no—
1124C23—124no—
1125C23—124no—
1126C23—124no—
1127C23—124no—
1128C23—124no—
1129C23C3×D3×D412yes—
1130C23C23×C3×D311yescharacteristic
1131D4—44no—
1132D4—124no—
1133D4—124no—
1134D4—124no—
1135D4—124no—
1136D4—124no—
1137D4—124no—
1138D4—124no—
1139D4—124no—
1140D4—124no—
1141D4—124no—
1142D4—124no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—32no—
1157C2×C4—32no—
1158C2×C4—32no—
1159C2×C4—61no—
1160C2×C4—61no—
1161C2×C4—61no—
1162C2×C4—61no—
1163C2×C4—61no—
1164C2×C4—61no—
1165C2×C4—61no—
1166C2×C4—61no—
1167C2×C4—61no—
1168C2×C4—124no—
1169C2×C4C3×D3×D412yes—
1170C2×C4C3×D3×D412yes—
1171C2×C3—21no—
1172C2×C3—21no—
1173C2×C3—21no—
1174C2×C3—21no—
1175C2×C3—21no—
1176C2×C3—21no—
1177C2×C3—21no—
1178C2×C3—42no—
1179C2×C3—42no—
1180C2×C3—82no—
1181C2×C3—82no—
1182C2×C3—81no—
1183C2×C3—81no—
1184C2×C3—122no—
1185C2×C3—122no—
1186C2×C3—122no—
1187C2×C3—241no—
1188C2×C3#559011yescharacteristic
1189C2×C3#560711yescharacteristic
1190C2×C3#560911yescharacteristic
1191C2×C3#560911yescharacteristic
1192C2×C3#565311yescharacteristic
1193C2×C3#566611yescharacteristic
1194C2×C3#567411yescharacteristic
1195C2×C3C3×#53411yescharacteristic
1196C2×C3C3×#53511yescharacteristic
1197C2×C3C3×#53511yescharacteristic
1198C2×C3C3×D4211yescharacteristic
1199C2×C3C3×D4211yescharacteristic
1200C2×C3C3×D4211yescharacteristic
1201C2×C3C3×#56011yescharacteristic
1202D3—42no—
1203D3—42no—
1204D3—42no—
1205D3—81no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—62no—
1221C22—62no—
1222C22—62no—
1223C22—62no—
1224C22—62no—
1225C22—62no—
1226C22—62no—
1227C22—62no—
1228C22—62no—
1229C22—1216no—
1230C22—121no—
1231C22—121no—
1232C22—121no—
1233C22—121no—
1234C22—121no—
1235C22—121no—
1236C22—121no—
1237C22—121no—
1238C22—121no—
1239C22—121no—
1240C22—121no—
1241C22—121no—
1242C22—121no—
1243C22—121no—
1244C22—121no—
1245C22—121no—
1246C22—121no—
1247C22—121no—
1248C22—121no—
1249C22C2×C3×D3×D411yescharacteristic
1250C22C2×C3×D3×D411yescharacteristic
1251C22C2×C3×D3×D411yescharacteristic
1252C22C3×#100411yescharacteristic
1253C22C3×#100911yescharacteristic
1254C22C3×#100911yescharacteristic
1255C22C3×#100911yescharacteristic
1256C4—22no—
1257C4—22no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—62no—
1262C4—62no—
1263C4—62no—
1264C4—121no—
1265C3—21no—
1266C3#7712811yescharacteristic, direct product factor
1267C3C3×#266911yescharacteristic, complemented
1268C2—42no—
1269C2—81no—
1270C2—122no—
1271C2—122no—
1272C2—122no—
1273C2—241no—
1274C2C3×#559011yescharacteristic
1275C2C3×#560711yescharacteristic
1276C2C3×#560911yescharacteristic
1277C2C3×#560911yescharacteristic
1278C2C3×#565311yescharacteristic
1279C2C3×#566611yescharacteristic
1280C2C3×#567411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#394C2
socleC23×C32C24
hypercenterC3×#394D3
hypocenterC3C3×#2669
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#394

Complements

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

NH ≅ G/Ntype
1. C2×C3×#940C2semidirect
2. C2×C3×#937C2semidirect
3. C2×C3×#895C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×#882C2semidirect
6. C2×C3×#882C2semidirect
7. C32×#394C2semidirect
8. C3×#4990C2semidirect
9. C3×#4960C2semidirect
10. C3×#4960C2semidirect
11. C3×#4960C2semidirect
12. C3×#4959C2semidirect
13. C3×#4956C2semidirect
14. C3×#4671C2semidirect
15. C3×#4669C2semidirect
17. #77128C3direct (N × H)
24. C22×C3×#67C22semidirect
25. C22×C3×#67C22semidirect
30. C22×C3×D12C22semidirect
31. C22×C3×C4×D3C22semidirect
32. C2×C32×C4⋊C4C22semidirect
35. C2×C32×C22⋊C4C22semidirect
36. C2×C32×C22⋊C4C22semidirect
46. C2×C3×(C2×D3)⋊C4C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
50. C2×C3×C4×Dic3C22semidirect
55. C32×#95C22semidirect
56. C3×C3⋊#95C22semidirect
57. C3×C3⋊#95C22semidirect
58. C3×C3⋊#95C22semidirect
65. C2×#940C2×C3semidirect
66. C2×#937C2×C3semidirect
67. C2×#895C2×C3semidirect
68. C2×#884C2×C3semidirect
69. C2×#882C2×C3semidirect
70. C2×#882C2×C3semidirect
73. C3×#394D3semidirect
74. C3×#394C2×C3semidirect
82. #4990C2×C3semidirect
83. #4960C2×C3semidirect
84. #4960C2×C3semidirect
85. #4960C2×C3semidirect
86. #4959C2×C3semidirect
87. #4956C2×C3semidirect
88. #4671C2×C3semidirect
89. #4669C2×C3semidirect
128. C2×C3×#67D4semidirect
164. C3×(C2×D3)⋊C4D4semidirect
165. C3×(C2×D3)⋊C4D4semidirect
190. C22×#67C22×C3semidirect
191. C22×#67C22×C3semidirect
196. C22×D12C22×C3semidirect
197. C22×C4×D3C22×C3semidirect
206. C2×C3×C4⋊C4C2×D3semidirect
207. C2×C3×C4⋊C4C22×C3semidirect
224. C2×C3×C22⋊C4C2×D3semidirect
225. C2×C3×C22⋊C4C2×D3semidirect
228. C2×C3×C22⋊C4C22×C3semidirect
229. C2×C3×C22⋊C4C22×C3semidirect
240. C2×(C2×D3)⋊C4C22×C3semidirect
241. C2×(C2×D3)⋊C4C22×C3semidirect
242. C2×(C2×D3)⋊C4C22×C3semidirect
243. C2×Dic3⋊C4C22×C3semidirect
244. C2×C4×Dic3C22×C3semidirect
253. C3×#95C2×D3semidirect
254. C3×#95C22×C3semidirect
255. C3⋊#95C22×C3semidirect
256. C3⋊#95C22×C3semidirect
257. C3⋊#95C22×C3semidirect
355. #394C3×D3semidirect
472. C2×#67C3×D4semidirect
530. (C2×D3)⋊C4C3×D4semidirect
531. (C2×D3)⋊C4C3×D4semidirect
614. C2×C4⋊C4C2×C3×D3semidirect
627. C2×C22⋊C4C2×C3×D3semidirect
628. C2×C22⋊C4C2×C3×D3semidirect
633. #95C2×C3×D3semidirect
1080. C32#2669semidirect
1266. C3#77128direct (N × H)
1267. C3C3×#2669semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×C3×#9372
C2×C3×#8952
C2×C3×#8842
C2×C3×#8822
C32×#3942
C3×#49902
C3×#49602
C3×#49592
C3×#49562
C3×#46712
C3×#46692
C3×#26693
#771283