Finite Group Databasebeta

← C3×#82609 #11836021

Subgroups — C3×#82609 #11836021

Order 1152.

2195 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#120C211yesmaximal, characteristic, complemented
2C2×C3×#953C211yesmaximal, characteristic, complemented
3C2×C3×#953C211yesmaximal, characteristic, complemented
4C2×C3×#940C211yesmaximal, characteristic, complemented
5C2×C3×#938C211yesmaximal, characteristic, complemented
6C2×C3×#884C211yesmaximal, characteristic, complemented
7C3×#5223C211yesmaximal, characteristic, complemented
8C3×#5223C211yesmaximal, characteristic, complemented
9C3×#5223C211yesmaximal, characteristic, complemented
10C3×#5222C211yesmaximal, characteristic, complemented
11C3×#4961C211yesmaximal, characteristic, complemented
12C3×#4960C211yesmaximal, characteristic, complemented
13C3×#4956C211yesmaximal, characteristic, complemented
14C3×#4951C211yesmaximal, characteristic, complemented
15C3×#4945C211yesmaximal, characteristic, complemented
16C3×#2669—31nomaximal
17#82609C311yesmaximal, characteristic, direct product factor
18C25×C32C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
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, complemented
31C22×C3×C4×D3C2211yescharacteristic, complemented
32C32×#120—24no—
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×C32×C22⋊C4C2211yescharacteristic
36C3×#953—24no—
37C3×#953—24no—
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C2×C3×#217C2211yescharacteristic
42C2×C3×#217C2211yescharacteristic
43C2×C3×#217C2211yescharacteristic
44C2×C3×#217C2211yescharacteristic, complemented
45C2×C3×#217C2211yescharacteristic, complemented
46C3×#940—24no—
47C3×#938—24no—
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
52C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
53C2×C3×C4×Dic3C2211yescharacteristic, complemented
54C3×#884—24no—
55C3×C3⋊#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—21no—
63C2×C3×#120—31no—
64C2×C3×#120—31no—
65C2×C3×#120D311yescharacteristic, complemented
66C2×C3×#120C2×C311yescharacteristic, complemented
67C2×#953C2×C311yescharacteristic, complemented
68C2×#953C2×C311yescharacteristic, complemented
69C2×#940C2×C311yescharacteristic, complemented
70C2×#938C2×C311yescharacteristic, complemented
71C2×#884C2×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#5222C2×C311yescharacteristic, complemented
85#4961C2×C311yescharacteristic, complemented
86#4960C2×C311yescharacteristic, complemented
87#4956C2×C311yescharacteristic, complemented
88#4951C2×C311yescharacteristic, complemented
89#4945C2×C311yescharacteristic, complemented
90C24×C32—22no—
91C24×C32—22no—
92C24×C32—22no—
93C24×C32—41no—
94C24×C32—41no—
95C24×C32—41no—
96C24×C32—41no—
97C24×C32C2311yescharacteristic
98C24×C32C2311yescharacteristic
99C24×C32C2311yescharacteristic
100C24×C32C2311yescharacteristic
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—41no—
109C2×C32×D4—41no—
110C2×C32×D4—41no—
111C2×C32×D4—41no—
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C2×C3×#67—22no—
116C2×C3×#67—22no—
117C2×C3×#67—22no—
118C2×C3×#67—22no—
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—41no—
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×#67D414yescomplemented
139C22×C3×Dic3C2311yescharacteristic
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—41no—
148C2×C3×C4×D3—22no—
149C2×C3×C4×D3—22no—
150C2×C3×C4×D3—41no—
151C32×C22⋊C4—22no—
152C32×C22⋊C4—22no—
153C32×C22⋊C4D414yescomplemented
154C3×#217—22no—
155C3×#217—22no—
156C3×#217—22no—
157C3×#217—22no—
158C3×#217—22no—
159C3×#217—22no—
160C3×#217—41no—
161C3×#217D414yescomplemented
162C3×(C2×D3)⋊C4—22no—
163C3×(C2×D3)⋊C4—41no—
164C3×(C2×D3)⋊C4—41no—
165C3×C4⋊Dic3—22no—
166C3×Dic3⋊C4—22no—
167C3×C4×Dic3—22no—
168#2669—31noSylow
169C25×C3—21no—
170C25×C3C2×D311yescharacteristic
171C25×C3C22×C311yescharacteristic
172C22×C3×D4—21no—
173C22×C3×D4—21no—
174C22×C3×D4—21no—
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×D4—31no—
184C22×C3×D4C2×D311yescharacteristic
185C22×C3×D4C2×D311yescharacteristic
186C22×C3×D4C2×D311yescharacteristic
187C22×C3×D4C22×C311yescharacteristic
188C22×C3×D4C22×C311yescharacteristic
189C22×C3×D4C22×C311yescharacteristic
190C23×C3×C4—31no—
191C22×#67C22×C311yescharacteristic
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, complemented
200C22×C4×D3C22×C311yescharacteristic, complemented
201C3×#127—64no—
202C3×#121—64no—
203C3×#121—64no—
204C3×#120—28no—
205C3×#120—24no—
206C3×#120—24no—
207C3×#120—64no—
208C3×#120—64no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C22⋊C4—21no—
212C2×C3×C22⋊C4—21no—
213C2×C3×C22⋊C4—21no—
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⋊C4—31no—
223C2×C3×C22⋊C4—31no—
224C2×C3×C22⋊C4—31no—
225C2×C3×C22⋊C4C2×D311yescharacteristic
226C2×C3×C22⋊C4C2×D311yescharacteristic
227C2×C3×C22⋊C4C2×D311yescharacteristic
228C2×C3×C22⋊C4C22×C311yescharacteristic
229C2×C3×C22⋊C4C22×C311yescharacteristic
230C2×C3×C22⋊C4C22×C311yescharacteristic
231C2×C3×C42—31no—
232#953—24no—
233#953—24no—
234C2×#217C22×C311yescharacteristic
235C2×#217C22×C311yescharacteristic
236C2×#217C22×C311yescharacteristic
237C2×#217C22×C311yescharacteristic
238C2×#217C22×C311yescharacteristic
239C2×#217C22×C311yescharacteristic
240C2×#217C22×C311yescharacteristic, complemented
241C2×#217C22×C311yescharacteristic, complemented
242#940—24no—
243#938—24no—
244C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
245C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
246C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
247C2×C4⋊Dic3C22×C311yescharacteristic, complemented
248C2×Dic3⋊C4C22×C311yescharacteristic, complemented
249C2×C4×Dic3C22×C311yescharacteristic, complemented
250#884—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×C32—21no—
279C23×C32—21no—
280C23×C32—21no—
281C23×C32—21no—
282C23×C32—21no—
283C23×C32—21no—
284C23×C32—44no—
285C23×C32—44no—
286C23×C32—44no—
287C23×C32—44no—
288C23×C32—44no—
289C23×C32—44no—
290C23×C32—44no—
291C23×C32C2×D412yes—
292C23×C32C2×D412yes—
293C23×C32C2×D412yes—
294C23×C32C2411yescharacteristic
295C22×C3×D3—21no—
296C22×C3×D3—21no—
297C22×C3×D3—21no—
298C22×C3×D3—21no—
299C22×C3×D3—21no—
300C22×C3×D3—21no—
301C22×C3×D3—21no—
302C22×C3×D3—21no—
303C22×C3×D3—21no—
304C22×C3×D3—21no—
305C22×C3×D3—21no—
306C22×C3×D3—21no—
307C22×C3×D3—21no—
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×C4C2×D412yes—
320C2×C32×C4C2×D412yes—
321C3×#67—44no—
322C3×#67—44no—
323C3×#67—44no—
324C3×#67—44no—
325C3×#67—44no—
326C3×#67—44no—
327C3×#67—44no—
328C3×#67—44no—
329C2×C3×Dic3—21no—
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×Dic3—21no—
340C2×C3×Dic3—21no—
341C2×C3×Dic3—21no—
342C2×C3×Dic3—21no—
343C2×C3×Dic3—21no—
344C2×C3×Dic3C2×D412yes—
345C2×C3×Dic3C2×D412yes—
346C2×C3×Dic3C2×D412yes—
347C3×D12—44no—
348C3×C4×D3—44no—
349C2×#127—31no—
350C2×#121—31no—
351C2×#121—31no—
352C2×#120—31no—
353C2×#120—31no—
354C2×#120C3×D311yescharacteristic, complemented
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—24no—
365C24×C3—22no—
366C24×C3—22no—
367C24×C3—22no—
368C24×C3—22no—
369C24×C3—22no—
370C24×C3—22no—
371C24×C3—21no—
372C24×C3—21no—
373C24×C3—21no—
374C24×C3—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—42no—
378C24×C3—42no—
379C24×C3—41no—
380C24×C3—41no—
381C24×C3—41no—
382C24×C3—41no—
383C24×C3—41no—
384C24×C3—41no—
385C24×C3—41no—
386C24×C3—41no—
387C24×C3—42no—
388C24×C3—42no—
389C24×C3—42no—
390C24×C3—42no—
391C24×C3C22×D311yescharacteristic
392C24×C3C22×D311yescharacteristic
393C24×C3C22×D311yescharacteristic
394C24×C3C22×D311yescharacteristic
395C24×C3C23×C311yescharacteristic
396C24×C3C23×C311yescharacteristic
397C24×C3C23×C311yescharacteristic
398C24×C3C23×C311yescharacteristic
399C23×D3C23×C311yescharacteristic
400C23×D3C23×C311yescharacteristic
401C2×C3×D4—24no—
402C2×C3×D4—24no—
403C2×C3×D4—24no—
404C2×C3×D4—22no—
405C2×C3×D4—22no—
406C2×C3×D4—22no—
407C2×C3×D4—22no—
408C2×C3×D4—22no—
409C2×C3×D4—22no—
410C2×C3×D4—22no—
411C2×C3×D4—22no—
412C2×C3×D4—22no—
413C2×C3×D4—22no—
414C2×C3×D4—34no—
415C2×C3×D4—42no—
416C2×C3×D4—42no—
417C2×C3×D4—41no—
418C2×C3×D4—41no—
419C2×C3×D4—41no—
420C2×C3×D4—41no—
421C2×C3×D4—41no—
422C2×C3×D4—41no—
423C2×C3×D4—41no—
424C2×C3×D4—41no—
425C2×C3×D4—42no—
426C2×C3×D4—42no—
427C2×C3×D4—42no—
428C2×C3×D4—42no—
429C2×C3×D4—62no—
430C2×C3×D4—62no—
431C2×C3×D4—62no—
432C2×C3×D4—62no—
433C2×C3×D4—62no—
434C2×C3×D4—62no—
435C2×C3×D4—62no—
436C2×C3×D4—62no—
437C2×C3×D4—62no—
438C2×C3×D4—62no—
439C2×C3×D4—62no—
440C2×C3×D4—62no—
441C2×C3×D4—62no—
442C2×C3×D4—62no—
443C2×C3×D4—121no—
444C2×C3×D4—121no—
445C2×C3×D4—121no—
446C2×C3×D4—121no—
447C2×C3×D4—121no—
448C2×C3×D4—121no—
449C2×C3×D4—121no—
450C2×C3×D4—121no—
451C2×C3×D4—121no—
452C2×C3×D4—121no—
453C2×C3×D4—121no—
454C2×C3×D4—121no—
455C22×C3×C4—21no—
456C22×C3×C4—21no—
457C22×C3×C4—21no—
458C22×C3×C4—31no—
459C22×C3×C4—31no—
460C22×C3×C4—31no—
461C22×C3×C4—31no—
462C22×C3×C4—31no—
463C22×C3×C4—31no—
464C22×C3×C4—62no—
465C22×C3×C4—62no—
466C22×C3×C4—121no—
467C22×C3×C4C22×D311yescharacteristic
468C22×C3×C4C22×D311yescharacteristic
469C22×C3×C4C22×D311yescharacteristic
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—22no—
483C2×#67—22no—
484C2×#67—22no—
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×#67—41no—
494C2×#67—41no—
495C2×#67—41no—
496C2×#67C3×D414yescomplemented
497C22×Dic3C23×C311yescharacteristic
498C22×Dic3C23×C311yescharacteristic
499C22×Dic3C23×C311yescharacteristic
500C22×Dic3C23×C311yescharacteristic
501C22×Dic3C23×C311yescharacteristic
502C22×Dic3C23×C311yescharacteristic
503C2×D12—22no—
504C2×D12—22no—
505C2×D12—41no—
506C2×C4×D3—22no—
507C2×C4×D3—22no—
508C2×C4×D3—41no—
509C3×C4⋊C4—62no—
510C3×C4⋊C4—62no—
511C3×C22⋊C4—24no—
512C3×C22⋊C4—24no—
513C3×C22⋊C4—22no—
514C3×C22⋊C4—22no—
515C3×C22⋊C4—22no—
516C3×C22⋊C4—22no—
517C3×C22⋊C4—24no—
518C3×C22⋊C4—34no—
519C3×C22⋊C4—62no—
520C3×C22⋊C4—62no—
521C3×C22⋊C4—62no—
522C3×C22⋊C4—62no—
523C3×C22⋊C4—62no—
524C3×C22⋊C4—62no—
525C3×C22⋊C4—62no—
526C3×C22⋊C4—121no—
527C3×C22⋊C4—121no—
528C3×C22⋊C4—121no—
529C3×C22⋊C4#6714yescomplemented
530C3×C22⋊C4C3×D414yescomplemented
531C3×C42—62no—
532#217—22no—
533#217—22no—
534#217—22no—
535#217—22no—
536#217—22no—
537#217—22no—
538#217—41no—
539#217C3×D414yescomplemented
540(C2×D3)⋊C4—22no—
541(C2×D3)⋊C4—41no—
542(C2×D3)⋊C4—41no—
543C4⋊Dic3—22no—
544Dic3⋊C4—22no—
545C4×Dic3—22no—
546C22×C32—22no—
547C22×C32—22no—
548C22×C32—22no—
549C22×C32—22no—
550C22×C32—22no—
551C22×C32—22no—
552C22×C32—22no—
553C22×C32—22no—
554C22×C32—22no—
555C22×C32—416no—
556C22×C32—41no—
557C22×C32—41no—
558C22×C32—41no—
559C22×C32—41no—
560C22×C32—41no—
561C22×C32—41no—
562C22×C32—41no—
563C22×C32—41no—
564C22×C32—41no—
565C22×C32—41no—
566C22×C32—41no—
567C22×C32—41no—
568C22×C32—41no—
569C22×C32—41no—
570C22×C32—41no—
571C22×C32—41no—
572C22×C32—41no—
573C22×C32—41no—
574C22×C32—41no—
575C22×C32C22×D411yescharacteristic
576C22×C32C22×D411yescharacteristic
577C22×C32C22×D411yescharacteristic
578C22×C32H(5,𝔽2)11yescharacteristic
579C22×C32H(5,𝔽2)11yescharacteristic
580C22×C32H(5,𝔽2)11yescharacteristic
581C22×C32H(5,𝔽2)11yescharacteristic
582C2×C3×D3—22no—
583C2×C3×D3—22no—
584C2×C3×D3—22no—
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—
592C2×C3×D3—41no—
593C2×C3×D3—41no—
594C2×C3×D3—41no—
595C2×C3×D3—41no—
596C32×C4—22no—
597C32×C4—22no—
598C32×C4—41no—
599C3×Dic3—22no—
600C3×Dic3—22no—
601C3×Dic3—22no—
602C3×Dic3—41no—
603C3×Dic3—41no—
604C3×Dic3—41no—
605C25C2×C3×D311yescharacteristic
606C22×D4—31no—
607C22×D4—31no—
608C22×D4—31no—
609C22×D4—31no—
610C22×D4—31no—
611C22×D4—31no—
612C22×D4—31no—
613C22×D4—31no—
614C22×D4—31no—
615C22×D4C2×C3×D311yescharacteristic
616C22×D4C2×C3×D311yescharacteristic
617C22×D4C2×C3×D311yescharacteristic
618C23×C4—31no—
619#127—64no—
620#121—64no—
621#121—64no—
622#120—24no—
623#120—64no—
624#120—64no—
625C2×C4⋊C4—31no—
626C2×C4⋊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⋊C4—31no—
636C2×C22⋊C4—31no—
637C2×C22⋊C4—31no—
638C2×C22⋊C4C2×C3×D311yescharacteristic
639C2×C22⋊C4C2×C3×D311yescharacteristic
640C2×C22⋊C4C2×C3×D311yescharacteristic
641C2×C42—31no—
642#95—31no—
643#95—31no—
644#95—31no—
645#95—31no—
646C23×C3—22no—
647C23×C3—22no—
648C23×C3—22no—
649C23×C3—22no—
650C23×C3—22no—
651C23×C3—22no—
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—21no—
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—21no—
685C23×C3—21no—
686C23×C3—21no—
687C23×C3—21no—
688C23×C3—22no—
689C23×C3—21no—
690C23×C3—21no—
691C23×C3—21no—
692C23×C3—21no—
693C23×C3—21no—
694C23×C3—21no—
695C23×C3—21no—
696C23×C3—21no—
697C23×C3—21no—
698C23×C3—21no—
699C23×C3—21no—
700C23×C3—21no—
701C23×C3—21no—
702C23×C3—21no—
703C23×C3—21no—
704C23×C3—22no—
705C23×C3—22no—
706C23×C3—22no—
707C23×C3—32no—
708C23×C3—41no—
709C23×C3—41no—
710C23×C3—41no—
711C23×C3—41no—
712C23×C3—41no—
713C23×C3—41no—
714C23×C3—41no—
715C23×C3—41no—
716C23×C3—41no—
717C23×C3—41no—
718C23×C3—41no—
719C23×C3—41no—
720C23×C3—41no—
721C23×C3—41no—
722C23×C3—41no—
723C23×C3—41no—
724C23×C3—41no—
725C23×C3—41no—
726C23×C3—44no—
727C23×C3—44no—
728C23×C3—44no—
729C23×C3—44no—
730C23×C3—44no—
731C23×C3—44no—
732C23×C3—48no—
733C23×C3—48no—
734C23×C3—48no—
735C23×C3—44no—
736C23×C3—44no—
737C23×C3—44no—
738C23×C3—44no—
739C23×C3—44no—
740C23×C3—44no—
741C23×C3—48no—
742C23×C3—48no—
743C23×C3—48no—
744C23×C3—48no—
745C23×C3—44no—
746C23×C3—44no—
747C23×C3—61no—
748C23×C3—61no—
749C23×C3—61no—
750C23×C3—61no—
751C23×C3—61no—
752C23×C3—61no—
753C23×C3—61no—
754C23×C3—61no—
755C23×C3—61no—
756C23×C3—61no—
757C23×C3—61no—
758C23×C3—61no—
759C23×C3—61no—
760C23×C3D3×D412yes—
761C23×C3D3×D412yes—
762C23×C3C2×#6712yes—
763C23×C3C2×C3×D412yes—
764C23×C3C2×C3×D412yes—
765C23×C3C2×C3×D412yes—
766C23×C3C23×D311yescharacteristic
767C23×C3C24×C311yescharacteristic
768C22×D3—21no—
769C22×D3—21no—
770C22×D3—21no—
771C22×D3—21no—
772C22×D3—21no—
773C22×D3—21no—
774C22×D3—21no—
775C22×D3—21no—
776C22×D3—21no—
777C22×D3—21no—
778C22×D3—21no—
779C22×D3—21no—
780C22×D3—21no—
781C22×D3C2×C3×D412yes—
782C3×D4—44no—
783C3×D4—44no—
784C3×D4—44no—
785C3×D4—44no—
786C3×D4—48no—
787C3×D4—48no—
788C3×D4—48no—
789C3×D4—44no—
790C3×D4—44no—
791C3×D4—124no—
792C3×D4—124no—
793C3×D4—124no—
794C3×D4—124no—
795C3×D4—124no—
796C3×D4—124no—
797C3×D4—124no—
798C3×D4—124no—
799C3×D4—124no—
800C2×C3×C4—21no—
801C2×C3×C4—21no—
802C2×C3×C4—21no—
803C2×C3×C4—21no—
804C2×C3×C4—21no—
805C2×C3×C4—21no—
806C2×C3×C4—21no—
807C2×C3×C4—21no—
808C2×C3×C4—22no—
809C2×C3×C4—21no—
810C2×C3×C4—21no—
811C2×C3×C4—21no—
812C2×C3×C4—21no—
813C2×C3×C4—21no—
814C2×C3×C4—21no—
815C2×C3×C4—22no—
816C2×C3×C4—22no—
817C2×C3×C4—32no—
818C2×C3×C4—32no—
819C2×C3×C4—32no—
820C2×C3×C4—41no—
821C2×C3×C4—41no—
822C2×C3×C4—41no—
823C2×C3×C4—41no—
824C2×C3×C4—41no—
825C2×C3×C4—41no—
826C2×C3×C4—61no—
827C2×C3×C4—61no—
828C2×C3×C4—61no—
829C2×C3×C4—61no—
830C2×C3×C4—61no—
831C2×C3×C4—61no—
832C2×C3×C4—61no—
833C2×C3×C4—61no—
834C2×C3×C4—61no—
835C2×C3×C4—61no—
836C2×C3×C4—61no—
837C2×C3×C4—61no—
838C2×C3×C4—61no—
839C2×C3×C4—61no—
840C2×C3×C4—61no—
841C2×C3×C4—124no—
842C2×C3×C4C2×#6712yes—
843C2×C3×C4C2×#6712yes—
844C2×C3×C4C2×C3×D412yes—
845C2×C3×C4C2×C3×D412yes—
846#67—44no—
847#67—44no—
848#67—44no—
849#67—44no—
850#67—44no—
851#67—44no—
852#67—44no—
853#67—44no—
854C2×Dic3—21no—
855C2×Dic3—21no—
856C2×Dic3—21no—
857C2×Dic3—21no—
858C2×Dic3—21no—
859C2×Dic3—21no—
860C2×Dic3—21no—
861C2×Dic3—21no—
862C2×Dic3—21no—
863C2×Dic3—21no—
864C2×Dic3—21no—
865C2×Dic3—21no—
866C2×Dic3—21no—
867C2×Dic3—21no—
868C2×Dic3—21no—
869C2×Dic3C2×C3×D412yes—
870C2×Dic3C2×C3×D412yes—
871C2×Dic3C2×C3×D412yes—
872D12—44no—
873C4×D3—44no—
874C2×C32—42no—
875C2×C32—42no—
876C2×C32—42no—
877C2×C32—81no—
878C2×C32#53411yescharacteristic
879C2×C32#53511yescharacteristic
880C2×C32#53511yescharacteristic
881C2×C32D4211yescharacteristic
882C2×C32D4211yescharacteristic
883C2×C32D4211yescharacteristic
884C2×C32#56011yescharacteristic
885C3×D3—42no—
886C3×D3—81no—
887C24—22no—
888C24—22no—
889C24—22no—
890C24—31no—
891C24—31no—
892C24—41no—
893C24—41no—
894C24—41no—
895C24—41no—
896C24C22×C3×D311yescharacteristic
897C24C22×C3×D311yescharacteristic
898C24C22×C3×D311yescharacteristic
899C24C22×C3×D311yescharacteristic
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—22no—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4—34no—
906C2×D4—41no—
907C2×D4—41no—
908C2×D4—41no—
909C2×D4—41no—
910C2×D4—62no—
911C2×D4—62no—
912C2×D4—62no—
913C2×D4—62no—
914C2×D4—62no—
915C2×D4—62no—
916C2×D4—62no—
917C2×D4—62no—
918C2×D4—62no—
919C2×D4—62no—
920C2×D4—62no—
921C2×D4—62no—
922C2×D4—62no—
923C2×D4—62no—
924C2×D4—121no—
925C2×D4—121no—
926C2×D4—121no—
927C2×D4—121no—
928C2×D4—121no—
929C2×D4—121no—
930C2×D4—121no—
931C2×D4—121no—
932C2×D4—121no—
933C2×D4—121no—
934C2×D4—121no—
935C2×D4—121no—
936C22×C4—31no—
937C22×C4—31no—
938C22×C4—31no—
939C22×C4—31no—
940C22×C4—31no—
941C22×C4—31no—
942C22×C4—62no—
943C22×C4—62no—
944C22×C4—121no—
945C22×C4C22×C3×D311yescharacteristic
946C22×C4C22×C3×D311yescharacteristic
947C22×C4C22×C3×D311yescharacteristic
948C4⋊C4—62no—
949C4⋊C4—62no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—34no—
953C22⋊C4—62no—
954C22⋊C4—62no—
955C22⋊C4—62no—
956C22⋊C4—62no—
957C22⋊C4—62no—
958C22⋊C4—62no—
959C22⋊C4—62no—
960C22⋊C4—121no—
961C22⋊C4—121no—
962C22⋊C4—121no—
963C22⋊C4C3×#6714yescomplemented
964C42—62no—
965C22×C3—24no—
966C22×C3—24no—
967C22×C3—24no—
968C22×C3—22no—
969C22×C3—22no—
970C22×C3—22no—
971C22×C3—22no—
972C22×C3—22no—
973C22×C3—22no—
974C22×C3—22no—
975C22×C3—22no—
976C22×C3—22no—
977C22×C3—22no—
978C22×C3—22no—
979C22×C3—22no—
980C22×C3—22no—
981C22×C3—22no—
982C22×C3—22no—
983C22×C3—22no—
984C22×C3—22no—
985C22×C3—22no—
986C22×C3—21no—
987C22×C3—21no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—21no—
992C22×C3—21no—
993C22×C3—42no—
994C22×C3—42no—
995C22×C3—42no—
996C22×C3—42no—
997C22×C3—42no—
998C22×C3—42no—
999C22×C3—42no—
1000C22×C3—42no—
1001C22×C3—42no—
1002C22×C3—42no—
1003C22×C3—42no—
1004C22×C3—42no—
1005C22×C3—42no—
1006C22×C3—42no—
1007C22×C3—42no—
1008C22×C3—42no—
1009C22×C3—42no—
1010C22×C3—42no—
1011C22×C3—42no—
1012C22×C3—42no—
1013C22×C3—42no—
1014C22×C3—432no—
1015C22×C3—416no—
1016C22×C3—416no—
1017C22×C3—41no—
1018C22×C3—41no—
1019C22×C3—41no—
1020C22×C3—41no—
1021C22×C3—41no—
1022C22×C3—41no—
1023C22×C3—41no—
1024C22×C3—41no—
1025C22×C3—41no—
1026C22×C3—41no—
1027C22×C3—41no—
1028C22×C3—41no—
1029C22×C3—41no—
1030C22×C3—41no—
1031C22×C3—41no—
1032C22×C3—41no—
1033C22×C3—41no—
1034C22×C3—41no—
1035C22×C3—41no—
1036C22×C3—41no—
1037C22×C3—41no—
1038C22×C3—41no—
1039C22×C3—41no—
1040C22×C3—41no—
1041C22×C3—41no—
1042C22×C3—41no—
1043C22×C3—41no—
1044C22×C3—41no—
1045C22×C3—41no—
1046C22×C3—41no—
1047C22×C3—41no—
1048C22×C3—41no—
1049C22×C3—41no—
1050C22×C3—41no—
1051C22×C3—41no—
1052C22×C3—41no—
1053C22×C3—41no—
1054C22×C3—41no—
1055C22×C3—62no—
1056C22×C3—62no—
1057C22×C3—62no—
1058C22×C3—81no—
1059C22×C3—81no—
1060C22×C3—81no—
1061C22×C3—81no—
1062C22×C3—121no—
1063C22×C3—121no—
1064C22×C3—121no—
1065C22×C3—121no—
1066C22×C3—121no—
1067C22×C3—121no—
1068C22×C3—121no—
1069C22×C3—121no—
1070C22×C3—121no—
1071C22×C3—121no—
1072C22×C3—121no—
1073C22×C3C2×D3×D411yescharacteristic
1074C22×C3C2×D3×D411yescharacteristic
1075C22×C3#100411yescharacteristic
1076C22×C3#100411yescharacteristic
1077C22×C3#100411yescharacteristic
1078C22×C3#100411yescharacteristic
1079C22×C3C22×#6711yescharacteristic
1080C22×C3C22×C3×D411yescharacteristic
1081C22×C3C22×C3×D411yescharacteristic
1082C22×C3C22×C3×D411yescharacteristic
1083C22×C3C3×H(5,𝔽2)11yescharacteristic
1084C22×C3C3×H(5,𝔽2)11yescharacteristic
1085C22×C3C3×H(5,𝔽2)11yescharacteristic
1086C22×C3C3×H(5,𝔽2)11yescharacteristic
1087C2×D3—22no—
1088C2×D3—22no—
1089C2×D3—22no—
1090C2×D3—41no—
1091C2×D3—41no—
1092C2×D3—41no—
1093C2×D3—41no—
1094C2×D3—41no—
1095C2×D3—41no—
1096C2×D3—41no—
1097C2×D3—41no—
1098C2×D3—41no—
1099C2×D3—41no—
1100C2×D3—41no—
1101C3×C4—22no—
1102C3×C4—22no—
1103C3×C4—22no—
1104C3×C4—22no—
1105C3×C4—42no—
1106C3×C4—42no—
1107C3×C4—42no—
1108C3×C4—41no—
1109C3×C4—41no—
1110C3×C4—62no—
1111C3×C4—62no—
1112C3×C4—62no—
1113C3×C4—121no—
1114C3×C4—121no—
1115C3×C4—121no—
1116Dic3—22no—
1117Dic3—22no—
1118Dic3—22no—
1119Dic3—41no—
1120Dic3—41no—
1121Dic3—41no—
1122C32#266911yescharacteristic, complemented, Sylow
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—32no—
1149C23—44no—
1150C23—44no—
1151C23—44no—
1152C23—44no—
1153C23—44no—
1154C23—44no—
1155C23—44no—
1156C23—61no—
1157C23—61no—
1158C23—61no—
1159C23—61no—
1160C23—61no—
1161C23—61no—
1162C23—61no—
1163C23—61no—
1164C23—61no—
1165C23—61no—
1166C23—61no—
1167C23—61no—
1168C23—61no—
1169C23C3×D3×D412yes—
1170C23C3×D3×D412yes—
1171C23C2×C3×#6712yes—
1172C23C23×C3×D311yescharacteristic
1173D4—44no—
1174D4—44no—
1175D4—44no—
1176D4—124no—
1177D4—124no—
1178D4—124no—
1179D4—124no—
1180D4—124no—
1181D4—124no—
1182D4—124no—
1183D4—124no—
1184D4—124no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—32no—
1193C2×C4—32no—
1194C2×C4—32no—
1195C2×C4—61no—
1196C2×C4—61no—
1197C2×C4—61no—
1198C2×C4—61no—
1199C2×C4—61no—
1200C2×C4—61no—
1201C2×C4—61no—
1202C2×C4—61no—
1203C2×C4—61no—
1204C2×C4—61no—
1205C2×C4—61no—
1206C2×C4—61no—
1207C2×C4—61no—
1208C2×C4—61no—
1209C2×C4—61no—
1210C2×C4—124no—
1211C2×C4C2×C3×#6712yes—
1212C2×C4C2×C3×#6712yes—
1213C2×C3—21no—
1214C2×C3—21no—
1215C2×C3—21no—
1216C2×C3—21no—
1217C2×C3—21no—
1218C2×C3—21no—
1219C2×C3—21no—
1220C2×C3—44no—
1221C2×C3—44no—
1222C2×C3—44no—
1223C2×C3—42no—
1224C2×C3—42no—
1225C2×C3—42no—
1226C2×C3—42no—
1227C2×C3—42no—
1228C2×C3—42no—
1229C2×C3—82no—
1230C2×C3—81no—
1231C2×C3—81no—
1232C2×C3—122no—
1233C2×C3—241no—
1234C2×C3#558911yescharacteristic
1235C2×C3#559011yescharacteristic
1236C2×C3#559211yescharacteristic
1237C2×C3#559511yescharacteristic
1238C2×C3D4×#6711yescharacteristic
1239C2×C3D4×#6711yescharacteristic
1240C2×C3#580511yescharacteristic
1241C2×C3C3×#53411yescharacteristic
1242C2×C3C3×#53511yescharacteristic
1243C2×C3C3×#53511yescharacteristic
1244C2×C3C3×D4211yescharacteristic
1245C2×C3C3×D4211yescharacteristic
1246C2×C3C3×D4211yescharacteristic
1247C2×C3C3×#56011yescharacteristic
1248D3—42no—
1249D3—81no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—416no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—62no—
1280C22—62no—
1281C22—62no—
1282C22—121no—
1283C22—121no—
1284C22—121no—
1285C22—121no—
1286C22—121no—
1287C22—121no—
1288C22—121no—
1289C22—121no—
1290C22—121no—
1291C22—121no—
1292C22—121no—
1293C22C2×C3×D3×D411yescharacteristic
1294C22C2×C3×D3×D411yescharacteristic
1295C22C3×#100411yescharacteristic
1296C22C3×#100411yescharacteristic
1297C22C3×#100411yescharacteristic
1298C22C3×#100411yescharacteristic
1299C22C22×C3×#6711yescharacteristic
1300C4—22no—
1301C4—22no—
1302C4—41no—
1303C4—62no—
1304C4—62no—
1305C4—62no—
1306C4—121no—
1307C4—121no—
1308C4—121no—
1309C3—21no—
1310C3#8260911yescharacteristic, direct product factor
1311C3C3×#266911yescharacteristic, complemented
1312C2—42no—
1313C2—42no—
1314C2—42no—
1315C2—81no—
1316C2—122no—
1317C2—241no—
1318C2C3×#558911yescharacteristic
1319C2C3×#559011yescharacteristic
1320C2C3×#559211yescharacteristic
1321C2C3×#559511yescharacteristic
1322C2C3×D4×#6711yescharacteristic
1323C2C3×D4×#6711yescharacteristic
1324C2C3×#580511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#120C2
socleC23×C32C24
hypercenterC2×C3×#120D3
hypocenterC3C3×#2669
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#120

Complements

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

NH ≅ G/Ntype
1. C2×C32×#120C2semidirect
2. C2×C3×#953C2semidirect
3. C2×C3×#953C2semidirect
4. C2×C3×#940C2semidirect
5. C2×C3×#938C2semidirect
6. C2×C3×#884C2semidirect
7. C3×#5223C2semidirect
8. C3×#5223C2semidirect
9. C3×#5223C2semidirect
10. C3×#5222C2semidirect
11. C3×#4961C2semidirect
12. C3×#4960C2semidirect
13. C3×#4956C2semidirect
14. C3×#4951C2semidirect
15. C3×#4945C2semidirect
17. #82609C3direct (N × H)
28. C22×C3×#67C22semidirect
29. C22×C3×#67C22semidirect
30. C22×C3×D12C22semidirect
31. C22×C3×C4×D3C22semidirect
44. C2×C3×#217C22semidirect
45. C2×C3×#217C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×C4⋊Dic3C22semidirect
52. C2×C3×Dic3⋊C4C22semidirect
53. C2×C3×C4×Dic3C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
57. C3×C3⋊#95C22semidirect
58. C3×C3⋊#95C22semidirect
65. C2×C3×#120D3semidirect
66. C2×C3×#120C2×C3semidirect
67. C2×#953C2×C3semidirect
68. C2×#953C2×C3semidirect
69. C2×#940C2×C3semidirect
70. C2×#938C2×C3semidirect
71. C2×#884C2×C3semidirect
81. #5223C2×C3semidirect
82. #5223C2×C3semidirect
83. #5223C2×C3semidirect
84. #5222C2×C3semidirect
85. #4961C2×C3semidirect
86. #4960C2×C3semidirect
87. #4956C2×C3semidirect
88. #4951C2×C3semidirect
89. #4945C2×C3semidirect
138. C2×C3×#67D4semidirect
153. C32×C22⋊C4D4semidirect
161. C3×#217D4semidirect
197. C22×#67C22×C3semidirect
198. C22×#67C22×C3semidirect
199. C22×D12C22×C3semidirect
200. C22×C4×D3C22×C3semidirect
240. C2×#217C22×C3semidirect
241. C2×#217C22×C3semidirect
244. C2×(C2×D3)⋊C4C22×C3semidirect
245. C2×(C2×D3)⋊C4C22×C3semidirect
246. C2×(C2×D3)⋊C4C22×C3semidirect
247. C2×C4⋊Dic3C22×C3semidirect
248. C2×Dic3⋊C4C22×C3semidirect
249. C2×C4×Dic3C22×C3semidirect
255. C3⋊#95C22×C3semidirect
256. C3⋊#95C22×C3semidirect
257. C3⋊#95C22×C3semidirect
258. C3⋊#95C22×C3semidirect
354. C2×#120C3×D3semidirect
496. C2×#67C3×D4semidirect
529. C3×C22⋊C4#67semidirect
530. C3×C22⋊C4C3×D4semidirect
539. #217C3×D4semidirect
963. C22⋊C4C3×#67semidirect
1122. C32#2669semidirect
1310. C3#82609direct (N × H)
1311. C3C3×#2669semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1202
C2×C3×#9532
C2×C3×#9402
C2×C3×#9382
C2×C3×#8842
C3×#52232
C3×#52222
C3×#49612
C3×#49602
C3×#49562
C3×#49512
C3×#49452
C3×#26693
#826093