Finite Group Databasebeta

← C3×#80641 #11882295

Subgroups — C3×#80641 #11882295

Order 1152.

858 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5624C211yesmaximal, characteristic, complemented
2C3×#5596C211yesmaximal, characteristic, complemented
3C32×#465C211yesmaximal, characteristic, complemented
4C3×#5165C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic, complemented
6C3×#5115C211yesmaximal, characteristic, complemented
7C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
8C3×#5048C211yesmaximal, characteristic, complemented
9C3×#5038C211yesmaximal, characteristic, complemented
10C3×#4871C211yesmaximal, characteristic, complemented
11C3×#4870C211yesmaximal, characteristic, complemented
12C3×#4819C211yesmaximal, characteristic, complemented
13C3×#4793C211yesmaximal, characteristic, complemented
14C3×#4786C211yesmaximal, characteristic, complemented
15C3×#4766C211yesmaximal, characteristic, complemented
16C3×#3247—31nomaximal
17#80641C311yesmaximal, characteristic, direct product factor
18C2×C3×#237—21no—
19C2×C32×SD16C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C32×#121C2211yescharacteristic
23C3×#947C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#940C2211yescharacteristic
27C3×#939—21no—
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#930C2211yescharacteristic
31C3×#930C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34C2×C3×D24C2211yescharacteristic
35C3×#898—21no—
36C3×#893C2211yescharacteristic
37C3×#893C2211yescharacteristic
38C3×#892—21no—
39C3×#890C2211yescharacteristic
40C3×#888C2211yescharacteristic
41C3×#886—21no—
42C3×#885—21no—
43C3×#67⋊C4—21no—
44C3×#67⋊C4—21no—
45C32×#106C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#532—31no—
62C3×#529—31no—
63#5624C2×C311yescharacteristic, complemented
64#5596C2×C311yescharacteristic, complemented
65C3×#478—31no—
66C3×#478—31no—
67C3×#477—31no—
68C3×#476—31no—
69C3×#466—31no—
70C3×#466—31no—
71C3×#465—21no—
72C3×#465—31no—
73C3×#465D311yescharacteristic, complemented
74C3×#465C2×C311yescharacteristic, complemented
75C3×#463—31no—
76C3×#463—31no—
77C3×#460—31no—
78C3×#459—31no—
79C2×C3×C4⋊C8—31no—
80#5165C2×C311yescharacteristic, complemented
81#5163C2×C311yescharacteristic, complemented
82#5115C2×C311yescharacteristic, complemented
83C2×Dic3⋊C8C2×C311yescharacteristic, complemented
84#5048C2×C311yescharacteristic, complemented
85#5038C2×C311yescharacteristic, complemented
86#4871C2×C311yescharacteristic, complemented
87#4870C2×C311yescharacteristic, complemented
88#4819C2×C311yescharacteristic, complemented
89#4793C2×C311yescharacteristic, complemented
90#4786C2×C311yescharacteristic, complemented
91#4766C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3D411yescharacteristic
102C22×C3×Dic3D411yescharacteristic
103C3×#237—44no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×Dic6—21no—
109C32×SD16—41no—
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C3×#217—21no—
119C3×#215—41no—
120C3×#213—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3D411yescharacteristic
135C3×C4×Dic3D411yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—41no—
142#3247—31noSylow
143C2×C3×#41—61no—
144C2×#237—21no—
145C2×C3×SD16—21no—
146C2×C3×SD16—31no—
147C2×C3×SD16C2×D311yescharacteristic
148C2×C3×SD16C22×C311yescharacteristic
149C2×C3×D8—31no—
150C2×C3×D8—31no—
151C22×C3×C8—21no—
152C22×C3×C8—31no—
153C22×C3×C8C2×D311yescharacteristic
154C22×C3×C8C22×C311yescharacteristic
155C3×C4⋊Q8—31no—
156C3×#127—31no—
157C3×#126—61no—
158C3×#125—31no—
159C3×#124—31no—
160C3×#124—61no—
161C3×#123—61no—
162C3×C22⋊Q8—21no—
163C3×C22⋊Q8C2×D311yescharacteristic
164C3×C22⋊Q8C22×C311yescharacteristic
165C3×#121—21no—
166C3×#121—31no—
167C3×#121—31no—
168C3×#121—61no—
169C3×#121C2×D311yescharacteristic
170C3×#121C22×C311yescharacteristic
171C3×C4×Q8—31no—
172C3×C4×D4—31no—
173C3×C4×D4—31no—
174C3×C4×D4—31no—
175C3×C4×D4—61no—
176C3×C4×D4—61no—
177C3×#117—61no—
178C2×C3×C42—31no—
179#947C22×C311yescharacteristic
180Q8×Dic3C22×C311yescharacteristic
181C2×#215C22×C311yescharacteristic
182#940C22×C311yescharacteristic
183#939—21no—
184D4×Dic3C22×C311yescharacteristic
185C2×#213C22×C311yescharacteristic
186#930C22×C311yescharacteristic
187#930C22×C311yescharacteristic
188C2×C4×Dic3C22×C311yescharacteristic
189C22×C3⋊C8C22×C311yescharacteristic
190C2×D24C22×C311yescharacteristic
191#898—21no—
192#893C22×C311yescharacteristic
193#893C22×C311yescharacteristic
194#892—21no—
195#890C22×C311yescharacteristic
196#888C22×C311yescharacteristic
197#886—21no—
198#885—21no—
199#67⋊C4—21no—
200#67⋊C4—21no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#106—21no—
204C3×#106—31no—
205C3×#106C2×D311yescharacteristic
206C3×#106C22×C311yescharacteristic
207C3×C4⋊C8—31no—
208C3×C4⋊C8—31no—
209C3×C4⋊C8—31no—
210C3×C4⋊C8—31no—
211C3×#103—21no—
212C3×#103—31no—
213C3×#103C2×D311yescharacteristic
214C3×#103C22×C311yescharacteristic
215C3×#102—21no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102C2×D311yescharacteristic
222C3×#102C22×C311yescharacteristic
223#835C22×C311yescharacteristic
224#832C22×C311yescharacteristic
225#821C22×C311yescharacteristic
226#821C22×C311yescharacteristic
227#818C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231Dic3⋊C8C22×C311yescharacteristic
232#809C22×C311yescharacteristic
233#809C22×C311yescharacteristic
234#808C22×C311yescharacteristic
235#807C22×C311yescharacteristic
236C23×C32—21no—
237C23×C32C2×D411yescharacteristic
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C32×Q8—21no—
241C32×Q8—21no—
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—42no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C3×#67—42no—
253C3×#67—42no—
254C3×#67—42no—
255C3×#67—42no—
256C2×C3×Dic3—22no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×Dic6—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#532—31no—
277#529—31no—
278#478—31no—
279#478—31no—
280#477—31no—
281#476—31no—
282#466—31no—
283#466—31no—
284#465—31no—
285#465C3×D311yescharacteristic, complemented
286#463—31no—
287#463—31no—
288#460—31no—
289#459—31no—
290C2×C4⋊C8—31no—
291C3×#41—124no—
292C2×C3×Q8—21no—
293C2×C3×Q8—61no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C23×C311yescharacteristic
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—41no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C23×C311yescharacteristic
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C23×C311yescharacteristic
316C2×#67—21no—
317C2×#67—21no—
318C2×#67—21no—
319C2×#67—21no—
320C22×Dic3—21no—
321C22×Dic3C3×D411yescharacteristic
322C22×Dic3C3×D411yescharacteristic
323#237—44no—
324C2×D12C23×C311yescharacteristic
325C2×D12C23×C311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×Dic6—21no—
329C3×SD16—41no—
330C3×SD16—41no—
331C3×SD16—42no—
332C3×SD16—121no—
333C3×D8—121no—
334C3×D8—121no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—41no—
340C2×C3×C8—41no—
341C2×C3×C8—42no—
342C2×C3×C8—121no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C23×C311yescharacteristic
346C2×C3×C8C23×C311yescharacteristic
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—41no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C42—31no—
376C3×C42—31no—
377C3×C42—31no—
378C3×C42—31no—
379C3×C42—61no—
380#217—21no—
381#215—41no—
382#213—41no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3C23×C311yescharacteristic
392C4⋊Dic3C23×C311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395C4×Dic3—21no—
396C4×Dic3C3×D411yescharacteristic
397C4×Dic3C3×D411yescharacteristic
398C4×Dic3C23×C311yescharacteristic
399C4×Dic3C23×C311yescharacteristic
400C2×C3⋊C8—41no—
401C2×C3⋊C8C23×C311yescharacteristic
402C2×C3⋊C8C23×C311yescharacteristic
403D24—41no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32AGL(1,ℤ/8)12yes—
410C22×C32C22×D411yescharacteristic
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4—41no—
421C32×C4H(5,𝔽2)11yescharacteristic
422C32×C42−1+411yescharacteristic
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3#13512yes—
429C2×#41—61no—
430C2×SD16—31no—
431C2×SD16C2×C3×D311yescharacteristic
432C2×D8—31no—
433C2×D8—31no—
434C22×C8—31no—
435C22×C8C2×C3×D311yescharacteristic
436C4⋊Q8—31no—
437#127—31no—
438#126—61no—
439#125—31no—
440#124—31no—
441#124—61no—
442#123—61no—
443C22⋊Q8C2×C3×D311yescharacteristic
444#121—31no—
445#121—31no—
446#121—61no—
447#121C2×C3×D311yescharacteristic
448C4×Q8—31no—
449C4×D4—31no—
450C4×D4—31no—
451C4×D4—31no—
452C4×D4—61no—
453C4×D4—61no—
454#117—61no—
455C2×C42—31no—
456#107—31no—
457#107—31no—
458#106—31no—
459#106C2×C3×D311yescharacteristic
460C4⋊C8—31no—
461C4⋊C8—31no—
462C4⋊C8—31no—
463C4⋊C8—31no—
464#103—31no—
465#103C2×C3×D311yescharacteristic
466#102—31no—
467#102—31no—
468#102—31no—
469#102—31no—
470#102—31no—
471#102C2×C3×D311yescharacteristic
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—41no—
476C23×C3—61no—
477C23×C3—61no—
478C23×C3D3×D411yescharacteristic
479C23×C3C2×C3×D411yescharacteristic
480C22×D3—21no—
481C22×D3—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—122no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—41no—
494C3×D4—41no—
495C3×D4—42no—
496C3×D4—42no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—82no—
502C3×D4—122no—
503C3×D4—122no—
504C3×D4—122no—
505C3×D4—122no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—62no—
528C2×C3×C4—62no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—122no—
532C2×C3×C4—122no—
533C2×C3×C4—122no—
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C2×C3×D411yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C24×C311yescharacteristic
538#67—42no—
539#67—42no—
540#67—42no—
541#67—42no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—42no—
547C2×Dic3C2×C3×D411yescharacteristic
548C2×Dic3C2×C3×D411yescharacteristic
549C2×Dic3C2×C3×D411yescharacteristic
550C2×Dic3C2×C3×D411yescharacteristic
551D12—21no—
552D12—21no—
553D12—21no—
554D12—21no—
555C4×D3—42no—
556C4×D3—42no—
557Dic6—42no—
558C3×C8—22no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—41no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C2×C32—22no—
569C2×C32—81no—
570C2×C32#53711yescharacteristic
571C2×C32C2×#13511yescharacteristic
572C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
573C3×D3—81no—
574C3×D3—81no—
575#41—124no—
576C2×Q8—61no—
577C2×Q8C22×C3×D311yescharacteristic
578C2×D4—21no—
579C2×D4—31no—
580C2×D4—31no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4C22×C3×D311yescharacteristic
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4C22×C3×D311yescharacteristic
592SD16—41no—
593SD16—121no—
594D8—121no—
595D8—121no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—41no—
599C2×C8—121no—
600C2×C8C22×C3×D311yescharacteristic
601C2×C8C22×C3×D311yescharacteristic
602C4⋊C4—21no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4C22×C3×D311yescharacteristic
610C4⋊C4C22×C3×D311yescharacteristic
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C42—31no—
621C42—31no—
622C42—31no—
623C42—31no—
624C42—61no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3#91412yes—
649C22×C3C3×AGL(1,ℤ/8)12yes—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C22×C3×D411yescharacteristic
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—32no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—81no—
674C3×C4—81no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4#100411yescharacteristic
679C3×C4#101011yescharacteristic
680C3×C4C3×H(5,𝔽2)11yescharacteristic
681C3×C4C3×2−1+411yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3C3×#13512yes—
688C32#324711yescharacteristic, complemented, Sylow
689C23—21no—
690C23—61no—
691C23—61no—
692C23C3×D3×D411yescharacteristic
693Q8—21no—
694Q8—21no—
695Q8—122no—
696D4—21no—
697D4—21no—
698D4—42no—
699D4—61no—
700D4—61no—
701D4—61no—
702D4—61no—
703D4—122no—
704D4—122no—
705D4—122no—
706D4—122no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4C3×D3×D411yescharacteristic
724C2×C4C23×C3×D311yescharacteristic
725C8—21no—
726C8—21no—
727C8—61no—
728C8—61no—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—42no—
735C2×C3—81no—
736C2×C3—81no—
737C2×C3—161no—
738C2×C3—241no—
739C2×C3—241no—
740C2×C3#559711yescharacteristic
741C2×C3C2×#91411yescharacteristic
742C2×C3D3×#13511yescharacteristic
743C2×C3C3×#53711yescharacteristic
744C2×C3C2×C3×#13511yescharacteristic
745C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
746D3—81no—
747D3—81no—
748C22—21no—
749C22—21no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22C3×#91412yes—
760C22C2×C3×D3×D411yescharacteristic
761C4—21no—
762C4—32no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—61no—
767C4—61no—
768C4—61no—
769C4—121no—
770C4—121no—
771C4C3×#100411yescharacteristic
772C4C3×#101011yescharacteristic
773C3—21no—
774C3#8064111yescharacteristic, direct product factor
775C3C3×#324711yescharacteristic, complemented
776C2—22no—
777C2—81no—
778C2—241no—
779C2—241no—
780C2C3×#559711yescharacteristic
781C2C2×C3×#91411yescharacteristic
782C2C3×D3×#13511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#465C2
socleC22×C32C22×D4
hypercenterC3×#465D3
hypocenterC3C3×#3247
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#465

Complements

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

NH ≅ G/Ntype
1. C3×#5624C2semidirect
2. C3×#5596C2semidirect
3. C32×#465C2semidirect
4. C3×#5165C2semidirect
5. C3×#5163C2semidirect
6. C3×#5115C2semidirect
7. C2×C3×Dic3⋊C8C2semidirect
8. C3×#5048C2semidirect
9. C3×#5038C2semidirect
10. C3×#4871C2semidirect
11. C3×#4870C2semidirect
12. C3×#4819C2semidirect
13. C3×#4793C2semidirect
14. C3×#4786C2semidirect
15. C3×#4766C2semidirect
17. #80641C3direct (N × H)
63. #5624C2×C3semidirect
64. #5596C2×C3semidirect
73. C3×#465D3semidirect
74. C3×#465C2×C3semidirect
80. #5165C2×C3semidirect
81. #5163C2×C3semidirect
82. #5115C2×C3semidirect
83. C2×Dic3⋊C8C2×C3semidirect
84. #5048C2×C3semidirect
85. #5038C2×C3semidirect
86. #4871C2×C3semidirect
87. #4870C2×C3semidirect
88. #4819C2×C3semidirect
89. #4793C2×C3semidirect
90. #4786C2×C3semidirect
91. #4766C2×C3semidirect
285. #465C3×D3semidirect
688. C32#3247semidirect
774. C3#80641direct (N × H)
775. C3C3×#3247semidirect

Maximal subgroups

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

subgroupindex
C3×#56242
C3×#55962
C32×#4652
C3×#51652
C3×#51632
C3×#51152
C2×C3×Dic3⋊C82
C3×#50482
C3×#50382
C3×#48712
C3×#48702
C3×#48192
C3×#47932
C3×#47862
C3×#47662
C3×#32473
#806413