Finite Group Databasebeta

← C3×#80671 #11887184

Subgroups — C3×#80671 #11887184

Order 1152.

878 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5639C211yesmaximal, characteristic, complemented
2C3×#5612C211yesmaximal, characteristic
3C32×#465C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic, complemented
5C3×#5166C211yesmaximal, characteristic, complemented
6C3×#5113C211yesmaximal, characteristic, complemented
7C3×C8×#67C211yesmaximal, characteristic, complemented
8C3×#5047C211yesmaximal, characteristic, complemented
9C3×#5035C211yesmaximal, characteristic, complemented
10C3×#4871C211yesmaximal, characteristic, complemented
11C3×#4862C211yesmaximal, characteristic, complemented
12C3×#4813C211yesmaximal, characteristic, complemented
13C3×#4788C211yesmaximal, characteristic, complemented
14C3×D3×#102C211yesmaximal, characteristic, complemented
15C3×#4768C211yesmaximal, characteristic, complemented
16C3×#3296—31nomaximal
17#80671C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic, complemented
22C32×C22⋊Q8C2211yescharacteristic, complemented
23C32×#121C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#938—21no—
29C3×#937—21no—
30C3×#936C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C3×#926C2211yescharacteristic, complemented
33C2×C3×D3×C8C2211yescharacteristic
34C3×#897C2211yescharacteristic
35C3×#893C2211yescharacteristic
36C3×#892—21no—
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#890C2211yescharacteristic, complemented
39C3×#889—21no—
40C3×#883—21no—
41C3×#883—21no—
42C3×D3×C22⋊C4—21no—
43C3×#879—21no—
44C32×#106C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#830C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#816C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×C8×Dic3C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#552—31no—
62C3×#546—31no—
63#5639C2×C311yescharacteristic, complemented
64#5612C2×C311yescharacteristic
65C3×#488—31no—
66C3×#483—31no—
67C3×#482—31no—
68C3×#478—31no—
69C3×#467—31no—
70C3×#465—21no—
71C3×#465D311yescharacteristic, complemented
72C3×#465C2×C311yescharacteristic, complemented
73C3×#464—31no—
74C3×#452—31no—
75C3×#450—31no—
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#102—31no—
80#5169C2×C311yescharacteristic, complemented
81#5166C2×C311yescharacteristic, complemented
82#5113C2×C311yescharacteristic, complemented
83C8×#67C2×C311yescharacteristic, complemented
84#5047C2×C311yescharacteristic, complemented
85#5035C2×C311yescharacteristic, complemented
86#4871C2×C311yescharacteristic, complemented
87#4862C2×C311yescharacteristic, complemented
88#4813C2×C311yescharacteristic, complemented
89#4788C2×C311yescharacteristic, complemented
90D3×#102C2×C311yescharacteristic, complemented
91#4768C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C3×#235—22no—
103C3×#235—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C32×SD16—41no—
111C2×C32×C8—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C32×C22⋊C4—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217D411yescharacteristic
123C3×#216—41no—
124C3×#215—22no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3296—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×D3×D4C22×C311yescharacteristic
148C2×#235C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—21no—
151C2×C3×SD16—31no—
152C2×C3×SD16C2×D311yescharacteristic
153C2×C3×SD16C22×C311yescharacteristic
154C22×C3×C8—21no—
155C22×C3×C8—31no—
156C22×C3×C8C2×D311yescharacteristic, complemented
157C22×C3×C8C22×C311yescharacteristic, complemented
158C3×#126—61no—
159C3×#125—31no—
160C3×#125—61no—
161C3×#124—31no—
162C3×#123—61no—
163C3×#123—61no—
164C3×C22⋊Q8—21no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8C2×D311yescharacteristic, complemented
168C3×C22⋊Q8C22×C311yescharacteristic, complemented
169C3×#121—21no—
170C3×#121—61no—
171C3×#121C2×D311yescharacteristic
172C3×#121C22×C311yescharacteristic
173C3×#120—61no—
174C3×C4×Q8—31no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C3×#117—31no—
178C3×#117—61no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C22⋊C4—61no—
181#946C22×C311yescharacteristic
182Q8×Dic3C22×C311yescharacteristic, complemented
183C2×#216C22×C311yescharacteristic, complemented
184C2×#215C22×C311yescharacteristic
185#938—21no—
186#937—21no—
187#936C22×C311yescharacteristic
188C4×#67C22×C311yescharacteristic
189#926C22×C311yescharacteristic, complemented
190C2×D3×C8C22×C311yescharacteristic
191#897C22×C311yescharacteristic
192#893C22×C311yescharacteristic
193#892—21no—
194D3×C4⋊C4C22×C311yescharacteristic
195#890C22×C311yescharacteristic, complemented
196#889—21no—
197#883—21no—
198#883—21no—
199D3×C22⋊C4—21no—
200#879—21no—
201C3×#107—31no—
202C3×#106—21no—
203C3×#106—31no—
204C3×#106C2×D311yescharacteristic, complemented
205C3×#106C22×C311yescharacteristic, complemented
206C3×C4⋊C8—31no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103C2×D311yescharacteristic, complemented
212C3×#103C22×C311yescharacteristic, complemented
213C3×#102—21no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102C2×D311yescharacteristic
220C3×#102C22×C311yescharacteristic
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×C4×C8—31no—
224#832C22×C311yescharacteristic
225#832C22×C311yescharacteristic
226#830C22×C311yescharacteristic, complemented
227#821C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230#816C22×C311yescharacteristic, complemented
231#816C22×C311yescharacteristic, complemented
232Dic3⋊C8C22×C311yescharacteristic, complemented
233C8×Dic3C22×C311yescharacteristic, complemented
234#810C22×C311yescharacteristic, complemented
235#809C22×C311yescharacteristic
236#808C22×C311yescharacteristic, complemented
237#807C22×C311yescharacteristic, complemented
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—21no—
249C32×D4—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C3×#67—22no—
258C3×#67—42no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—31no—
281#488—31no—
282#483—31no—
283#482—31no—
284#478—31no—
285#467—31no—
286#465C3×D311yescharacteristic, complemented
287#464—31no—
288#452—31no—
289#450—31no—
290C4×SD16—31no—
291C8×D4—31no—
292#416—31no—
293C2×#102—31no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C23×C311yescharacteristic
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—41no—
308C2×C3×D4—61no—
309C2×C3×D4—62no—
310C2×C3×D4—61no—
311C2×C3×D4—121no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C23×C311yescharacteristic
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C23×C311yescharacteristic
321C2×#67—21no—
322C2×#67—21no—
323C2×#67C3×D411yescharacteristic
324D3×D4—22no—
325D3×D4—41no—
326#235—22no—
327#235—41no—
328C2×D12C23×C311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3C23×C311yescharacteristic
333C2×Dic6C23×C311yescharacteristic
334C3×Q16—121no—
335C3×SD16—41no—
336C3×SD16—41no—
337C3×SD16—42no—
338C3×SD16—62no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—41no—
344C2×C3×C8—41no—
345C2×C3×C8—42no—
346C2×C3×C8—121no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C23×C311yescharacteristic
350C2×C3×C8C23×C311yescharacteristic
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—41no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C23×C311yescharacteristic
368C3×C4⋊C4C23×C311yescharacteristic
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—41no—
376C3×C22⋊C4—41no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C42—31no—
384C3×C42—61no—
385C3×C42—61no—
386#217—21no—
387#217—21no—
388#217—21no—
389#217C3×D411yescharacteristic
390#216—41no—
391#215—22no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4C3×D411yescharacteristic
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3—21no—
399C4⋊Dic3C23×C311yescharacteristic
400C4⋊Dic3C23×C311yescharacteristic
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4C3×D411yescharacteristic
405C4×Dic3—21no—
406C4×Dic3—21no—
407C4×Dic3C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410D3×C8—41no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—84no—
424C2×C3×D3#13512yes—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—31no—
439C2×Q16—31no—
440C2×SD16—31no—
441C2×SD16C2×C3×D311yescharacteristic
442C22×C8—31no—
443C22×C8C2×C3×D311yescharacteristic, complemented
444#126—61no—
445#125—31no—
446#125—61no—
447#124—31no—
448#123—61no—
449#123—61no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8C2×C3×D311yescharacteristic, complemented
453#121—61no—
454#121C2×C3×D311yescharacteristic
455#120—61no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4—31no—
459#117—31no—
460#117—61no—
461C2×C4⋊C4—31no—
462C2×C22⋊C4—61no—
463#107—31no—
464#106—31no—
465#106C2×C3×D311yescharacteristic, complemented
466C4⋊C8—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103C2×C3×D311yescharacteristic, complemented
471#102—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102C2×C3×D311yescharacteristic
477C22⋊C8—31no—
478C22⋊C8—31no—
479C4×C8—31no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3—241no—
489C23×C3D3×D411yescharacteristic
490C23×C3C2×C3×D411yescharacteristic
491C22×D3—21no—
492C22×D3—42no—
493C22×D3—42no—
494C22×D3—81no—
495C22×D3C2×C3×D411yescharacteristic
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—41no—
501C3×Q8—41no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—32no—
509C3×D4—41no—
510C3×D4—41no—
511C3×D4—62no—
512C3×D4—61no—
513C3×D4—81no—
514C3×D4—81no—
515C3×D4—82no—
516C3×D4—122no—
517C3×D4—122no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—122no—
544C2×C3×C4—122no—
545C2×C3×C4—241no—
546C2×C3×C4D3×D411yescharacteristic
547C2×C3×C4C2×C3×D411yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C24×C311yescharacteristic
550#67—22no—
551#67—42no—
552#67—42no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3C2×C3×D411yescharacteristic
557C2×Dic3C2×C3×D411yescharacteristic
558C2×Dic3C2×C3×D411yescharacteristic
559D12—21no—
560D12C3×#4112yes—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—42no—
564C4×D3—42no—
565C4×D3—81no—
566Dic6—21no—
567Dic6—21no—
568C3×C8—22no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C2×C32—41no—
579C2×C32—81no—
580C2×C32#54611yescharacteristic
581C2×C32C2×#13511yescharacteristic
582C2×C32#57711yescharacteristic
583C3×D3—22no—
584C3×D3—42no—
585C24—61no—
586#41—62no—
587#41—121no—
588C2×Q8—31no—
589C2×Q8C22×C3×D311yescharacteristic
590C2×D4—21no—
591C2×D4—31no—
592C2×D4—31no—
593C2×D4—61no—
594C2×D4—62no—
595C2×D4—61no—
596C2×D4—121no—
597C2×D4C22×C3×D311yescharacteristic
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4C22×C3×D311yescharacteristic
603Q16—121no—
604SD16—41no—
605SD16—62no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—41no—
609C2×C8—121no—
610C2×C8C22×C3×D311yescharacteristic
611C2×C8C22×C3×D311yescharacteristic
612C4⋊C4—21no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4C22×C3×D311yescharacteristic
623C4⋊C4C22×C3×D311yescharacteristic
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—31no—
627C22⋊C4—31no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C42—31no—
635C42—61no—
636C42—61no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—32no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—62no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—244no—
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C22×C3×D411yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—22no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—84no—
671C2×D3C3×#13512yes—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—81no—
687C3×C4—81no—
688C3×C4—81no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4#100411yescharacteristic
693C3×C4D3×#4111yescharacteristic
694C3×C4C2×C3×#4111yescharacteristic
695C3×C4C3×H(5,𝔽2)11yescharacteristic
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702C32#329611yescharacteristic, complemented, Sylow
703C23—21no—
704C23—31no—
705C23—61no—
706C23—122no—
707C23—122no—
708C23—241no—
709C23C3×D3×D411yescharacteristic
710Q8—21no—
711Q8—21no—
712Q8—61no—
713Q8—61no—
714D4—21no—
715D4—21no—
716D4—32no—
717D4—62no—
718D4—61no—
719D4—81no—
720D4—122no—
721D4—122no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—241no—
738C2×C4C3×D3×D411yescharacteristic
739C2×C4C23×C3×D311yescharacteristic
740C8—21no—
741C8—21no—
742C8—61no—
743C8—61no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—41no—
749C2×C3—41no—
750C2×C3—62no—
751C2×C3—81no—
752C2×C3—81no—
753C2×C3—122no—
754C2×C3—161no—
755C2×C3#561011yescharacteristic
756C2×C3#576211yescharacteristic
757C2×C3D3×#13511yescharacteristic
758C2×C3C3×#54611yescharacteristic
759C2×C3C2×C3×#13511yescharacteristic
760C2×C3C3×#57711yescharacteristic
761D3—22no—
762D3—42no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—32no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—61no—
771C22—61no—
772C22—62no—
773C22—121no—
774C22—121no—
775C22—244no—
776C22C2×C3×D3×D411yescharacteristic
777C4—21no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—61no—
782C4—61no—
783C4—61no—
784C4—121no—
785C4—121no—
786C4—121no—
787C4C3×#100411yescharacteristic
788C4C3×D3×#4111yescharacteristic
789C3—21no—
790C3#8067111yescharacteristic, direct product factor
791C3C3×#329611yescharacteristic, complemented
792C2—41no—
793C2—62no—
794C2—81no—
795C2—122no—
796C2C3×#561011yescharacteristic
797C2C3×#576211yescharacteristic
798C2C3×D3×#13511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#465C2
socleC22×C32C22×D4
prime radicalC3×#5612C2
hypercenterC3×#465D3
hypocenterC3C3×#3296
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×#5639C2semidirect
3. C32×#465C2semidirect
4. C3×#5169C2semidirect
5. C3×#5166C2semidirect
6. C3×#5113C2semidirect
7. C3×C8×#67C2semidirect
8. C3×#5047C2semidirect
9. C3×#5035C2semidirect
10. C3×#4871C2semidirect
11. C3×#4862C2semidirect
12. C3×#4813C2semidirect
13. C3×#4788C2semidirect
14. C3×D3×#102C2semidirect
15. C3×#4768C2semidirect
17. #80671C3direct (N × H)
21. C22×C32×C8C22semidirect
22. C32×C22⋊Q8C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
32. C3×#926C22semidirect
38. C3×#890C22semidirect
44. C32×#106C22semidirect
45. C32×#103C22semidirect
49. C3×#830C22semidirect
53. C3×#816C22semidirect
54. C3×#816C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×C8×Dic3C22semidirect
57. C3×#810C22semidirect
59. C3×#808C22semidirect
60. C3×#807C22semidirect
63. #5639C2×C3semidirect
71. C3×#465D3semidirect
72. C3×#465C2×C3semidirect
80. #5169C2×C3semidirect
81. #5166C2×C3semidirect
82. #5113C2×C3semidirect
83. C8×#67C2×C3semidirect
84. #5047C2×C3semidirect
85. #5035C2×C3semidirect
86. #4871C2×C3semidirect
87. #4862C2×C3semidirect
88. #4813C2×C3semidirect
89. #4788C2×C3semidirect
90. D3×#102C2×C3semidirect
91. #4768C2×C3semidirect
156. C22×C3×C8C2×D3semidirect
157. C22×C3×C8C22×C3semidirect
167. C3×C22⋊Q8C2×D3semidirect
168. C3×C22⋊Q8C22×C3semidirect
182. Q8×Dic3C22×C3semidirect
183. C2×#216C22×C3semidirect
189. #926C22×C3semidirect
195. #890C22×C3semidirect
204. C3×#106C2×D3semidirect
205. C3×#106C22×C3semidirect
211. C3×#103C2×D3semidirect
212. C3×#103C22×C3semidirect
226. #830C22×C3semidirect
230. #816C22×C3semidirect
231. #816C22×C3semidirect
232. Dic3⋊C8C22×C3semidirect
233. C8×Dic3C22×C3semidirect
234. #810C22×C3semidirect
236. #808C22×C3semidirect
237. #807C22×C3semidirect
286. #465C3×D3semidirect
443. C22×C8C2×C3×D3semidirect
452. C22⋊Q8C2×C3×D3semidirect
465. #106C2×C3×D3semidirect
470. #103C2×C3×D3semidirect
702. C32#3296semidirect
790. C3#80671direct (N × H)
791. C3C3×#3296semidirect

Maximal subgroups

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

subgroupindex
C3×#56392
C3×#56122
C32×#4652
C3×#51692
C3×#51662
C3×#51132
C3×C8×#672
C3×#50472
C3×#50352
C3×#48712
C3×#48622
C3×#48132
C3×#47882
C3×D3×#1022
C3×#47682
C3×#32963
#806713