Finite Group Databasebeta

← C3×#80640 #11882219

Subgroups — C3×#80640 #11882219

Order 1152.

846 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5622C211yesmaximal, characteristic, complemented
2C3×#5596C211yesmaximal, characteristic
3C32×#465C211yesmaximal, characteristic, complemented
4C3×#5163C211yesmaximal, characteristic, complemented
5C3×#5162C211yesmaximal, characteristic, complemented
6C3×#5114C211yesmaximal, characteristic, complemented
7C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
8C3×#5048C211yesmaximal, characteristic, complemented
9C3×#5041C211yesmaximal, characteristic, complemented
10C3×#4870C211yesmaximal, characteristic, complemented
11C3×#4854C211yesmaximal, characteristic, complemented
12C3×#4818C211yesmaximal, characteristic, complemented
13C3×#4791C211yesmaximal, characteristic, complemented
14C3×#4762C211yesmaximal, characteristic, complemented
15C3×#4761C211yesmaximal, characteristic, complemented
16C3×#3246—31nomaximal
17#80640C311yesmaximal, characteristic, direct product factor
18C2×C3×#237—21no—
19C2×C32×SD16C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C32×#121C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#940C2211yescharacteristic
27C3×#939—21no—
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C3×#930C2211yescharacteristic
31C3×#924C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34C2×C3×#204C2211yescharacteristic
35C3×#893C2211yescharacteristic
36C3×#889—21no—
37C3×#888C2211yescharacteristic
38C3×#888C2211yescharacteristic
39C3×#887—21no—
40C3×#887C2211yescharacteristic
41C3×#885—21no—
42C3×#67⋊C4—21no—
43C3×#878—21no—
44C3×#877—21no—
45C32×#106C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#533—31no—
62C3×#532—31no—
63#5622C2×C311yescharacteristic, complemented
64#5596C2×C311yescharacteristic
65C3×#476—31no—
66C3×#476—31no—
67C3×#475—31no—
68C3×#475—31no—
69C3×#465—21no—
70C3×#465—31no—
71C3×#465—31no—
72C3×#465—31no—
73C3×#465D311yescharacteristic, complemented
74C3×#465C2×C311yescharacteristic, complemented
75C3×#461—31no—
76C3×#461—31no—
77C3×#460—31no—
78C3×#460—31no—
79C2×C3×C4⋊C8—31no—
80#5163C2×C311yescharacteristic, complemented
81#5162C2×C311yescharacteristic, complemented
82#5114C2×C311yescharacteristic, complemented
83C2×Dic3⋊C8C2×C311yescharacteristic, complemented
84#5048C2×C311yescharacteristic, complemented
85#5041C2×C311yescharacteristic, complemented
86#4870C2×C311yescharacteristic, complemented
87#4854C2×C311yescharacteristic, complemented
88#4818C2×C311yescharacteristic, complemented
89#4791C2×C311yescharacteristic, complemented
90#4762C2×C311yescharacteristic, complemented
91#4761C2×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—
99C22×C3×Dic3—21no—
100C22×C3×Dic3D411yescharacteristic
101C22×C3×Dic3D411yescharacteristic
102C3×#237—44no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C32×SD16—41no—
109C2×C32×C8—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C22⋊C4—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#215—41no—
120C3×#214—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—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×#204—41no—
142#3246—31noSylow
143C2×C3×#41—61no—
144C2×#237—21no—
145C2×C3×SD16—21no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C2×C3×SD16—31no—
149C2×C3×SD16C2×D311yescharacteristic
150C2×C3×SD16C22×C311yescharacteristic
151C22×C3×C8—21no—
152C22×C3×C8—31no—
153C22×C3×C8C2×D311yescharacteristic
154C22×C3×C8C22×C311yescharacteristic
155C3×C4⋊Q8—31no—
156C3×C4⋊Q8—31no—
157C3×C4⋊Q8—31no—
158C3×#127—31no—
159C3×#125—61no—
160C3×#124—61no—
161C3×C22⋊Q8—21no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—61no—
164C3×C22⋊Q8C2×D311yescharacteristic
165C3×C22⋊Q8C22×C311yescharacteristic
166C3×#121—21no—
167C3×#121—31no—
168C3×#121—61no—
169C3×#121C2×D311yescharacteristic
170C3×#121C22×C311yescharacteristic
171C3×C4×Q8—31no—
172C3×C4×Q8—31no—
173C3×C4×Q8—61no—
174C3×C4×D4—31no—
175C3×C4×D4—31no—
176C3×C4×D4—61no—
177C3×#117—61no—
178C2×C3×C42—31no—
179Q8×Dic3C22×C311yescharacteristic
180#944C22×C311yescharacteristic
181C2×#215C22×C311yescharacteristic
182#940C22×C311yescharacteristic
183#939—21no—
184D4×Dic3C22×C311yescharacteristic
185C2×#214C22×C311yescharacteristic
186#930C22×C311yescharacteristic
187#924C22×C311yescharacteristic
188C2×C4×Dic3C22×C311yescharacteristic
189C22×C3⋊C8C22×C311yescharacteristic
190C2×#204C22×C311yescharacteristic
191#893C22×C311yescharacteristic
192#889—21no—
193#888C22×C311yescharacteristic
194#888C22×C311yescharacteristic
195#887—21no—
196#887C22×C311yescharacteristic
197#885—21no—
198#67⋊C4—21no—
199#878—21no—
200#877—21no—
201C3×#106—21no—
202C3×#106—31no—
203C3×#106—31no—
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×#103—31no—
214C3×#103—31no—
215C3×#103C2×D311yescharacteristic
216C3×#103C22×C311yescharacteristic
217C3×#102—21no—
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#817C22×C311yescharacteristic
227#816C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231Dic3⋊C8C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#809C22×C311yescharacteristic
234#808C22×C311yescharacteristic
235#808C22×C311yescharacteristic
236C23×C32—21no—
237C23×C32C2×D411yescharacteristic
238C22×C3×D3—21no—
239C32×Q8—21no—
240C32×Q8—21no—
241C32×D4—21no—
242C32×D4—21no—
243C32×D4—42no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C3×#67—42no—
252C3×#67—42no—
253C3×#67—42no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—41no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3SD1614yescomplemented
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6—42no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#533—31no—
276#532—31no—
277#476—31no—
278#476—31no—
279#475—31no—
280#475—31no—
281#465—31no—
282#465—31no—
283#465—31no—
284#465C3×D311yescharacteristic, complemented
285#461—31no—
286#461—31no—
287#460—31no—
288#460—31no—
289C2×C4⋊C8—31no—
290C3×#41—124no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×Q8—61no—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C23×C311yescharacteristic
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—41no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C23×C311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C23×C311yescharacteristic
314C2×#67—21no—
315C2×#67—21no—
316C2×#67—21no—
317C22×Dic3—21no—
318C22×Dic3C3×D411yescharacteristic
319C22×Dic3C3×D411yescharacteristic
320#237—44no—
321C2×D12C23×C311yescharacteristic
322C2×C4×D3—21no—
323C2×Dic6—21no—
324C2×Dic6—21no—
325C2×Dic6C23×C311yescharacteristic
326C3×SD16—41no—
327C3×SD16—41no—
328C3×SD16—42no—
329C3×SD16—121no—
330C3×SD16—121no—
331C3×SD16—121no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—41no—
337C2×C3×C8—41no—
338C2×C3×C8—42no—
339C2×C3×C8—121no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C23×C311yescharacteristic
343C2×C3×C8C23×C311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—41no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
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×C42—31no—
373C3×C42—31no—
374C3×C42—31no—
375C3×C42—31no—
376C3×C42—61no—
377C3×C42—61no—
378#217—21no—
379#217—21no—
380#215—41no—
381#214—41no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384C4⋊Dic3—21no—
385C4⋊Dic3C23×C311yescharacteristic
386C4⋊Dic3C23×C311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3C3×D411yescharacteristic
396C4×Dic3C3×D411yescharacteristic
397C4×Dic3C23×C311yescharacteristic
398C4×Dic3C23×C311yescharacteristic
399C2×C3⋊C8—41no—
400C2×C3⋊C8C23×C311yescharacteristic
401C2×C3⋊C8C23×C311yescharacteristic
402#204—41no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32C2×SD1612yes—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C32×C4—21no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4H(5,𝔽2)11yescharacteristic
418C32×C42−1+411yescharacteristic
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3C2×SD1612yes—
425C3×Dic3C2×SD1612yes—
426C2×#41—61no—
427C2×SD16—31no—
428C2×SD16—31no—
429C2×SD16—31no—
430C2×SD16C2×C3×D311yescharacteristic
431C22×C8—31no—
432C22×C8C2×C3×D311yescharacteristic
433C4⋊Q8—31no—
434C4⋊Q8—31no—
435C4⋊Q8—31no—
436#127—31no—
437#125—61no—
438#124—61no—
439C22⋊Q8—31no—
440C22⋊Q8—61no—
441C22⋊Q8C2×C3×D311yescharacteristic
442#121—31no—
443#121—61no—
444#121C2×C3×D311yescharacteristic
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—61no—
448C4×D4—31no—
449C4×D4—31no—
450C4×D4—61no—
451#117—61no—
452C2×C42—31no—
453#106—31no—
454#106—31no—
455#106—31no—
456#106C2×C3×D311yescharacteristic
457C4⋊C8—31no—
458C4⋊C8—31no—
459C4⋊C8—31no—
460C4⋊C8—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103C2×C3×D311yescharacteristic
465#102—31no—
466#102—31no—
467#102—31no—
468#102C2×C3×D311yescharacteristic
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—41no—
473C23×C3—61no—
474C23×C3D3×D411yescharacteristic
475C23×C3C2×C3×D411yescharacteristic
476C22×D3—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—122no—
486C3×Q8—122no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—42no—
494C3×D4—42no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—82no—
498C3×D4—122no—
499C3×D4—122no—
500C3×D4—122no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
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—34no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—122no—
527C2×C3×C4—122no—
528C2×C3×C4—121no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×C3×D411yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C24×C311yescharacteristic
533#67—42no—
534#67—42no—
535#67—42no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—41no—
540C2×Dic3—42no—
541C2×Dic3C3×SD1614yescomplemented
542C2×Dic3C2×C3×D411yescharacteristic
543C2×Dic3C2×C3×D411yescharacteristic
544C2×Dic3C2×C3×D411yescharacteristic
545C2×Dic3C2×C3×D411yescharacteristic
546D12—21no—
547D12—21no—
548C4×D3—42no—
549Dic6—21no—
550Dic6—21no—
551Dic6—42no—
552Dic6—42no—
553C3×C8—22no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C2×C32—22no—
564C2×C32—81no—
565C2×C32#53711yescharacteristic
566C2×C32C22×SD1611yescharacteristic
567C2×C32#57511yescharacteristic
568C3×D3—81no—
569#41—124no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×Q8—61no—
573C2×Q8C22×C3×D311yescharacteristic
574C2×D4—21no—
575C2×D4—31no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4C22×C3×D311yescharacteristic
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4C22×C3×D311yescharacteristic
585SD16—41no—
586SD16—121no—
587SD16—121no—
588SD16—121no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—41no—
592C2×C8—121no—
593C2×C8C22×C3×D311yescharacteristic
594C2×C8C22×C3×D311yescharacteristic
595C4⋊C4—21no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4C22×C3×D311yescharacteristic
606C4⋊C4C22×C3×D311yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C42—31no—
614C42—31no—
615C42—31no—
616C42—31no—
617C42—61no—
618C42—61no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3D3×SD1612yes—
640C22×C3C2×C3×SD1612yes—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C22×C3×D411yescharacteristic
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—32no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—81no—
662C3×C4—81no—
663C3×C4—81no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4#100411yescharacteristic
668C3×C4#101011yescharacteristic
669C3×C4C3×H(5,𝔽2)11yescharacteristic
670C3×C4C3×2−1+411yescharacteristic
671Dic3—21no—
672Dic3—21no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3C2×C3×SD1612yes—
677Dic3C2×C3×SD1612yes—
678C32#324611yescharacteristic, complemented, Sylow
679C23—21no—
680C23—61no—
681C23C3×D3×D411yescharacteristic
682Q8—21no—
683Q8—21no—
684Q8—61no—
685Q8—61no—
686Q8—122no—
687Q8—122no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—61no—
692D4—61no—
693D4—122no—
694D4—122no—
695D4—122no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—34no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—121no—
712C2×C4C3×D3×D411yescharacteristic
713C2×C4C23×C3×D311yescharacteristic
714C8—21no—
715C8—21no—
716C8—61no—
717C8—61no—
718C2×C3—22no—
719C2×C3—22no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—42no—
724C2×C3—81no—
725C2×C3—81no—
726C2×C3—161no—
727C2×C3—241no—
728C2×C3#559711yescharacteristic
729C2×C3C2×D3×SD1611yescharacteristic
730C2×C3#576811yescharacteristic
731C2×C3C3×#53711yescharacteristic
732C2×C3C22×C3×SD1611yescharacteristic
733C2×C3C3×#57511yescharacteristic
734D3—81no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22C3×D3×SD1612yes—
744C22C2×C3×D3×D411yescharacteristic
745C4—21no—
746C4—32no—
747C4—32no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—61no—
752C4—61no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4C3×#100411yescharacteristic
757C4C3×#101011yescharacteristic
758C3—21no—
759C3#8064011yescharacteristic, direct product factor
760C3C3×#324611yescharacteristic, complemented
761C2—22no—
762C2—81no—
763C2—241no—
764C2C3×#559711yescharacteristic
765C2C2×C3×D3×SD1611yescharacteristic
766C2C3×#576811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#465C2
socleC22×C32C22×D4
prime radicalC3×#5596C2
hypercenterC3×#465D3
hypocenterC3C3×#3246
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×#5622C2semidirect
3. C32×#465C2semidirect
4. C3×#5163C2semidirect
5. C3×#5162C2semidirect
6. C3×#5114C2semidirect
7. C2×C3×Dic3⋊C8C2semidirect
8. C3×#5048C2semidirect
9. C3×#5041C2semidirect
10. C3×#4870C2semidirect
11. C3×#4854C2semidirect
12. C3×#4818C2semidirect
13. C3×#4791C2semidirect
14. C3×#4762C2semidirect
15. C3×#4761C2semidirect
17. #80640C3direct (N × H)
63. #5622C2×C3semidirect
73. C3×#465D3semidirect
74. C3×#465C2×C3semidirect
80. #5163C2×C3semidirect
81. #5162C2×C3semidirect
82. #5114C2×C3semidirect
83. C2×Dic3⋊C8C2×C3semidirect
84. #5048C2×C3semidirect
85. #5041C2×C3semidirect
86. #4870C2×C3semidirect
87. #4854C2×C3semidirect
88. #4818C2×C3semidirect
89. #4791C2×C3semidirect
90. #4762C2×C3semidirect
91. #4761C2×C3semidirect
259. C2×C3×Dic3SD16semidirect
284. #465C3×D3semidirect
541. C2×Dic3C3×SD16semidirect
678. C32#3246semidirect
759. C3#80640direct (N × H)
760. C3C3×#3246semidirect

Maximal subgroups

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

subgroupindex
C3×#56222
C3×#55962
C32×#4652
C3×#51632
C3×#51622
C3×#51142
C2×C3×Dic3⋊C82
C3×#50482
C3×#50412
C3×#48702
C3×#48542
C3×#48182
C3×#47912
C3×#47622
C3×#47612
C3×#32463
#806403