Finite Group Databasebeta

← C3×#79752 #11895928

Subgroups — C3×#79752 #11895928

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5569C211yesmaximal, characteristic, complemented
2C3×#5553C211yesmaximal, characteristic
3C32×#440C211yesmaximal, characteristic, complemented
4C3×#5163C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic, complemented
6C3×#5027C211yesmaximal, characteristic, complemented
7C3×#5009C211yesmaximal, characteristic, complemented
8C3×#4891C211yesmaximal, characteristic, complemented
9C3×#4890C211yesmaximal, characteristic, complemented
10C3×#4817C211yesmaximal, characteristic, complemented
11C3×#4788C211yesmaximal, characteristic, complemented
12C3×#4764C211yesmaximal, characteristic, complemented
13C3×#4760C211yesmaximal, characteristic, complemented
14C3×#4713C211yesmaximal, characteristic, complemented
15C3×#4701C211yesmaximal, characteristic, complemented
16C3×#3368—31nomaximal
17#79752C311yesmaximal, characteristic, direct product factor
18C2×C3×#235—21no—
19C2×C32×SD16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#940C2211yescharacteristic
27C3×#940C2211yescharacteristic
28C3×#930—21no—
29C3×#893C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×#890—21no—
32C3×#890C2211yescharacteristic
33C3×#888—21no—
34C3×#888C2211yescharacteristic
35C3×#884—21no—
36C3×#884—21no—
37C3×#874C2211yescharacteristic
38C3×#870—21no—
39C3×#870C2211yescharacteristic
40C3×C4×Dic6—21no—
41C3×C4×Dic6C2211yescharacteristic
42C32×#107C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#97C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#557—31no—
62C3×#550—31no—
63#5569C2×C311yescharacteristic, complemented
64#5553C2×C311yescharacteristic
65C3×#490—31no—
66C3×#490—31no—
67C3×#486—31no—
68C3×#478—31no—
69C3×#478—31no—
70C3×#474—31no—
71C3×#460—31no—
72C3×#460—31no—
73C3×#460—31no—
74C3×#446—31no—
75C3×#440—21no—
76C3×#440—31no—
77C3×#440D311yescharacteristic, complemented
78C3×#440C2×C311yescharacteristic, complemented
79C3×C4×SD16—31no—
80#5163C2×C311yescharacteristic, complemented
81#5163C2×C311yescharacteristic, complemented
82#5027C2×C311yescharacteristic, complemented
83#5009C2×C311yescharacteristic, complemented
84#4891C2×C311yescharacteristic, complemented
85#4890C2×C311yescharacteristic, complemented
86#4817C2×C311yescharacteristic, complemented
87#4788C2×C311yescharacteristic, complemented
88#4764C2×C311yescharacteristic, complemented
89#4760C2×C311yescharacteristic, complemented
90#4713C2×C311yescharacteristic, complemented
91#4701C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C3×#235—44no—
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6D411yescharacteristic
108C32×SD16—22no—
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C42—21no—
116C32×C42C2311yescharacteristic
117C3×#215—22no—
118C3×#215—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3368—31noSylow
140C2×C3×#41—61no—
141C2×#235—21no—
142C2×C3×SD16—21no—
143C2×C3×SD16—31no—
144C2×C3×SD16—31no—
145C2×C3×SD16C2×D311yescharacteristic
146C2×C3×SD16C22×C311yescharacteristic
147C3×C4⋊Q8—31no—
148C3×C4⋊Q8—61no—
149C3×#127—31no—
150C3×#127—31no—
151C3×#127—31no—
152C3×#125—31no—
153C3×#125—31no—
154C3×#125—61no—
155C3×#125—61no—
156C3×#121—61no—
157C3×#121—61no—
158C3×#121—61no—
159C3×C4×Q8—21no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—61no—
164C3×C4×Q8C2×D311yescharacteristic
165C3×C4×Q8C22×C311yescharacteristic
166C3×C4×D4—21no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4C2×D311yescharacteristic
170C3×C4×D4C22×C311yescharacteristic
171Q8×Dic3C22×C311yescharacteristic
172Q8×Dic3C22×C311yescharacteristic
173C2×#215C22×C311yescharacteristic
174C2×#215C22×C311yescharacteristic
175#940C22×C311yescharacteristic
176#940C22×C311yescharacteristic
177#930—21no—
178#893C22×C311yescharacteristic
179#893C22×C311yescharacteristic
180#890—21no—
181#890C22×C311yescharacteristic
182#888—21no—
183#888C22×C311yescharacteristic
184#884—21no—
185#884—21no—
186#874C22×C311yescharacteristic
187#870—21no—
188#870C22×C311yescharacteristic
189C4×Dic6—21no—
190C4×Dic6C22×C311yescharacteristic
191C3×#107—21no—
192C3×#107—31no—
193C3×#107C2×D311yescharacteristic
194C3×#107C22×C311yescharacteristic
195C3×#106—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×C4⋊C8—31no—
199C3×#103—21no—
200C3×#103C2×D311yescharacteristic
201C3×#103C22×C311yescharacteristic
202C3×#102—21no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×#97—21no—
214C3×#97—31no—
215C3×#97C2×D311yescharacteristic
216C3×#97C22×C311yescharacteristic
217C3×C4×C8—31no—
218#832C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#821C22×C311yescharacteristic
221#821C22×C311yescharacteristic
222#821C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224#815C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227C8×Dic3C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#808C22×C311yescharacteristic
231#807C22×C311yescharacteristic
232C4⋊(C3⋊C8)C22×C311yescharacteristic
233C23×C32—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C32×Q8—21no—
237C32×Q8#4112yescomplemented
238C32×D4—21no—
239C32×D4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—42no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C3×#67—42no—
248C3×#67—42no—
249C3×#67—81no—
250C3×#67—81no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—42no—
262C3×D12—81no—
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×Dic6—22no—
266C3×Dic6—42no—
267C32×C8—21no—
268C32×C8—21no—
269C3×C3⋊C8—21no—
270C3×C3⋊C8—21no—
271#557—31no—
272#550—31no—
273#490—31no—
274#490—31no—
275#486—31no—
276#478—31no—
277#478—31no—
278#474—31no—
279#460—31no—
280#460—31no—
281#460—31no—
282#446—31no—
283#440—31no—
284#440C3×D311yescharacteristic, complemented
285C4×SD16—31no—
286C3×#41—124no—
287C2×C3×Q8—21no—
288C2×C3×Q8—31no—
289C2×C3×Q8—61no—
290C2×C3×Q8C22×D311yescharacteristic
291C2×C3×Q8C23×C311yescharacteristic
292C2×C3×D4—21no—
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C23×C311yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—41no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—21no—
309C2×#67—21no—
310C2×#67—21no—
311C2×#67—21no—
312#235—44no—
313C2×D12—21no—
314C2×D12—21no—
315C2×D12C23×C311yescharacteristic
316C2×D12C23×C311yescharacteristic
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×Dic6—21no—
320C2×Dic6C3×D411yescharacteristic
321C3×SD16—24no—
322C3×SD16—22no—
323C3×SD16—22no—
324C3×SD16—62no—
325C3×SD16—62no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C23×C311yescharacteristic
333C2×C3×C8C23×C311yescharacteristic
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—41no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C23×C311yescharacteristic
354C3×C4⋊C4C23×C311yescharacteristic
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—41no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C42—21no—
361C3×C42—21no—
362C3×C42—21no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—41no—
366C3×C42—61no—
367C3×C42—61no—
368C3×C42C22×D311yescharacteristic
369C3×C42C23×C311yescharacteristic
370#215—22no—
371#215—22no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374C4⋊Dic3—21no—
375C4⋊Dic3—21no—
376C4⋊Dic3—21no—
377C4⋊Dic3C3×D411yescharacteristic
378C4⋊Dic3C23×C311yescharacteristic
379C4⋊Dic3C23×C311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4C3×D411yescharacteristic
385Dic3⋊C4C3×D411yescharacteristic
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3C23×C311yescharacteristic
389C4×Dic3C23×C311yescharacteristic
390C2×C3⋊C8C23×C311yescharacteristic
391C2×C3⋊C8C23×C311yescharacteristic
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32C22×D411yescharacteristic
396C2×C3×D3—41no—
397C2×C3×D3—41no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C2×C3×D3—41no—
402C32×C4—22no—
403C32×C4—21no—
404C32×C4—21no—
405C32×C4—41no—
406C32×C4—41no—
407C32×C4C2×#4111yescharacteristic
408C32×C42−1+411yescharacteristic
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C3×Dic3AGL(1,ℤ/8)12yes—
415C2×#41—61no—
416C2×SD16—31no—
417C2×SD16—31no—
418C2×SD16C2×C3×D311yescharacteristic
419C4⋊Q8—31no—
420C4⋊Q8—61no—
421#127—31no—
422#127—31no—
423#127—31no—
424#125—31no—
425#125—31no—
426#125—61no—
427#125—61no—
428#121—61no—
429#121—61no—
430#121—61no—
431C4×Q8—31no—
432C4×Q8—31no—
433C4×Q8—31no—
434C4×Q8—61no—
435C4×Q8C2×C3×D311yescharacteristic
436C4×D4—31no—
437C4×D4—31no—
438C4×D4C2×C3×D311yescharacteristic
439#107—31no—
440#107C2×C3×D311yescharacteristic
441#106—31no—
442C4⋊C8—31no—
443C4⋊C8—31no—
444C4⋊C8—31no—
445#103C2×C3×D311yescharacteristic
446#102—31no—
447#102—31no—
448#102—31no—
449#102—31no—
450#102—31no—
451#102—31no—
452#102—31no—
453#102—31no—
454#102C2×C3×D311yescharacteristic
455#97—31no—
456#97C2×C3×D311yescharacteristic
457C4×C8—31no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—41no—
461C23×C3—61no—
462C23×C3—61no—
463C22×D3—21no—
464C22×D3—21no—
465C3×Q8—21no—
466C3×Q8—21no—
467C3×Q8—22no—
468C3×Q8—41no—
469C3×Q8—62no—
470C3×Q8—122no—
471C3×Q8#23512yescomplemented
472C3×Q8C3×#4112yescomplemented
473C3×D4—22no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—41no—
479C3×D4—61no—
480C3×D4—61no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—122no—
484C3×D4—122no—
485C3×D4—122no—
486C3×D4—241no—
487C3×D4—241no—
488C3×D4—241no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—42no—
506C2×C3×C4—42no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—82no—
510C2×C3×C4—122no—
511C2×C3×C4—122no—
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C2×C3×D411yescharacteristic
515C2×C3×C4C2×C3×D411yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C24×C311yescharacteristic
518#67—42no—
519#67—42no—
520#67—81no—
521#67—81no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3C2×C3×D411yescharacteristic
525C2×Dic3C2×C3×D411yescharacteristic
526C2×Dic3C2×C3×D411yescharacteristic
527C2×Dic3C2×C3×D411yescharacteristic
528D12—21no—
529D12—21no—
530D12—21no—
531D12—21no—
532D12—42no—
533D12—81no—
534C4×D3—42no—
535C4×D3—42no—
536Dic6—22no—
537Dic6—42no—
538C3×C8—22no—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—21no—
543C3×C8—41no—
544C3×C8—61no—
545C3×C8—61no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C2×C32—81no—
549C2×C32#54811yescharacteristic
550C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
551C2×C32#57711yescharacteristic
552C3×D3—81no—
553C3×D3—81no—
554#41—124no—
555C2×Q8—31no—
556C2×Q8—61no—
557C2×Q8C22×C3×D311yescharacteristic
558C2×D4—31no—
559C2×D4—31no—
560C2×D4—61no—
561C2×D4—61no—
562C2×D4—61no—
563C2×D4—61no—
564C2×D4—61no—
565C2×D4—61no—
566C2×D4C22×C3×D311yescharacteristic
567C22×C4—21no—
568C22×C4—61no—
569C22×C4—61no—
570SD16—22no—
571SD16—62no—
572SD16—62no—
573C2×C8—31no—
574C2×C8—31no—
575C2×C8C22×C3×D311yescharacteristic
576C2×C8C22×C3×D311yescharacteristic
577C4⋊C4—21no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4C22×C3×D311yescharacteristic
591C4⋊C4C22×C3×D311yescharacteristic
592C22⋊C4—21no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C42—21no—
596C42—31no—
597C42—31no—
598C42—61no—
599C42—61no—
600C42C22×C3×D311yescharacteristic
601C22×C3—21no—
602C22×C3—42no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3C2×D3×D411yescharacteristic
618C22×C3C22×C3×D411yescharacteristic
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—41no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—41no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—32no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—42no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—81no—
645C3×C4—81no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4C2×#23511yescharacteristic
649C3×C4#101011yescharacteristic
650C3×C4C2×C3×#4111yescharacteristic
651C3×C4C3×2−1+411yescharacteristic
652Dic3—21no—
653Dic3—21no—
654Dic3—21no—
655Dic3—41no—
656Dic3—41no—
657Dic3C3×AGL(1,ℤ/8)12yes—
658C32#336811yescharacteristic, complemented, Sylow
659C23—21no—
660C23—61no—
661C23—61no—
662Q8—21no—
663Q8—62no—
664Q8—122no—
665Q8C3×#23512yescomplemented
666D4—21no—
667D4—21no—
668D4—61no—
669D4—61no—
670D4—61no—
671D4—61no—
672D4—122no—
673D4—122no—
674D4—122no—
675D4—241no—
676D4—241no—
677D4—241no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—42no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—122no—
689C2×C4—122no—
690C2×C4C3×D3×D411yescharacteristic
691C2×C4C3×D3×D411yescharacteristic
692C2×C4C23×C3×D311yescharacteristic
693C8—21no—
694C8—21no—
695C8—61no—
696C8—61no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—82no—
701C2×C3—81no—
702C2×C3—81no—
703C2×C3—241no—
704C2×C3—241no—
705C2×C3#555211yescharacteristic
706C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
707C2×C3#577811yescharacteristic
708C2×C3C3×#54811yescharacteristic
709C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
710C2×C3C3×#57711yescharacteristic
711D3—81no—
712D3—81no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—121no—
717C22—121no—
718C22—121no—
719C22—121no—
720C22—121no—
721C22—121no—
722C22C2×C3×D3×D411yescharacteristic
723C4—21no—
724C4—21no—
725C4—22no—
726C4—32no—
727C4—41no—
728C4—41no—
729C4—61no—
730C4—61no—
731C4—61no—
732C4—121no—
733C4—121no—
734C4C2×C3×#23511yescharacteristic
735C4C3×#101011yescharacteristic
736C3—21no—
737C3#7975211yescharacteristic, direct product factor
738C3C3×#336811yescharacteristic, complemented
739C2—81no—
740C2—241no—
741C2—241no—
742C2C3×#555211yescharacteristic
743C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
744C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC3×#5553C2
hypercenterC3×#440D3
hypocenterC3C3×#3368
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
1. C3×#5569C2semidirect
3. C32×#440C2semidirect
4. C3×#5163C2semidirect
5. C3×#5163C2semidirect
6. C3×#5027C2semidirect
7. C3×#5009C2semidirect
8. C3×#4891C2semidirect
9. C3×#4890C2semidirect
10. C3×#4817C2semidirect
11. C3×#4788C2semidirect
12. C3×#4764C2semidirect
13. C3×#4760C2semidirect
14. C3×#4713C2semidirect
15. C3×#4701C2semidirect
17. #79752C3direct (N × H)
63. #5569C2×C3semidirect
77. C3×#440D3semidirect
78. C3×#440C2×C3semidirect
80. #5163C2×C3semidirect
81. #5163C2×C3semidirect
82. #5027C2×C3semidirect
83. #5009C2×C3semidirect
84. #4891C2×C3semidirect
85. #4890C2×C3semidirect
86. #4817C2×C3semidirect
87. #4788C2×C3semidirect
88. #4764C2×C3semidirect
89. #4760C2×C3semidirect
90. #4713C2×C3semidirect
91. #4701C2×C3semidirect
237. C32×Q8#41semidirect
284. #440C3×D3semidirect
471. C3×Q8#235semidirect
472. C3×Q8C3×#41semidirect
658. C32#3368semidirect
665. Q8C3×#235semidirect
737. C3#79752direct (N × H)
738. C3C3×#3368semidirect

Maximal subgroups

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

subgroupindex
C3×#55692
C3×#55532
C32×#4402
C3×#51632
C3×#50272
C3×#50092
C3×#48912
C3×#48902
C3×#48172
C3×#47882
C3×#47642
C3×#47602
C3×#47132
C3×#47012
C3×#33683
#797523