Finite Group Databasebeta

← #10956158

Subgroups — #10956158

Order 768.

2442 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5523C211yesmaximal, characteristic
2C3×#2296C211yesmaximal, characteristic, complemented
3#82270C211yesmaximal, characteristic
4#82233C211yesmaximal, characteristic, complemented
5#82223C211yesmaximal, characteristic, complemented
6#82070C211yesmaximal, characteristic
7C2×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
8#76201C212yesmaximal, complemented
9#76200C212yesmaximal, complemented
10#75980C212yesmaximal, complemented
11#75979C212yesmaximal, complemented
12#74383C214yesmaximal, complemented
13#74377C214yesmaximal, complemented
14#73645C212yesmaximal, complemented
15#73643C212yesmaximal, complemented
16#73640C212yesmaximal, complemented
17#73638C212yesmaximal, complemented
18#34252—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C2×C3×#117C2211yescharacteristic
21C2×C3×#117C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
23C2×#926C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×C4×Dic3C2212yes—
27#5523C4116yescomplemented
28C2×#892C2214yes—
29C2×#892C2212yes—
30C2×D3×C4⋊C4C2212yes—
31C2×#67⋊C4C2214yes—
32C2×C4×D12C2212yes—
33C2×C4×Dic6C2212yes—
34C3×#389C2211yescharacteristic
35C3×#389C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C3×#389C2211yescharacteristic
38C3×#385C2212yes—
39C3×#385C2212yes—
40C3×C4×C4⋊C4C2212yes—
41C3×C4×C4⋊C4C2212yes—
42#5213C2212yes—
43#5213C2212yes—
44C2×C3⋊#95C2212yes—
45#4990C2214yes—
46#4990C2214yes—
47#4987C2212yes—
48#4987C2212yes—
49#4987C2214yes—
50#4984C2212yes—
51#4984C2212yes—
52#4978C2214yes—
53#4978C2214yes—
54#4977C2214yes—
55Dic3×C4⋊C4C2212yes—
56Dic3×C4⋊C4C2212yes—
57Dic3×C4⋊C4C2214yes—
58#4958C2214yes—
59#4950C2214yes—
60Dic3×C22⋊C4C2214yes—
61#4939C2212yes—
62#4939C2211yescharacteristic
63#4939C2211yescharacteristic
64C4×(C2×D3)⋊C4C2212yes—
65C4×(C2×D3)⋊C4C2212yes—
66#4936C2212yes—
67#4935C2212yes—
68C4×C4⋊Dic3C2212yes—
69C4×C4⋊Dic3C2212yes—
70C4×C4⋊Dic3C2212yes—
71C4×C4⋊Dic3C2212yes—
72C4×C4⋊Dic3C2212yes—
73C4×C4⋊Dic3C2212yes—
74#4929C2212yes—
75#4929C2211yescharacteristic
76#4929C2211yescharacteristic
77#4670C2214yes—
78#4670C2214yes—
79#4666C2214yes—
80#4664C2214yes—
81#4655C2214yes—
82#4655C2214yes—
83#4651C2214yes—
84#4648C2214yes—
85C2×#520—31no—
86#2357—32no—
87#2356—32no—
88#2355—32no—
89#2354—32no—
90#2347—32no—
91#2346—32no—
92#2345—32no—
93#2344—32no—
94#2318—34no—
95#2317—31no—
96#2311—31no—
97#2297—31no—
98#2296D311yescharacteristic, complemented
99#2290—34no—
100#2274—31no—
101C2×C4×C4⋊C4—31no—
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C22×#67C2312yes—
106C23×Dic3C2312yes—
107C23×Dic3C2312yes—
108C2×#235—24no—
109C2×#235—24no—
110C2×#235C2×C418yes—
111C22×D12C2311yescharacteristic
112C22×C4×D3C2312yes—
113C22×C4×D3C2314yes—
114C22×Dic6C2311yescharacteristic
115C3×#117—24no—
116C3×#117C2×C418yes—
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2312yes—
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C22⋊C4C2312yes—
126C2×C3×C22⋊C4C2312yes—
127C2×C3×C42—24no—
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2312yes—
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2311yescharacteristic
133C2×C3×C42C2312yes—
134C2×#217C2312yes—
135C2×(C2×D3)⋊C4C2312yes—
136C2×(C2×D3)⋊C4C2312yes—
137C2×(C2×D3)⋊C4C2312yes—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2314yes—
142#926—24no—
143C2×C4⋊Dic3—24no—
144C2×C4⋊Dic3C2×C418yes—
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2312yes—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2314yes—
150C2×C4⋊Dic3C2314yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2312yes—
153C2×Dic3⋊C4C2314yes—
154C2×C4×Dic3—44no—
155C2×C4×Dic3C2314yes—
156C2×C4×Dic3C2312yes—
157C2×C4×Dic3C2314yes—
158C2×C4×Dic3C2314yes—
159C2×C4×Dic3C2314yes—
160C2×C4×Dic3C2314yes—
161#892—48no—
162#892C2×C4116yescomplemented
163D3×C4⋊C4C2×C4116yescomplemented
164#67⋊C4C2×C4132yes—
165C4×D12C2×C4116yescomplemented
166C4×Dic6C2×C4116yescomplemented
167C3×#95C2312yes—
168C3×#95C2312yes—
169C3×#95C2312yes—
170C3×#95C2312yes—
171C3⋊#95C2312yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2312yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2312yes—
179C3⋊#95C2312yes—
180C3⋊#95C2314yes—
181C3⋊#95C2314yes—
182C3⋊#95C2314yes—
183C22×#41—31no—
184#520—316no—
185C2×C4×Q8—32no—
186C2×C4×D4—34no—
187C2×C4×D4—32no—
188C2×#117—31no—
189C2×#117—32no—
190C2×#117—34no—
191C2×#117C2×D311yescharacteristic
192C2×#117C2×D311yescharacteristic
193C22×C4⋊C4—31no—
194C22×C4⋊C4—32no—
195C22×C4⋊C4—31no—
196C22×C42—32no—
197C22×C42C2×D311yescharacteristic
198#391—32no—
199#391—31no—
200#391—31no—
201#390—32no—
202#390—31no—
203#390—31no—
204#389—32no—
205#389—32no—
206#389C2×D311yescharacteristic
207#389C2×D311yescharacteristic
208#389C2×D311yescharacteristic
209#389C2×D311yescharacteristic
210#388—34no—
211#388—34no—
212#388—34no—
213#388—34no—
214#387—34no—
215#387—34no—
216#387—34no—
217#387—34no—
218#386—32no—
219#386—32no—
220#386—34no—
221#385—34no—
222#385C2×D312yes—
223#385C2×D312yes—
224#384—32no—
225#383—34no—
226#382—34no—
227#382—32no—
228#381—34no—
229#380—32no—
230#380—32no—
231#380—34no—
232C4×C4⋊C4—32no—
233C4×C4⋊C4—32no—
234C4×C4⋊C4—34no—
235C4×C4⋊C4—32no—
236C4×C4⋊C4—32no—
237C4×C4⋊C4—32no—
238C4×C4⋊C4—32no—
239C4×C4⋊C4—32no—
240C4×C4⋊C4—32no—
241C4×C4⋊C4C2×D312yes—
242C4×C4⋊C4C2×D312yes—
243C4×C22⋊C4—34no—
244C4×C22⋊C4—32no—
245C4×C22⋊C4—32no—
246C4×C22⋊C4—34no—
247#376—34no—
248C2×#95—32no—
249C24×C3C2411yescharacteristic
250C23×D3C2412yes—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—41no—
256C22×C3×C4—41no—
257C22×C3×C4C22×C414yes—
258C22×C3×C4#4114yes—
259C22×C3×C4#4114yes—
260C22×C3×C4C2411yescharacteristic
261C22×C3×C4C2411yescharacteristic
262C22×C3×C4C2412yes—
263C22×C3×C4C2412yes—
264C22×C3×C4C2412yes—
265C22×C3×C4C2412yes—
266C22×C3×C4C2411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C22×C3×C4C2411yescharacteristic
270C2×#67—24no—
271C2×#67—24no—
272C2×#67C22×C418yes—
273C22×Dic3—24no—
274C22×Dic3—42no—
275C22×Dic3—42no—
276C22×Dic3—42no—
277C22×Dic3—42no—
278C22×Dic3C22×C418yes—
279C22×Dic3C2412yes—
280C22×Dic3C2414yes—
281C22×Dic3C2412yes—
282C22×Dic3C2412yes—
283C22×Dic3C2414yes—
284#235—232no—
285C2×D12—22no—
286C2×D12—22no—
287C2×D12C22×C414yes—
288C2×C4×D3—24no—
289C2×C4×D3—24no—
290C2×C4×D3—44no—
291C2×C4×D3—44no—
292C2×C4×D3C22×C418yes—
293C2×C4×D3C22×C4116yes—
294C2×Dic6—22no—
295C2×Dic6—22no—
296C2×Dic6C22×C414yes—
297C3×C4⋊C4—22no—
298C3×C4⋊C4—22no—
299C3×C4⋊C4—24no—
300C3×C4⋊C4—24no—
301C3×C4⋊C4—42no—
302C3×C4⋊C4—42no—
303C3×C4⋊C4C22×C414yes—
304C3×C4⋊C4C22×C414yes—
305C3×C22⋊C4—24no—
306C3×C22⋊C4C22×C418yes—
307C3×C42—22no—
308C3×C42—22no—
309C3×C42—22no—
310C3×C42—22no—
311C3×C42—24no—
312C3×C42C22×C418yes—
313#217—24no—
314(C2×D3)⋊C4—24no—
315(C2×D3)⋊C4—24no—
316(C2×D3)⋊C4—44no—
317(C2×D3)⋊C4—42no—
318(C2×D3)⋊C4—42no—
319(C2×D3)⋊C4—44no—
320(C2×D3)⋊C4C22×C4116yes—
321C4⋊Dic3—24no—
322C4⋊Dic3—24no—
323C4⋊Dic3—22no—
324C4⋊Dic3—22no—
325C4⋊Dic3—44no—
326C4⋊Dic3—44no—
327C4⋊Dic3C22×C418yes—
328C4⋊Dic3C22×C418yes—
329Dic3⋊C4C22×C4116yes—
330C4×Dic3—24no—
331C4×Dic3—28no—
332C4×Dic3—44no—
333C4×Dic3—44no—
334C4×Dic3—44no—
335C4×Dic3C22×C4116yes—
336C2×#41—38no—
337C2×#41—64no—
338C2×#41—64no—
339C22×Q8—31no—
340C22×D4—32no—
341C22×D4—31no—
342C23×C4—32no—
343C23×C4—32no—
344C23×C4—34no—
345C23×C4—32no—
346C23×C4C22×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348C23×C4C22×D311yescharacteristic
349C4×Q8—316no—
350C4×D4—332no—
351C4×D4—316no—
352#117—24no—
353#117—316no—
354#117—64no—
355#117—128no—
356#117C4×D318yes—
357C2×C4⋊C4—38no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—34no—
361C2×C4⋊C4—316no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4—32no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—34no—
367C2×C4⋊C4—34no—
368C2×C4⋊C4—64no—
369C2×C4⋊C4C22×D312yes—
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D312yes—
373C2×C4⋊C4C22×D312yes—
374C2×C4⋊C4C22×D312yes—
375C2×C4⋊C4C22×D311yescharacteristic
376C2×C4⋊C4C22×D311yescharacteristic
377C2×C22⋊C4—34no—
378C2×C22⋊C4—32no—
379C2×C22⋊C4—32no—
380C2×C22⋊C4—32no—
381C2×C22⋊C4—34no—
382C2×C22⋊C4—34no—
383C2×C22⋊C4—32no—
384C2×C22⋊C4—32no—
385C2×C22⋊C4C22×D312yes—
386C2×C22⋊C4C22×D312yes—
387C2×C42—24no—
388C2×C42—34no—
389C2×C42—34no—
390C2×C42—32no—
391C2×C42—34no—
392C2×C42—34no—
393C2×C42—34no—
394C2×C42—124no—
395C2×C42C22×D312yes—
396C2×C42C22×D311yescharacteristic
397C2×C42C22×D311yescharacteristic
398C2×C42C22×D311yescharacteristic
399C2×C42C22×D311yescharacteristic
400C2×C42C22×D312yes—
401#95—34no—
402#95—34no—
403#95—32no—
404#95—34no—
405#95—34no—
406#95—34no—
407#95—34no—
408#95—32no—
409#95—34no—
410#95—32no—
411#95—32no—
412#95—34no—
413#95C22×D312yes—
414#95C22×D312yes—
415#95C22×D312yes—
416#95C22×D312yes—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3C23×C412yes—
422C23×C3C2×#4112yes—
423C23×C3C2×#4112yes—
424C23×C3C2511yescharacteristic
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3C23×C414yes—
432C2×C3×C4—28no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—44no—
454C2×C3×C4#117116yescomplemented
455C2×C3×C4C23×C414yes—
456C2×C3×C4C23×C414yes—
457C2×C3×C4C23×C412yes—
458C2×C3×C4C23×C412yes—
459C2×C3×C4C2×#4112yes—
460C2×C3×C4C2×#4112yes—
461C2×C3×C4C2×#4112yes—
462C2×C3×C4C2×#4112yes—
463C2×C3×C4H(5,𝔽2)12yes—
464C2×C3×C42−1+412yes—
465#67—216no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—24no—
469C2×Dic3—24no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—24no—
473C2×Dic3—24no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—24no—
479C2×Dic3—48no—
480C2×Dic3—48no—
481C2×Dic3C23×C414yes—
482C2×Dic3C23×C418yes—
483D12—28no—
484C4×D3—216no—
485C4×D3—416no—
486Dic6—28no—
487C24—32no—
488C24C23×D311yescharacteristic
489#41—632no—
490C2×Q8—34no—
491C2×Q8—62no—
492C2×Q8—62no—
493C2×D4—38no—
494C2×D4—34no—
495C2×D4—64no—
496C2×D4—64no—
497C2×D4—62no—
498C2×D4—62no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—32no—
504C22×C4—34no—
505C22×C4—38no—
506C22×C4—38no—
507C22×C4—316no—
508C22×C4—32no—
509C22×C4—34no—
510C22×C4—32no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—64no—
514C22×C4—64no—
515C22×C4—64no—
516C22×C4—124no—
517C22×C4—124no—
518C22×C4—122no—
519C22×C4—122no—
520C22×C4—122no—
521C22×C4—122no—
522C22×C4C2×C4×D314yes—
523C22×C4#23714yes—
524C22×C4#23914yes—
525C22×C4C23×D311yescharacteristic
526C22×C4C23×D311yescharacteristic
527C22×C4C23×D312yes—
528C22×C4C23×D312yes—
529C22×C4C23×D312yes—
530C22×C4C23×D312yes—
531C22×C4C23×D311yescharacteristic
532C22×C4C23×D311yescharacteristic
533C22×C4C23×D311yescharacteristic
534C22×C4C23×D311yescharacteristic
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—38no—
540C4⋊C4—316no—
541C4⋊C4—38no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—64no—
545C4⋊C4—64no—
546C4⋊C4—62no—
547C4⋊C4—62no—
548C4⋊C4—124no—
549C4⋊C4—124no—
550C4⋊C4C2×C4×D314yes—
551C4⋊C4C2×C4×D314yes—
552C22⋊C4—24no—
553C22⋊C4—316no—
554C22⋊C4—64no—
555C22⋊C4—64no—
556C22⋊C4—64no—
557C22⋊C4—124no—
558C22⋊C4—124no—
559C22⋊C4—122no—
560C22⋊C4—122no—
561C22⋊C4C2×C4×D318yes—
562C42—22no—
563C42—22no—
564C42—22no—
565C42—22no—
566C42—24no—
567C42—316no—
568C42—64no—
569C42—68no—
570C42—124no—
571C42—124no—
572C42—124no—
573C42C2×C4×D318yes—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3C2×#11714yes—
581C22×C3C24×C411yescharacteristic
582C22×C3C22×#4111yescharacteristic
583C22×C3C22×#4111yescharacteristic
584C22×C3C2×H(5,𝔽2)11yescharacteristic
585C22×C3C2×2−1+411yescharacteristic
586C22×C3#58511yescharacteristic
587C22×C3#58511yescharacteristic
588C2×D3—24no—
589C2×D3—24no—
590C2×D3—24no—
591C2×D3—42no—
592C2×D3—42no—
593C2×D3—42no—
594C2×D3—42no—
595C3×C4—24no—
596C3×C4—24no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—42no—
600C3×C4—42no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4C2×#11714yes—
604C3×C4C2×#11714yes—
605Dic3—24no—
606Dic3—28no—
607Dic3—42no—
608Dic3—44no—
609Dic3—42no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—34no—
615C23—62no—
616C23—62no—
617C23—62no—
618C23—62no—
619C23—62no—
620C23—62no—
621C23C22×C4×D312yes—
622C23C2×#23712yes—
623C23C2×#23912yes—
624C23C24×D311yescharacteristic
625Q8—68no—
626D4—616no—
627D4—68no—
628C2×C4—28no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—34no—
650C2×C4—38no—
651C2×C4—44no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—64no—
655C2×C4—64no—
656C2×C4—616no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—64no—
660C2×C4—64no—
661C2×C4—62no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—64no—
666C2×C4—1216no—
667C2×C4—128no—
668C2×C4—128no—
669C2×C4#892116yescomplemented
670C2×C4C22×C4×D314yes—
671C2×C4C22×C4×D314yes—
672C2×C4C22×C4×D312yes—
673C2×C4C22×C4×D312yes—
674C2×C4C2×#23712yes—
675C2×C4C2×#23712yes—
676C2×C4C2×#23912yes—
677C2×C4C2×#23912yes—
678C2×C4#100912yes—
679C2×C4#101012yes—
680C2×C3—24no—
681C2×C3C22×#11711yescharacteristic
682C2×C3C4×H(5,𝔽2)11yescharacteristic
683C2×C3C4×2−1+411yescharacteristic
684C2×C3#349211yescharacteristic
685C2×C3#349311yescharacteristic
686C2×C3#350611yescharacteristic
687C2×C3#350711yescharacteristic
688D3—44no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—64no—
696C22—64no—
697C22—64no—
698C22—122no—
699C22—122no—
700C22—122no—
701C22—122no—
702C22C2×#89214yes—
703C22C23×C4×D311yescharacteristic
704C22C22×#23711yescharacteristic
705C22C22×#23911yescharacteristic
706C22C2×#100911yescharacteristic
707C22C2×#101011yescharacteristic
708C22#596411yescharacteristic
709C22#596411yescharacteristic
710C4—22no—
711C4—22no—
712C4—24no—
713C4—24no—
714C4—42no—
715C4—41no—
716C4—41no—
717C4—42no—
718C4—68no—
719C4—64no—
720C4—124no—
721C4—122no—
722C4—122no—
723C4C2×#89214yes—
724C4C2×#89214yes—
725C3#3425211yescharacteristic, complemented, Sylow
726C2—24no—
727C2—124no—
728C2C22×#89211yescharacteristic
729C2C4×#101011yescharacteristic
730C2C4×#100911yescharacteristic
731C2#8602411yescharacteristic
732C2#8602611yescharacteristic
733C2#8625911yescharacteristic
734C2#8626011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutatorC22×C3C24×C4
FittingC3×#2296C2
socle, cosocleC23×C3C25
prime radicalC22×#235C22
hypercenter#2296D3
hypocenterC3#34252
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2296

Complements

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

NH ≅ G/Ntype
2. C3×#2296C2semidirect
4. #82233C2semidirect
5. #82223C2semidirect
7. C2×C4×C4⋊Dic3C2semidirect
8. #76201C2semidirect
9. #76200C2semidirect
10. #75980C2semidirect
11. #75979C2semidirect
12. #74383C2semidirect
13. #74377C2semidirect
14. #73645C2semidirect
15. #73643C2semidirect
16. #73640C2semidirect
17. #73638C2semidirect
27. #5523C4semidirect
98. #2296D3semidirect
162. #892C2×C4semidirect
163. D3×C4⋊C4C2×C4semidirect
165. C4×D12C2×C4semidirect
166. C4×Dic6C2×C4semidirect
454. C2×C3×C4#117semidirect
669. C2×C4#892semidirect
725. C3#34252semidirect

Maximal subgroups

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

subgroupindex
C2×#55232
C3×#22962
#822702
#822332
#822232
#820702
C2×C4×C4⋊Dic32
#762012
#762002
#759802
#759792
#743832
#743772
#736452
#736432
#736402
#736382
#342523