Finite Group Databasebeta

← #10992708

Subgroups — #10992708

Order 768.

1802 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×C42×D4C211yesmaximal, characteristic
2#82383C212yesmaximal
3#82372C212yesmaximal
4#82351C212yesmaximal
5#82076C211yesmaximal, characteristic, complemented
6#82076C211yesmaximal, characteristic, complemented
7#82062C211yesmaximal, characteristic, complemented
8#82062C211yesmaximal, characteristic, complemented
9#73696C212yesmaximal, complemented
10#73688C212yesmaximal, complemented
11#73659C212yesmaximal, complemented
12#73511C212yesmaximal, complemented
13#73510C212yesmaximal, complemented
14#73510C212yesmaximal, complemented
15#73483C212yesmaximal, complemented
16#73468C212yesmaximal, complemented
17#73460C212yesmaximal, complemented
18#73307C211yesmaximal, characteristic, complemented
19C4×#869C211yesmaximal, characteristic, complemented
20#36210—31nomaximal, Sylow
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic
26C2×#926C2212yes—
27C2×#926C2212yes—
28C2×#924C2212yes—
29C2×#924C2212yes—
30C2×#870C2212yes—
31C2×#869C2211yescharacteristic
32C2×C4×Dic6C2212yes—
33C3×C4×C4⋊C4C2211yescharacteristic
34C3×C4×C4⋊C4C2211yescharacteristic
35C3×C4×C4⋊C4C2211yescharacteristic
36C3×C4×C22⋊C4C2211yescharacteristic
37C3×C4×C22⋊C4C2211yescharacteristic
38C3×C4×C22⋊C4C2211yescharacteristic
39C3×C4×C22⋊C4C2211yescharacteristic
40C3×C4×C22⋊C4C2211yescharacteristic
41C3×C4×C22⋊C4C2211yescharacteristic
42C3×C43C2211yescharacteristic
43#5222C2214yes—
44#5212C2212yes—
45#5212C2212yes—
46#5212C2212yes—
47#5212C2212yes—
48#5212C2212yes—
49#5212C2212yes—
50#5212C2212yes—
51#5212C2212yes—
52#4985C2214yes—
53#4978C2214yes—
54#4976C2214yes—
55#4952C2214yes—
56#4952C2214yes—
57#4945C2214yes—
58#4945C2214yes—
59#4945C2214yes—
60#4944C2214yes—
61#4936C2212yes—
62#4936C2212yes—
63#4936C2212yes—
64#4935C2211yescharacteristic
65#4935C2211yescharacteristic
66#4935C2211yescharacteristic
67C4×C4⋊Dic3C2212yes—
68C4×C4⋊Dic3C2212yes—
69C4×C4⋊Dic3C2212yes—
70C4×C4⋊Dic3C2212yes—
71C4×C4⋊Dic3C2212yes—
72C4×C4⋊Dic3C2212yes—
73#4929C2212yes—
74#4929C2212yes—
75#4929C2212yes—
76#4928C2212yes—
77#4928C2212yes—
78#4928C2212yes—
79#4928C2212yes—
80#4928C2212yes—
81#4928C2212yes—
82#4928C2212yes—
83#4928C2212yes—
84#4928C2212yes—
85#4928C2212yes—
86C3⋊#401C2214yes—
87#4658C2214yes—
88#4652C2214yes—
89#4652C2214yes—
90#4651C2214yes—
91#4649C2214yes—
92#2859—31no—
93#2857—31no—
94#2857—31no—
95#2562—32no—
96#2514—32no—
97#2509—32no—
98#2495—32no—
99#2494—32no—
100#2494—32no—
101#2485—32no—
102#2421—32no—
103#2415—32no—
104#2370—32no—
105#2362—32no—
106#2347—32no—
107C4×C4⋊Q8—31no—
108#2285—31no—
109#2285—31no—
110C42×D4D311yescharacteristic
111C22×C3×D4C2311yescharacteristic
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2311yescharacteristic
117C23×C3×C4C2311yescharacteristic
118C22×Dic6C2312yes—
119C3×C4×D4—24no—
120C3×C4×D4—24no—
121C3×C4×D4—24no—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C22⋊C4C2311yescharacteristic
126C2×C3×C22⋊C4C2311yescharacteristic
127C2×C3×C22⋊C4C2311yescharacteristic
128C2×C3×C22⋊C4C2311yescharacteristic
129C2×C3×C22⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4C2311yescharacteristic
131C2×C3×C42—24no—
132C2×C3×C42—24no—
133C2×C3×C42C2311yescharacteristic
134C2×C3×C42C2311yescharacteristic
135C2×C3×C42C2311yescharacteristic
136C2×C3×C42C2311yescharacteristic
137C2×C3×C42C2311yescharacteristic
138C2×C3×C42C2311yescharacteristic
139C2×C3×C42C2311yescharacteristic
140C2×C3×C42C2311yescharacteristic
141C2×C3×C42C2311yescharacteristic
142C2×C3×C42C2311yescharacteristic
143C2×C3×C42C2311yescharacteristic
144C2×C3×C42C2311yescharacteristic
145C2×C3×C42C2311yescharacteristic
146C2×#217C2314yes—
147C2×#217C2314yes—
148C2×#217C2314yes—
149C2×#217C2314yes—
150#926—28no—
151#926—44no—
152C2×C4⋊Dic3C2312yes—
153C2×C4⋊Dic3C2312yes—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2312yes—
160C2×C4⋊Dic3C2312yes—
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2312yes—
163#924—28no—
164#924—44no—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×C4×Dic3C2314yes—
171C2×C4×Dic3C2314yes—
172C2×C4×Dic3C2314yes—
173#870—28no—
174#869—24no—
175C4×Dic6—44no—
176C3×#95C2311yescharacteristic
177C3×#95C2311yescharacteristic
178C3×#95C2311yescharacteristic
179C3×#95C2311yescharacteristic
180C3×#95C2311yescharacteristic
181C3×#95C2311yescharacteristic
182C3⋊#95C2314yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C2×C4⋊Q8—31no—
195C2×#125—32no—
196C2×C22⋊Q8—32no—
197C2×C22⋊Q8—32no—
198C2×C4×Q8—32no—
199C2×C4×D4C2×D311yescharacteristic
200C2×C4×D4C2×D311yescharacteristic
201C2×C4×D4C2×D311yescharacteristic
202C2×#117—32no—
203C2×#117—32no—
204C22×C42C2×D311yescharacteristic
205C22×C42C2×D311yescharacteristic
206#401—34no—
207#400—34no—
208#400—34no—
209#397—34no—
210#397—34no—
211#394—34no—
212#391—32no—
213#391—32no—
214#391—32no—
215#389—34no—
216#389—32no—
217#389—32no—
218#389—32no—
219#389—32no—
220#389—32no—
221#389—32no—
222#389—32no—
223#389—32no—
224#389—32no—
225#389—32no—
226#388—34no—
227#388—34no—
228#388—34no—
229#388—34no—
230#387—34no—
231#387—34no—
232#387—34no—
233#384—31no—
234#384—31no—
235#384—31no—
236#383—34no—
237#382—32no—
238#382—32no—
239#382—32no—
240#380—32no—
241#380—32no—
242#380—32no—
243#380—32no—
244#380—32no—
245#380—32no—
246#380—32no—
247#380—32no—
248C4×C4⋊C4—32no—
249C4×C4⋊C4—32no—
250C4×C4⋊C4—32no—
251C4×C4⋊C4—32no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4—32no—
254C4×C4⋊C4—34no—
255C4×C4⋊C4C2×D311yescharacteristic
256C4×C4⋊C4C2×D311yescharacteristic
257C4×C4⋊C4C2×D311yescharacteristic
258C4×C22⋊C4C2×D311yescharacteristic
259C4×C22⋊C4C2×D311yescharacteristic
260C4×C22⋊C4C2×D311yescharacteristic
261C4×C22⋊C4C2×D311yescharacteristic
262C4×C22⋊C4C2×D311yescharacteristic
263C4×C22⋊C4C2×D311yescharacteristic
264C43C2×D311yescharacteristic
265C24×C3C2411yescharacteristic
266C24×C3C2411yescharacteristic
267C2×C3×D4—22no—
268C2×C3×D4—22no—
269C2×C3×D4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4#4114yes—
287C22×C3×C4#4114yes—
288C22×C3×C4C2411yescharacteristic
289C22×C3×C4C2411yescharacteristic
290C22×C3×C4C2411yescharacteristic
291C22×C3×C4C2411yescharacteristic
292C22×C3×C4C2411yescharacteristic
293C22×C3×C4C2411yescharacteristic
294C22×C3×C4C2411yescharacteristic
295C22×C3×C4C2411yescharacteristic
296C22×C3×C4C2411yescharacteristic
297C22×C3×C4C2411yescharacteristic
298C22×C3×C4C2411yescharacteristic
299C22×C3×C4C2411yescharacteristic
300C22×C3×C4C2411yescharacteristic
301C22×Dic3C2414yes—
302C22×Dic3C2414yes—
303C22×Dic3C2414yes—
304C22×Dic3C2414yes—
305C2×Dic6—24no—
306C2×Dic6—24no—
307C2×Dic6—24no—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—22no—
310C3×C4⋊C4—22no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4—22no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—22no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—22no—
317C3×C42—22no—
318C3×C42—22no—
319C3×C42—22no—
320C3×C42—22no—
321C3×C42—22no—
322C3×C42—22no—
323C3×C42—22no—
324C3×C42—22no—
325C3×C42—22no—
326C3×C42—22no—
327C3×C42—22no—
328C3×C42#4114yes—
329C3×C42#4114yes—
330#217—28no—
331#217—28no—
332#217—44no—
333#217—44no—
334C4⋊Dic3—24no—
335C4⋊Dic3—24no—
336C4⋊Dic3—24no—
337C4⋊Dic3—24no—
338C4⋊Dic3—24no—
339C4⋊Dic3—24no—
340C4⋊Dic3—24no—
341C4⋊Dic3—24no—
342C4⋊Dic3—24no—
343C4⋊Dic3—24no—
344C4⋊Dic3—24no—
345Dic3⋊C4—28no—
346Dic3⋊C4—28no—
347Dic3⋊C4—28no—
348Dic3⋊C4—44no—
349Dic3⋊C4—44no—
350C4×Dic3—28no—
351C4×Dic3—44no—
352C4×Dic3—44no—
353C22×Q8—32no—
354C22×D4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C23×C4C22×D311yescharacteristic
357C23×C4C22×D311yescharacteristic
358C23×C4C22×D311yescharacteristic
359C23×C4C22×D311yescharacteristic
360C23×C4C22×D311yescharacteristic
361C4⋊Q8—64no—
362#125—68no—
363C22⋊Q8—68no—
364C22⋊Q8—124no—
365C4×Q8—124no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—24no—
369#117—68no—
370#117—124no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—34no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4—32no—
379C2×C4⋊C4—34no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4C22×D311yescharacteristic
388C2×C4⋊C4C22×D311yescharacteristic
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C22⋊C4—34no—
391C2×C22⋊C4—34no—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4C22×D311yescharacteristic
395C2×C22⋊C4C22×D311yescharacteristic
396C2×C22⋊C4C22×D311yescharacteristic
397C2×C22⋊C4C22×D311yescharacteristic
398C2×C22⋊C4C22×D311yescharacteristic
399C2×C22⋊C4C22×D311yescharacteristic
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—34no—
403C2×C42—34no—
404C2×C42—34no—
405C2×C42C22×D311yescharacteristic
406C2×C42C22×D311yescharacteristic
407C2×C42C22×D311yescharacteristic
408C2×C42C22×D311yescharacteristic
409C2×C42C22×D311yescharacteristic
410C2×C42C22×D311yescharacteristic
411C2×C42C22×D311yescharacteristic
412C2×C42C22×D311yescharacteristic
413C2×C42C22×D311yescharacteristic
414C2×C42C22×D311yescharacteristic
415C2×C42C22×D311yescharacteristic
416C2×C42C22×D311yescharacteristic
417C2×C42C22×D311yescharacteristic
418#95—34no—
419#95—34no—
420#95—34no—
421#95—34no—
422#95—34no—
423#95—34no—
424#95—34no—
425#95—34no—
426#95—34no—
427#95—34no—
428#95—34no—
429#95—34no—
430#95C22×D311yescharacteristic
431#95C22×D311yescharacteristic
432#95C22×D311yescharacteristic
433#95C22×D311yescharacteristic
434#95C22×D311yescharacteristic
435#95C22×D311yescharacteristic
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3C2×#4112yes—
449C23×C3C2×#4112yes—
450C23×C3C2511yescharacteristic
451C3×D4—28no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—28no—
461C2×C3×C4—28no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—44no—
481C2×C3×C4—44no—
482C2×C3×C4—44no—
483C2×C3×C4—44no—
484C2×C3×C4C2×#4112yes—
485C2×C3×C4C2×#4112yes—
486C2×C3×C4C2×#4112yes—
487C2×C3×C4C2×#4112yes—
488C2×C3×C4C2×#4112yes—
489C2×C3×C4C2×#4112yes—
490C2×C3×C4C2×#4112yes—
491C2×C3×C4C2×#4112yes—
492C2×C3×C4C2×#4112yes—
493C2×C3×C4C2×#4112yes—
494C2×C3×C4H(5,𝔽2)12yes—
495C2×C3×C42−1+412yes—
496C2×C3×C42−1+412yes—
497C2×Dic3—24no—
498C2×Dic3—24no—
499C2×Dic3—24no—
500C2×Dic3—24no—
501C2×Dic3—24no—
502C2×Dic3—24no—
503C2×Dic3—24no—
504C2×Dic3—24no—
505C2×Dic3—24no—
506C2×Dic3—24no—
507C2×Dic3—24no—
508C2×Dic3—24no—
509Dic6—48no—
510C24C23×D311yescharacteristic
511C24C23×D311yescharacteristic
512C2×Q8—64no—
513C2×Q8—64no—
514C2×Q8—64no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—34no—
535C22×C4—34no—
536C22×C4—34no—
537C22×C4—34no—
538C22×C4#23514yes—
539C22×C4#23514yes—
540C22×C4C23×D311yescharacteristic
541C22×C4C23×D311yescharacteristic
542C22×C4C23×D311yescharacteristic
543C22×C4C23×D311yescharacteristic
544C22×C4C23×D311yescharacteristic
545C22×C4C23×D311yescharacteristic
546C22×C4C23×D311yescharacteristic
547C22×C4C23×D311yescharacteristic
548C22×C4C23×D311yescharacteristic
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D311yescharacteristic
551C22×C4C23×D311yescharacteristic
552C22×C4C23×D311yescharacteristic
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—68no—
559C4⋊C4—64no—
560C4⋊C4—68no—
561C4⋊C4—68no—
562C4⋊C4—64no—
563C4⋊C4—64no—
564C4⋊C4—64no—
565C4⋊C4—64no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—124no—
571C4⋊C4—124no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—68no—
579C22⋊C4—68no—
580C22⋊C4—124no—
581C22⋊C4—124no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—68no—
594C42—124no—
595C42—124no—
596C42#23514yes—
597C42#23714yes—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3C22×#4111yescharacteristic
613C22×C3C22×#4111yescharacteristic
614C22×C3C22×#4111yescharacteristic
615C22×C3C22×#4111yescharacteristic
616C22×C3C2×H(5,𝔽2)11yescharacteristic
617C22×C3C2×2−1+411yescharacteristic
618C22×C3C2×2−1+411yescharacteristic
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4#55214yes—
630C3×C4#55314yes—
631C3×C4#55614yes—
632Dic3—44no—
633Dic3—44no—
634Dic3—44no—
635Dic3—44no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23C2×#23512yes—
649C23C2×#23512yes—
650C23C24×D311yescharacteristic
651Q8—128no—
652D4—28no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—28no—
662C2×C4—28no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—64no—
686C2×C4—64no—
687C2×C4—64no—
688C2×C4—64no—
689C2×C4—64no—
690C2×C4—64no—
691C2×C4—64no—
692C2×C4—64no—
693C2×C4—64no—
694C2×C4—64no—
695C2×C4—64no—
696C2×C4—64no—
697C2×C4C2×#23512yes—
698C2×C4C2×#23512yes—
699C2×C4C2×#23512yes—
700C2×C4C2×#23512yes—
701C2×C4C2×#23512yes—
702C2×C4C2×#23512yes—
703C2×C4C2×#23512yes—
704C2×C4C2×#23712yes—
705C2×C4C2×#23712yes—
706C2×C4C2×#23712yes—
707C2×C4#100912yes—
708C2×C4#101012yes—
709C2×C4#101012yes—
710C2×C3—42no—
711C2×C3—42no—
712C2×C3#344411yescharacteristic
713C2×C3C2×#55211yescharacteristic
714C2×C3C2×#55311yescharacteristic
715C2×C3C2×#55611yescharacteristic
716C2×C3#350911yescharacteristic
717C2×C3#351111yescharacteristic
718C2×C3#351111yescharacteristic
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22C22×#23511yescharacteristic
734C22C22×#23511yescharacteristic
735C22C22×#23511yescharacteristic
736C22C22×#23711yescharacteristic
737C22C2×#100911yescharacteristic
738C22C2×#101011yescharacteristic
739C22C2×#101011yescharacteristic
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—124no—
751C4—124no—
752C4—124no—
753C4—124no—
754C4#554114yes—
755C4#554214yes—
756C4#556514yes—
757C3#3621011yescharacteristic, complemented, Sylow
758C2—42no—
759C2—42no—
760C2#8568011yescharacteristic
761C2C2×#554111yescharacteristic
762C2C2×#556511yescharacteristic
763C2C2×#554211yescharacteristic
764C2#8583011yescharacteristic
765C2#8585011yescharacteristic
766C2#8585011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C42×D4C2
prime radicalC22×C3×D4C23
hypercenterC42×D4D3
hypocenterC3#36210
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
5. #82076C2semidirect
6. #82076C2semidirect
7. #82062C2semidirect
8. #82062C2semidirect
9. #73696C2semidirect
10. #73688C2semidirect
11. #73659C2semidirect
12. #73511C2semidirect
13. #73510C2semidirect
14. #73510C2semidirect
15. #73483C2semidirect
16. #73468C2semidirect
17. #73460C2semidirect
18. #73307C2semidirect
19. C4×#869C2semidirect
757. C3#36210semidirect

Maximal subgroups

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

subgroupindex
C3×C42×D42
#823832
#823722
#823512
#820762
#820622
#736962
#736882
#736592
#735112
#735102
#734832
#734682
#734602
#733072
C4×#8692
#362103