Finite Group Databasebeta

← #10848816

Subgroups — #10848816

Order 768.

1158 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5682C211yesmaximal, characteristic, complemented
2C2×#5059C211yesmaximal, characteristic, complemented
3C2×#4714C211yesmaximal, characteristic, complemented
4#74370C211yesmaximal, characteristic, complemented
5C3×#1959C211yesmaximal, characteristic, complemented
6#70273C211yesmaximal, characteristic, complemented
7#70272C211yesmaximal, characteristic, complemented
8#70240C211yesmaximal, characteristic, complemented
9#70239C211yesmaximal, characteristic, complemented
10#70205C211yesmaximal, characteristic, complemented
11#70204C211yesmaximal, characteristic
12#70172C211yesmaximal, characteristic, complemented
13#70171C211yesmaximal, characteristic, complemented
14#69830C211yesmaximal, characteristic, complemented
15#69582C211yesmaximal, characteristic, complemented
16#25610—31nomaximal, Sylow
17C2×C3×#124C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×Q8×Dic3C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C2×D4×Dic3C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C22×#213C2211yescharacteristic
26#5682—24no—
27#5682—24no—
28C2×#897C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#886—21no—
31C2×#885—21no—
32C2×#879—21no—
33C2×#878—21no—
34C2×#875C2211yescharacteristic
35C2×#872C2211yescharacteristic
36C2×#869C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#97C2211yescharacteristic
42C3×#384C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49#5059—24no—
50#4994—21no—
51#4994—21no—
52#4991—21no—
53#4991—21no—
54#4988C2211yescharacteristic
55#4973C2211yescharacteristic
56C2×C4×C3⋊C8C2211yescharacteristic
57#4714—24no—
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#542—31no—
65C2×#495—31no—
66C2×#489—31no—
67#2620—31no—
68#2001—31no—
69#2000—31no—
70#2000—31no—
71#1999—31no—
72#1990—31no—
73#1959D311yescharacteristic, complemented
74#1880—31no—
75#1879—31no—
76#1878—31no—
77#1877—31no—
78#1750—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C23×Dic3—21no—
83C22×D12—21no—
84C22×D12C2311yescharacteristic
85C22×C4×D3C2311yescharacteristic
86C22×Dic6—21no—
87C22×Dic6C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×#124—22no—
91C3×#124D414yescomplemented
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C22⋊C4—21no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C42C2311yescharacteristic
99C2×#217—21no—
100C2×#217—21no—
101#946—22no—
102#946—22no—
103Q8×Dic3—22no—
104Q8×Dic3—22no—
105C2×#216—22no—
106C2×#216—22no—
107C2×#216—41no—
108C2×#215—22no—
109C2×#215—22no—
110C2×#215—41no—
111#938—22no—
112#938—22no—
113D4×Dic3—22no—
114D4×Dic3—22no—
115C2×#214—22no—
116C2×#214—22no—
117C2×#214—41no—
118C2×#213—22no—
119C2×#213—22no—
120C2×#213—41no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4D411yescharacteristic
129C2×(C2×D3)⋊C4D411yescharacteristic
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4D411yescharacteristic
137C2×Dic3⋊C4D411yescharacteristic
138C2×C4×Dic3—21no—
139C2×C4×Dic3C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142#897—41no—
143#897—41no—
144#895—41no—
145#895—41no—
146#886—28no—
147#885—28no—
148#879—28no—
149#878—28no—
150#875—22no—
151#875—22no—
152#872—22no—
153#872—22no—
154#869—22no—
155#869D414yescomplemented
156C3×#103—41no—
157C3×#103—41no—
158C3×#102—41no—
159C3×#102—41no—
160C3×#97—22no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#821—22no—
164#821—22no—
165(C2×D3)⋊C8—22no—
166(C2×D3)⋊C8—22no—
167#816—22no—
168#816—22no—
169C4×C3⋊C8—22no—
170C22×Q16—31no—
171C22×SD16—31no—
172C22×SD16—31no—
173C22×D8—31no—
174#542—64no—
175#542—64no—
176C2×C4⋊Q8—31no—
177C2×#126—61no—
178C2×#124—31no—
179C2×#124—61no—
180C2×#124C2×D311yescharacteristic
181C2×#123—61no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—31no—
184C2×C22⋊Q8—61no—
185C2×#121—31no—
186C2×#121—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×#117—31no—
190#495—64no—
191#489—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103C2×D311yescharacteristic
195C2×#103C2×D311yescharacteristic
196C2×#102—31no—
197C2×#102—31no—
198C2×#102C2×D311yescharacteristic
199C2×#102C2×D311yescharacteristic
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202C2×#97C2×D311yescharacteristic
203C2×C4×C8—31no—
204#396—61no—
205#396—61no—
206#394—61no—
207#394—61no—
208#391—31no—
209#390—31no—
210#384C2×D311yescharacteristic
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C23×D3—21no—
219C23×D3C2×D411yescharacteristic
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8C2×D412yes—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4C2×D412yes—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C2×#67—24no—
239C2×#67—81no—
240C2×#67—81no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—24no—
244C22×Dic3—21no—
245C22×Dic3—81no—
246C22×Dic3—81no—
247C22×Dic3C2×D411yescharacteristic
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—42no—
257C2×D12—81no—
258C2×D12—81no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—24no—
272C2×Dic6—81no—
273C2×Dic6—81no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—81no—
285C3×C4⋊C4—81no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—24no—
288C3×C42C2×D412yes—
289C3×C42C2×D412yes—
290#217—24no—
291#217—24no—
292#216—44no—
293#215—44no—
294#214—44no—
295#213—44no—
296(C2×D3)⋊C4—24no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—22no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—81no—
304(C2×D3)⋊C4—81no—
305C4⋊Dic3—24no—
306C4⋊Dic3—24no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—42no—
310C4⋊Dic3C2×D412yes—
311C4⋊Dic3C2×D412yes—
312Dic3⋊C4—24no—
313Dic3⋊C4—22no—
314Dic3⋊C4—22no—
315C4×Dic3—24no—
316C4×Dic3—21no—
317C4×Dic3—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8#4112yes—
323C2×C3⋊C8#4112yes—
324C22×Q8—31no—
325C22×Q8—61no—
326C22×Q8C22×D311yescharacteristic
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4C22×D311yescharacteristic
331C23×C4—31no—
332C23×C4—61no—
333C2×Q16—62no—
334C2×Q16—62no—
335C2×Q16—121no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—121no—
341C2×SD16—121no—
342C2×D8—62no—
343C2×D8—62no—
344C2×D8—121no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8C22×D311yescharacteristic
348C22×C8C22×D311yescharacteristic
349C4⋊Q8—34no—
350C4⋊Q8—62no—
351#126—68no—
352#124—22no—
353#124—68no—
354#124—62no—
355#124—62no—
356#124D1214yescomplemented
357#123—68no—
358C22⋊Q8—68no—
359C22⋊Q8—62no—
360C22⋊Q8—62no—
361C22⋊Q8—121no—
362C22⋊Q8—121no—
363#121—62no—
364#121—62no—
365#121—121no—
366#121—121no—
367C4×Q8—62no—
368C4×Q8—62no—
369C4×D4—62no—
370C4×D4—62no—
371#117—62no—
372#117—62no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4—61no—
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—31no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C42—31no—
399C2×C42—61no—
400C2×C42C22×D311yescharacteristic
401#103—41no—
402#103—41no—
403#103—62no—
404#103—62no—
405#102—41no—
406#102—41no—
407#102—62no—
408#102—62no—
409C22⋊C8—62no—
410C22⋊C8—62no—
411#97—22no—
412C4×C8—62no—
413#95—61no—
414#95—61no—
415C23×C3—22no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3C22×D411yescharacteristic
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C3×Q8—22no—
438C3×Q8—22no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×D4—22no—
442C3×D4—22no—
443C3×D4—41no—
444C3×D4—41no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4#12012yes—
459C2×C3×C4#12012yes—
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4H(5,𝔽2)11yescharacteristic
465C2×C3×C4H(5,𝔽2)11yescharacteristic
466#67—84no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—22no—
470C2×Dic3—21no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—84no—
486D12—41no—
487D12—41no—
488D12—41no—
489D12—41no—
490D12—84no—
491C4×D3—41no—
492C4×D3—41no—
493C4×D3—41no—
494C4×D3—41no—
495Dic6—41no—
496Dic6—41no—
497Dic6—41no—
498Dic6—41no—
499Dic6—84no—
500C3×C8—41no—
501C3×C8—41no—
502C3⋊C8—22no—
503C3⋊C8—22no—
504C24—21no—
505C24—31no—
506C24—61no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—64no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8—241no—
520C2×Q8—241no—
521C2×Q8C2×D1212yes—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—64no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—122no—
535C2×D4—241no—
536C2×D4—241no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4C2×D1212yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—64no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—241no—
557C22×C4—241no—
558C22×C4D3×D411yescharacteristic
559C22×C4D3×D411yescharacteristic
560C22×C4C23×D311yescharacteristic
561Q16—124no—
562SD16—124no—
563SD16—124no—
564D8—124no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—32no—
572C2×C8—32no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—32no—
582C4⋊C4—32no—
583C4⋊C4—64no—
584C4⋊C4—64no—
585C4⋊C4—62no—
586C4⋊C4—62no—
587C4⋊C4—64no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—81no—
591C4⋊C4—81no—
592C4⋊C4—122no—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—62no—
599C22⋊C4—62no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—241no—
605C22⋊C4—241no—
606C42—64no—
607C42—61no—
608C42—61no—
609C42C2×D1212yes—
610C42D3×D412yes—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3C2×#12011yescharacteristic
619C22×C3#53211yescharacteristic
620C22×C3#53511yescharacteristic
621C22×C3#57611yescharacteristic
622C22×C3#57711yescharacteristic
623C22×C3#57711yescharacteristic
624C22×C3#57811yescharacteristic
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—81no—
633C2×D3—81no—
634C2×D3—81no—
635C2×D3—81no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—42no—
642C3×C4—81no—
643C3×C4—81no—
644C3×C4#54611yescharacteristic
645C3×C4#54611yescharacteristic
646C3×C4#55011yescharacteristic
647C3×C4#55011yescharacteristic
648Dic3—41no—
649Dic3—42no—
650Dic3—42no—
651Dic3—41no—
652Dic3—41no—
653Dic3—81no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—61no—
662C23—61no—
663C23—61no—
664C23—61no—
665C23—61no—
666C23—61no—
667C23—61no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23C2×D3×D411yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—41no—
679Q8—41no—
680Q8—121no—
681Q8—121no—
682Q8—121no—
683Q8—121no—
684Q8—244no—
685D4—22no—
686D4—22no—
687D4—41no—
688D4—41no—
689D4—121no—
690D4—121no—
691D4—121no—
692D4—121no—
693D4—244no—
694D4—244no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—62no—
712C2×C4—61no—
713C2×C4—62no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—244no—
731C2×C4#88212yes—
732C2×C4#88212yes—
733C2×C4C22×D1211yescharacteristic
734C2×C4C2×D3×D411yescharacteristic
735C2×C4#100411yescharacteristic
736C2×C4#100411yescharacteristic
737C2×C4D3×#4111yescharacteristic
738C2×C4D3×#4111yescharacteristic
739C8—41no—
740C8—41no—
741C8—62no—
742C8—62no—
743C2×C3—82no—
744C2×C3#243111yescharacteristic
745C2×C3#301211yescharacteristic
746C2×C3#301311yescharacteristic
747C2×C3#317311yescharacteristic
748C2×C3#317511yescharacteristic
749C2×C3#322411yescharacteristic
750C2×C3#322511yescharacteristic
751D3—81no—
752D3—161no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—241no—
768C22—241no—
769C22—241no—
770C22—241no—
771C22—241no—
772C22—241no—
773C22—241no—
774C22C2×#88211yescharacteristic
775C22#566811yescharacteristic
776C22#571511yescharacteristic
777C22#577411yescharacteristic
778C22#577511yescharacteristic
779C22#577811yescharacteristic
780C22#577911yescharacteristic
781C4—22no—
782C4—22no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—121no—
787C4—121no—
788C4—122no—
789C4—122no—
790C4—121no—
791C4—241no—
792C4#555411yescharacteristic
793C4#555411yescharacteristic
794C4#559911yescharacteristic
795C4#559911yescharacteristic
796C3#2561011yescharacteristic, complemented, Sylow
797C2—82no—
798C2—241no—
799C2—481no—
800C2#7631311yescharacteristic
801C2#7888611yescharacteristic
802C2#7888711yescharacteristic
803C2#8166611yescharacteristic
804C2#8166711yescharacteristic
805C2#8185511yescharacteristic
806C2#8188011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1959C2
socleC23×C3C22×D4
prime radical#70204C2
hypercenter#1959D3
hypocenterC3#25610
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
1. C2×#5682C2semidirect
2. C2×#5059C2semidirect
3. C2×#4714C2semidirect
4. #74370C2semidirect
5. C3×#1959C2semidirect
6. #70273C2semidirect
7. #70272C2semidirect
8. #70240C2semidirect
9. #70239C2semidirect
10. #70205C2semidirect
12. #70172C2semidirect
13. #70171C2semidirect
14. #69830C2semidirect
15. #69582C2semidirect
73. #1959D3semidirect
91. C3×#124D4semidirect
155. #869D4semidirect
356. #124D12semidirect
796. C3#25610semidirect

Maximal subgroups

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

subgroupindex
C2×#56822
C2×#50592
C2×#47142
#743702
C3×#19592
#702732
#702722
#702402
#702392
#702052
#702042
#701722
#701712
#698302
#695822
#256103