Finite Group Databasebeta

← #11872825

Subgroups — #11872825

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic
2#10593881C211yesmaximal, characteristic, complemented
3#10592718C211yesmaximal, characteristic, complemented
4C3×#5009C211yesmaximal, characteristic, complemented
5#10591459C211yesmaximal, characteristic
6#10591459C211yesmaximal, characteristic
7#10591405C211yesmaximal, characteristic, complemented
8#10591401C211yesmaximal, characteristic, complemented
9#10590590C211yesmaximal, characteristic, complemented
10#10590479C211yesmaximal, characteristic, complemented
11#10590429C211yesmaximal, characteristic, complemented
12#10590428C211yesmaximal, characteristic, complemented
13#10590365C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#82545—31nomaximal
17#81147—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64078C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×(C2×D3)⋊C4—21no—
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#872C2211yescharacteristic
32C3×#870C2211yescharacteristic, complemented
33#63861—21no—
34#63861—21no—
35#63857C2211yescharacteristic
36#63857C2211yescharacteristic
37#63845—21no—
38#63845—21no—
39#63844C2211yescharacteristic, complemented
40#63844C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43#63637C2211yescharacteristic, complemented
44#63637C2211yescharacteristic, complemented
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#808C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#518—31no—
62#5698—31no—
63#5545D311yescharacteristic
64#5518—31no—
65C3×#478—31no—
66#5218—31no—
67#5218—31no—
68#5066—31no—
69#5019—31no—
70#5019—31no—
71#5019—31no—
72#5019—61no—
73#5018—31no—
74#5018—31no—
75C4×#214—31no—
76C4×#214—31no—
77#5009—31no—
78#5009D311yescharacteristic, complemented
79#5000—31no—
80#4996—31no—
81#4996—31no—
82#4889—31no—
83#4888—31no—
84#4868—31no—
85#4852—31no—
86#4841—31no—
87#4840—31no—
88#4776—31no—
89#4776—31no—
90#4758—31no—
91#4757—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#634C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C22⋊C4—21no—
107C32×C42C2311yescharacteristic
108#3754—22no—
109#3754—22no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)—21no—
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4D411yescharacteristic
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4D411yescharacteristic
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139#3716—22no—
140#3716—22no—
141#3123—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C3×#125—31no—
145C3×C4×D4—21no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—61no—
150C3×C4×D4—61no—
151C3×C4×D4C2×D311yescharacteristic
152C3×C4×D4C2×D311yescharacteristic
153C3×#117—31no—
154C3×#117—31no—
155C2×C3×C22⋊C4—61no—
156C2×C3×C22⋊C4—61no—
157D4×Dic3C2×D311yescharacteristic
158C2×#214—31no—
159C2×#214—31no—
160C2×#214—31no—
161C2×#214—31no—
162C2×#214—31no—
163C2×#214—31no—
164C2×#214—61no—
165C2×#214—61no—
166C4×#67—21no—
167C2×(C2×D3)⋊C4—21no—
168#924—31no—
169#924—31no—
170C2×#204—31no—
171C2×#204—31no—
172#898—61no—
173#898—61no—
174#897—31no—
175#897—31no—
176#893C2×D311yescharacteristic
177#892C2×D311yescharacteristic
178#890—61no—
179#890—61no—
180#889—61no—
181#889—61no—
182#887—31no—
183#887—31no—
184#67⋊C4—21no—
185D3×C22⋊C4—21no—
186#879—61no—
187#879—61no—
188C4×D12C2×D311yescharacteristic
189#872C2×D311yescharacteristic
190#870C2×D311yescharacteristic, complemented
191#869—31no—
192#869—31no—
193#869—61no—
194C4×Dic6—31no—
195C4×Dic6—31no—
196C3×#107—31no—
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×#102—31no—
200C3×#102—31no—
201#832—31no—
202#832—31no—
203#832C2×D311yescharacteristic
204#832C2×D311yescharacteristic
205#830—31no—
206#830—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8—31no—
209#816—31no—
210#816—31no—
211#815—31no—
212C8×Dic3—31no—
213#810—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—61no—
220#810—61no—
221#809—31no—
222#809—31no—
223#808—31no—
224#808—31no—
225#808C2×D311yescharacteristic, complemented
226#807—31no—
227#807—31no—
228#807C2×D311yescharacteristic, complemented
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—81no—
239C22×C3×D3—81no—
240C22×C3×D3C2×D411yescharacteristic
241C32×D4—21no—
242C32×D4#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250#634—21no—
251#634—21no—
252#634—21no—
253#634—21no—
254C3×#67—24no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—91no—
273#518—31no—
274#485—91no—
275#485—91no—
276#478—31no—
277#478—91no—
278#461—91no—
279#461—91no—
280#450—91no—
281#450—91no—
282#440—91no—
283#440—91no—
284C4×SD16—91no—
285C4×SD16—91no—
286#433—91no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×D4—21no—
290C2×C3×D4—31no—
291C2×C3×D4—61no—
292C2×C3×D4—62no—
293C2×C3×D4—62no—
294C2×C3×D4C22×D311yescharacteristic
295C2×C3×D4C22×D311yescharacteristic
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—31no—
299C22×C3×C4—41no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C2×#67—21no—
304C22×Dic3—21no—
305D3×D4—22no—
306D3×D4—22no—
307C2×D12C22×D311yescharacteristic
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3C22×D311yescharacteristic
311C2×Dic6—31no—
312C2×Dic6—31no—
313C2×Dic6—31no—
314C2×Dic6—31no—
315C2×Dic6—61no—
316C2×Dic6—61no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4—61no—
327C3×C4⋊C4C22×D311yescharacteristic
328C3×C4⋊C4C22×D311yescharacteristic
329C3×C22⋊C4—21no—
330C3×C22⋊C4—21no—
331C3×C22⋊C4—31no—
332C3×C22⋊C4—31no—
333C3×C22⋊C4—41no—
334C3×C22⋊C4—61no—
335C3×C22⋊C4—61no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C42—21no—
339C3×C42—31no—
340C3×C42—61no—
341C3×C42C22×D311yescharacteristic
342C3×C42C22×D311yescharacteristic
343#217—21no—
344#217—61no—
345#217—61no—
346#214—62no—
347#214—62no—
348#214—62no—
349#214—62no—
350#214—62no—
351#214—62no—
352#214—122no—
353#214—122no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4#6711yescharacteristic
360(C2×D3)⋊C4#6711yescharacteristic
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—121no—
368C4⋊Dic3—121no—
369C4⋊Dic3C22×D311yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4#6711yescharacteristic
381Dic3⋊C4#6711yescharacteristic
382C4×Dic3—21no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3C22×D311yescharacteristic
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396#204—62no—
397#204—62no—
398C22×C32—22no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32C22×D411yescharacteristic
402C2×C3×D3—21no—
403C2×C3×D3—22no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—84no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C22×D4—31no—
423C2×SD16—91no—
424C2×SD16—91no—
425C2×SD16—91no—
426C2×SD16—91no—
427C4⋊Q8—91no—
428#126—181no—
429#126—181no—
430#125—31no—
431#125—181no—
432#125—181no—
433C22⋊Q8—91no—
434C22⋊Q8—91no—
435C4×Q8—91no—
436C4×Q8—91no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—31no—
440C4×D4—61no—
441C4×D4—61no—
442C4×D4D3211yescharacteristic
443#117—31no—
444#117—31no—
445C2×C22⋊C4—61no—
446C2×C22⋊C4—61no—
447#107—31no—
448#107—91no—
449#106—31no—
450#106—91no—
451C4⋊C8—31no—
452C4⋊C8—91no—
453#103—91no—
454#103—91no—
455#103—91no—
456#103—91no—
457#102—31no—
458#102—31no—
459#102—91no—
460#102—91no—
461C22⋊C8—91no—
462C22⋊C8—91no—
463#97—91no—
464C4×C8—91no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—31no—
468C23×C3—41no—
469C23×C3—64no—
470C23×C3—61no—
471C23×C3—241no—
472C23×C3—241no—
473C22×D3—21no—
474C22×D3—24no—
475C22×D3—81no—
476C22×D3—81no—
477C22×D3C2×#6711yescharacteristic
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—22no—
481C3×D4—32no—
482C3×D4—41no—
483C3×D4—64no—
484C3×D4—61no—
485C3×D4#23512yes—
486C3×D4#23912yes—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—81no—
502C2×C3×C4—81no—
503C2×C3×C4—82no—
504C2×C3×C4—241no—
505C2×C3×C4—241no—
506C2×C3×C4—241no—
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4C2×#6711yescharacteristic
510C2×C3×C4C2×#6711yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513#67—24no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—81no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3C2×#6711yescharacteristic
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527D12—21no—
528D12#23512yes—
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—81no—
532C4×D3—81no—
533Dic6—61no—
534Dic6—61no—
535Dic6—61no—
536Dic6—61no—
537Dic6—61no—
538Dic6—61no—
539Dic6—61no—
540Dic6—61no—
541Dic6—121no—
542Dic6—121no—
543Dic6—121no—
544Dic6—121no—
545C3×C8—61no—
546C3×C8—61no—
547C3⋊C8—21no—
548C3⋊C8—21no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—121no—
554C3⋊C8—121no—
555C2×C32—42no—
556C2×C32#52511yescharacteristic
557C2×C32#57711yescharacteristic
558C2×C32#57711yescharacteristic
559C3×D3—41no—
560C3×D3—42no—
561C24—61no—
562C2×Q8—91no—
563C2×Q8—91no—
564C2×D4—31no—
565C2×D4—61no—
566C2×D4—62no—
567C2×D4—62no—
568C2×D4C2×D3211yescharacteristic
569C22×C4—21no—
570C22×C4—31no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574SD16—182no—
575SD16—182no—
576SD16—182no—
577SD16—182no—
578C2×C8—31no—
579C2×C8—31no—
580C2×C8—91no—
581C2×C8—91no—
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—181no—
590C4⋊C4—181no—
591C4⋊C4—181no—
592C4⋊C4—181no—
593C4⋊C4—181no—
594C4⋊C4—181no—
595C4⋊C4C2×D3211yescharacteristic
596C22⋊C4—21no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—61no—
600C22⋊C4—61no—
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—181no—
604C22⋊C4—181no—
605C42—31no—
606C42—61no—
607C42—181no—
608C42—181no—
609C42C2×D3211yescharacteristic
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—42no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—62no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—244no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C22×#6711yescharacteristic
629C2×D3—21no—
630C2×D3—22no—
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—84no—
636C3×C4—22no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—81no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C2×#23511yescharacteristic
654C3×C4C2×#23511yescharacteristic
655C3×C4C2×#23911yescharacteristic
656C3×C4D3×#4111yescharacteristic
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—241no—
668Dic3—241no—
669C32#312311yescharacteristic, complemented, Sylow
670C23—21no—
671C23—31no—
672C23—64no—
673C23—61no—
674C23—241no—
675C23—241no—
676Q8—181no—
677Q8—181no—
678Q8—181no—
679Q8—181no—
680D4—21no—
681D4—32no—
682D4—64no—
683D4—61no—
684D4#379912yes—
685C2×C4—21no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—81no—
695C2×C4—181no—
696C2×C4—181no—
697C2×C4—241no—
698C2×C4—241no—
699C2×C4—241no—
700C2×C4D3×#6711yescharacteristic
701C2×C4D3×#6711yescharacteristic
702C2×C4C22×D3211yescharacteristic
703C8—61no—
704C8—61no—
705C8—181no—
706C8—181no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—42no—
711C2×C3—42no—
712C2×C3—82no—
713C2×C3—121no—
714C2×C3—122no—
715C2×C3#562711yescharacteristic
716C2×C3#577011yescharacteristic
717C2×C3#577511yescharacteristic
718C2×C3#579111yescharacteristic
719C2×C3#583611yescharacteristic
720C2×C3#583611yescharacteristic
721D3—41no—
722D3—42no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—61no—
727C22—61no—
728C22—61no—
729C22—62no—
730C22—121no—
731C22—121no—
732C22—244no—
733C22C2×D3×#6711yescharacteristic
734C4—21no—
735C4—21no—
736C4—41no—
737C4—61no—
738C4—61no—
739C4—61no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—361no—
744C4—361no—
745C4C2×#379911yescharacteristic
746C4D3×#23511yescharacteristic
747C3—21no—
748C3#8114711yescharacteristic, complemented
749C3#8254511yescharacteristic, complemented
750C2—42no—
751C2—121no—
752C2—122no—
753C2#1059500511yescharacteristic
754C2#1059510611yescharacteristic
755C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593881C2semidirect
3. #10592718C2semidirect
4. C3×#5009C2semidirect
7. #10591405C2semidirect
8. #10591401C2semidirect
9. #10590590C2semidirect
10. #10590479C2semidirect
11. #10590429C2semidirect
12. #10590428C2semidirect
13. #10590365C2semidirect
14. #10590270C2semidirect
15. #10590253C2semidirect
22. #64078C22semidirect
32. C3×#870C22semidirect
39. #63844C22semidirect
40. #63844C22semidirect
43. #63637C22semidirect
44. #63637C22semidirect
45. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#808C22semidirect
49. C3×#807C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63576C22semidirect
52. #63574C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
78. #5009D3semidirect
190. #870C2×D3semidirect
225. #808C2×D3semidirect
228. #807C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
669. C32#3123semidirect
748. C3#81147semidirect
749. C3#82545semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
#105938812
#105927182
C3×#50092
#105914592
#105914052
#105914012
#105905902
#105904792
#105904292
#105904282
#105903652
#105902702
#105902532
#825453
#811473