Finite Group Databasebeta

← #11872814

Subgroups — #11872814

Order 1152.

882 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595354C211yesmaximal, characteristic, complemented
2#10595223C211yesmaximal, characteristic
3#10592868C211yesmaximal, characteristic
4C3×#5162C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6#10591565C211yesmaximal, characteristic, complemented
7#10591561C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10591467C211yesmaximal, characteristic
10#10591440C211yesmaximal, characteristic, complemented
11#10591409C211yesmaximal, characteristic, complemented
12#10590792C211yesmaximal, characteristic, complemented
13#10590769C211yesmaximal, characteristic, complemented
14#10590713C211yesmaximal, characteristic, complemented
15#10590648C211yesmaximal, characteristic, complemented
16#80413—31nomaximal
17#79659—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20#64155C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic, complemented
23C3×#944C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27#63974—21no—
28C2×#3722—21no—
29#63952—21no—
30#63952—21no—
31#63894C2211yescharacteristic
32#63894C2211yescharacteristic
33#63874C2211yescharacteristic
34#63871C2211yescharacteristic
35#63869C2211yescharacteristic, complemented
36#63868—21no—
37#63867—21no—
38#63849C2211yescharacteristic
39#63848—21no—
40#63847—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43#63659C2211yescharacteristic
44#63648C2211yescharacteristic
45#63647C2211yescharacteristic
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#817C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5731—31no—
62#5583—31no—
63#5545—31no—
64#5545—31no—
65C3×#461—31no—
66C3×C4×SD16—31no—
67#5169—31no—
68#5169—31no—
69#5169—31no—
70#5169—61no—
71#5164—31no—
72#5162D311yescharacteristic, complemented
73Dic3×SD16D311yescharacteristic, complemented
74#5083—31no—
75#5026—31no—
76#5018—31no—
77#5009—31no—
78#4871—31no—
79#4868—31no—
80#4847—31no—
81#4840—31no—
82#4818—31no—
83#4817—31no—
84#4815—31no—
85#4815—31no—
86#4814—31no—
87#4788—31no—
88#4776—31no—
89#4763—31no—
90C4×#204—31no—
91#4690—31no—
92C23×C3⋊D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—22no—
97D4×C3⋊D3—22no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#624—21no—
104C2×#624—21no—
105C32×SD16—22no—
106C2×C32×C8C2311yescharacteristic
107#3755—22no—
108#3752—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×#217—21no—
113C3×#217—21no—
114C3×#214—22no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3C2311yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126#3724—21no—
127#3724D411yescharacteristic
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722D411yescharacteristic
137#3722D411yescharacteristic
138Dic32—21no—
139Dic32—21no—
140#3717—22no—
141#3123—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×D3×D4—61no—
145C2×C3×SD16—21no—
146C2×C3×SD16—31no—
147C2×C3×SD16C2×D311yescharacteristic
148C2×C3×SD16C2×D311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×D4—31no—
152C3×C4×D4—31no—
153#946—31no—
154#946—31no—
155#946—31no—
156#946—61no—
157Q8×Dic3—31no—
158Q8×Dic3C2×D311yescharacteristic, complemented
159#944C2×D311yescharacteristic, complemented
160C2×#215—31no—
161C2×#215—31no—
162C2×#215—31no—
163C2×#215—61no—
164D4×Dic3C2×D311yescharacteristic
165D4×Dic3C2×D311yescharacteristic
166C2×#214C2×D311yescharacteristic
167C4×#67—61no—
168C4×#67—61no—
169C2×(C2×D3)⋊C4—61no—
170C2×(C2×D3)⋊C4—61no—
171C2×#204—31no—
172#898—61no—
173#898—61no—
174#898—61no—
175#897—31no—
176#893—31no—
177#893—31no—
178#892—31no—
179#892—31no—
180#890—31no—
181#889—61no—
182#889—61no—
183#889—61no—
184#67⋊C4—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#876—61no—
189C4×D12—31no—
190C4×D12—31no—
191#872—31no—
192#872—31no—
193#870—31no—
194#870—61no—
195C4×Dic6—31no—
196C3×#106—31no—
197C3×C4⋊C8—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×C4×C8—31no—
203#835—31no—
204#835C2×D311yescharacteristic, complemented
205#835C2×D311yescharacteristic, complemented
206#832—31no—
207#832—31no—
208#832—61no—
209#832C2×D311yescharacteristic
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—61no—
219#818—31no—
220#817—31no—
221#817C2×D311yescharacteristic, complemented
222#816C2×D311yescharacteristic, complemented
223#815—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8C2×D311yescharacteristic, complemented
226C8×Dic3C2×D311yescharacteristic, complemented
227#810—31no—
228#809—31no—
229#808—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233C4⋊(C3⋊C8)—31no—
234#803—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×Q8—21no—
242C32×Q8—21no—
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247#638—24no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)#4112yes—
252C4×C3⋊D3—21no—
253C4×C3⋊D3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×Dic6—21no—
265C3×Dic6—21no—
266#624—81no—
267#624—81no—
268C32×C8—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—91no—
273#518—91no—
274#485—91no—
275#485—91no—
276#478—91no—
277#478—91no—
278#461—31no—
279#461—91no—
280#450—91no—
281#450—91no—
282#440—91no—
283#440—91no—
284C4×SD16—31no—
285C4×SD16—91no—
286#433—91no—
287C23×D3—61no—
288C23×D3—61no—
289C23×D3—121no—
290C2×C3×Q8—21no—
291C2×C3×Q8—31no—
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×D4—21no—
295C2×C3×D4C22×D311yescharacteristic
296C2×C3×D4C22×D311yescharacteristic
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C2×#67—61no—
300C2×#67—61no—
301C2×#67—121no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304D3×D4—62no—
305D3×D4—62no—
306D3×D4—62no—
307D3×D4—62no—
308D3×D4—122no—
309D3×D4—122no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—61no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×Dic6C22×D311yescharacteristic
321C3×SD16—22no—
322C3×SD16—22no—
323C3×SD16—42no—
324C3×SD16—62no—
325C2×C3×C8—21no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C2×C3×C8C22×D311yescharacteristic
329C2×C3×C8C22×D311yescharacteristic
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C42—31no—
339C3×C42—31no—
340C3×C42—61no—
341#217—21no—
342#217—21no—
343#215—62no—
344#215—62no—
345#215—62no—
346#215—122no—
347#214—22no—
348(C2×D3)⋊C4—31no—
349(C2×D3)⋊C4—31no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—121no—
363C4⋊Dic3—21no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372C4⋊Dic3C22×D311yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—31no—
376Dic3⋊C4—31no—
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—121no—
387C4×Dic3—21no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3C22×D311yescharacteristic
393C4×Dic3C22×D311yescharacteristic
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399#204—62no—
400C22×C32—22no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3⋊D3—22no—
407C2×C3⋊D3—21no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—84no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3⋊Dic3—21no—
415C3⋊Dic3—41no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—21no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C22×D4—91no—
425C2×SD16—31no—
426C2×SD16—91no—
427C2×SD16—91no—
428C2×SD16D3211yescharacteristic
429C4⋊Q8—31no—
430#126—181no—
431#126—181no—
432#125—91no—
433#125—181no—
434#125—181no—
435C22⋊Q8—91no—
436C22⋊Q8—91no—
437C4×Q8—31no—
438C4×Q8—91no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—181no—
444C4×D4—181no—
445#117—91no—
446#117—91no—
447C2×C22⋊C4—181no—
448C2×C22⋊C4—181no—
449#107—91no—
450#107—91no—
451#106—31no—
452#106—91no—
453C4⋊C8—31no—
454C4⋊C8—91no—
455#103—31no—
456#103—31no—
457#103—31no—
458#103—91no—
459#102—31no—
460#102—91no—
461#102—91no—
462#102—91no—
463C22⋊C8—91no—
464C22⋊C8—91no—
465#97—91no—
466C4×C8—31no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—41no—
470C22×D3—31no—
471C22×D3—31no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—64no—
476C22×D3—64no—
477C22×D3—121no—
478C22×D3—124no—
479C22×D3—241no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3—242no—
484C22×D3—242no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—22no—
496C3×D4—41no—
497C3×D4#23512yes—
498C3×D4#23712yes—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—241no—
512C2×C3×C4—241no—
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—64no—
516#67—64no—
517#67—124no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—81no—
528C2×Dic3—81no—
529C2×Dic3—121no—
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534D12—32no—
535D12—32no—
536D12—62no—
537D12—61no—
538D12—61no—
539D12—121no—
540C4×D3—61no—
541C4×D3—61no—
542C4×D3—61no—
543C4×D3—61no—
544C4×D3—121no—
545C4×D3—121no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550Dic6—21no—
551Dic6—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—41no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—121no—
562C2×C32—42no—
563C2×C32#52511yescharacteristic
564C2×C32#57711yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—41no—
567C3⋊D3—42no—
568C24—181no—
569C2×Q8—31no—
570C2×Q8C2×D3211yescharacteristic
571C2×D4—91no—
572C2×D4—181no—
573C2×D4—182no—
574C2×D4—182no—
575C2×D4C2×D3211yescharacteristic
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—91no—
579C22×C4—181no—
580C22×C4—181no—
581SD16—22no—
582SD16—62no—
583SD16—182no—
584SD16—182no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—91no—
588C2×C8C2×D3211yescharacteristic
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—91no—
596C4⋊C4—91no—
597C4⋊C4—91no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—91no—
606C22⋊C4—91no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C42—31no—
613C42—31no—
614C42—61no—
615C42—181no—
616C42—181no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—21no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—62no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—62no—
636C2×D3—61no—
637C2×D3—62no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—122no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—241no—
646C2×D3—241no—
647C2×D3—244no—
648C2×D3—244no—
649C2×D3—248no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—81no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4C2×#23511yescharacteristic
664C3×C4C2×#23711yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667Dic3—21no—
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—61no—
676Dic3—61no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681C32#312311yescharacteristic, complemented, Sylow
682C23—21no—
683C23—91no—
684C23—184no—
685C23—181no—
686C23—721no—
687C23—721no—
688Q8—21no—
689Q8—21no—
690Q8—61no—
691Q8—61no—
692D4—21no—
693D4—92no—
694D4—184no—
695D4—181no—
696D4#380412yes—
697C2×C4—21no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—91no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—241no—
711C2×C4—241no—
712C2×C4—721no—
713C2×C4—721no—
714C2×C4C22×D3211yescharacteristic
715C8—21no—
716C8—61no—
717C8—61no—
718C8—181no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—42no—
723C2×C3—42no—
724C2×C3—82no—
725C2×C3#554711yescharacteristic
726C2×C3#560611yescharacteristic
727C2×C3#576211yescharacteristic
728C2×C3#576211yescharacteristic
729C2×C3#577011yescharacteristic
730C2×C3#577811yescharacteristic
731D3—122no—
732D3—121no—
733D3—122no—
734D3—121no—
735D3—122no—
736D3—242no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—181no—
741C22—182no—
742C22—181no—
743C22—181no—
744C22—361no—
745C22—361no—
746C22—724no—
747C22D32×D411yescharacteristic
748C4—41no—
749C4—61no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4—121no—
757C4—181no—
758C4—361no—
759C4#6431211yescharacteristic
760C4C2×#380411yescharacteristic
761C3—21no—
762C3#7965911yescharacteristic, complemented
763C3#8041311yescharacteristic, complemented
764C2—42no—
765C2—361no—
766C2—362no—
767C2#1059475111yescharacteristic
768C2#1059475311yescharacteristic
769C2#1059513811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenterC2×SD16D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595354C2semidirect
4. C3×#5162C2semidirect
5. C3×Dic3×SD16C2semidirect
6. #10591565C2semidirect
7. #10591561C2semidirect
8. #10591540C2semidirect
10. #10591440C2semidirect
11. #10591409C2semidirect
12. #10590792C2semidirect
13. #10590769C2semidirect
14. #10590713C2semidirect
15. #10590648C2semidirect
22. C3×Q8×Dic3C22semidirect
23. C3×#944C22semidirect
35. #63869C22semidirect
41. Dic3×Dic6C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
49. C3×#817C22semidirect
50. C3×#816C22semidirect
51. C3×Dic3⋊C8C22semidirect
52. C3×C8×Dic3C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
60. #63554C22semidirect
72. #5162D3semidirect
73. Dic3×SD16D3semidirect
158. Q8×Dic3C2×D3semidirect
159. #944C2×D3semidirect
204. #835C2×D3semidirect
205. #835C2×D3semidirect
221. #817C2×D3semidirect
222. #816C2×D3semidirect
225. Dic3⋊C8C2×D3semidirect
226. C8×Dic3C2×D3semidirect
681. C32#3123semidirect
762. C3#79659semidirect
763. C3#80413semidirect

Maximal subgroups

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

subgroupindex
#105953542
#105952232
#105928682
C3×#51622
C3×Dic3×SD162
#105915652
#105915612
#105915402
#105914672
#105914402
#105914092
#105907922
#105907692
#105907132
#105906482
#804133
#796593