Finite Group Databasebeta

← #11872178

Subgroups — #11872178

Order 1152.

911 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595223C211yesmaximal, characteristic, complemented
2#10594352C211yesmaximal, characteristic, complemented
3#10592472C211yesmaximal, characteristic
4C3×#4759C211yesmaximal, characteristic, complemented
5C3×#4758C211yesmaximal, characteristic, complemented
6#10591471C211yesmaximal, characteristic, complemented
7#10591467C211yesmaximal, characteristic, complemented
8#10591404C211yesmaximal, characteristic, complemented
9#10590770C211yesmaximal, characteristic, complemented
10#10590763C211yesmaximal, characteristic, complemented
11#10590715C211yesmaximal, characteristic, complemented
12#10590648C211yesmaximal, characteristic, complemented
13#10590466C211yesmaximal, characteristic, complemented
14#10590457C211yesmaximal, characteristic, complemented
15#10590451C211yesmaximal, characteristic, complemented
16#80952—31nomaximal
17#79696—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3753C2211yescharacteristic
20C2×#3745C2211yescharacteristic
21#64104C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C3×#888C2211yescharacteristic, complemented
26C3×#887C2211yescharacteristic, complemented
27#63974—21no—
28C2×#3722—21no—
29#63952—21no—
30#63952—21no—
31#63897—21no—
32#63894C2211yescharacteristic
33#63894C2211yescharacteristic
34#63894C2211yescharacteristic, complemented
35#63888—21no—
36#63874C2211yescharacteristic
37#63871C2211yescharacteristic
38#63868—21no—
39#63864—21no—
40#63864C2211yescharacteristic, complemented
41#63849C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63647C2211yescharacteristic
45#63636C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#818C2211yescharacteristic, complemented
48C3×#816C2211yescharacteristic, complemented
49C3×Dic3⋊C8C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5733—31no—
62#5582—31no—
63#5545—31no—
64#5545—31no—
65C3×#474—31no—
66C3×C4×SD16—31no—
67#5169—31no—
68#5165—31no—
69#5084—31no—
70#5026—31no—
71#5016—31no—
72#5014—31no—
73#4889—31no—
74#4888—31no—
75#4885—31no—
76#4872—31no—
77#4870—31no—
78#4866—31no—
79#4844—31no—
80#4840—31no—
81#4819—31no—
82#4814—31no—
83#4785—31no—
84#4776—31no—
85#4773—31no—
86#4773—31no—
87#4773—61no—
88#4759D311yescharacteristic, complemented
89#4758D311yescharacteristic, complemented
90C4×D24—31no—
91#4690—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—22no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#624—21no—
106C2×#624—21no—
107C2×#624—21no—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110#3753—22no—
111#3752—21no—
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113#3745—22no—
114C3×#217—21no—
115C3×#217—21no—
116C3×#214—22no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724D411yescharacteristic
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130#3722—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137#3722D411yescharacteristic
138#3722D411yescharacteristic
139Dic32—21no—
140#3717—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×D3×D4—61no—
145C2×C3×SD16—31no—
146C3×C4⋊Q8—31no—
147C3×C4×Q8—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150#947—31no—
151#947—61no—
152#946—31no—
153#946—61no—
154C2×#215—31no—
155D4×Dic3C2×D311yescharacteristic
156D4×Dic3C2×D311yescharacteristic
157C2×#214C2×D311yescharacteristic
158C2×#213—31no—
159C2×#213—31no—
160C2×#213—61no—
161C4×#67—61no—
162C4×#67—61no—
163C2×(C2×D3)⋊C4—61no—
164C2×(C2×D3)⋊C4—61no—
165C2×D24—31no—
166C2×D24—31no—
167C2×D24—61no—
168C2×#204—31no—
169#898—61no—
170#897—31no—
171#896—61no—
172#895—31no—
173#895—31no—
174#895—61no—
175#894—61no—
176#894—61no—
177#893—31no—
178#893—31no—
179#893—31no—
180#892—31no—
181#892—31no—
182#888C2×D311yescharacteristic, complemented
183#887C2×D311yescharacteristic, complemented
184#67⋊C4—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#876—61no—
189#875—31no—
190#875—61no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194#872—31no—
195#872—31no—
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×C4⋊C8—31no—
200C3×#103—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102C2×D311yescharacteristic
204C3×#102C2×D311yescharacteristic
205C3×C4×C8—31no—
206#835—31no—
207#832C2×D311yescharacteristic
208#821—31no—
209#821—31no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—61no—
216#818C2×D311yescharacteristic, complemented
217#816C2×D311yescharacteristic, complemented
218#815—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8C2×D311yescharacteristic, complemented
221C8×Dic3C2×D311yescharacteristic, complemented
222#810—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#808—31no—
230#808—31no—
231#808C2×D311yescharacteristic, complemented
232#807C2×D311yescharacteristic, complemented
233C4⋊(C3⋊C8)—31no—
234#803—31no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—24no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—81no—
240C22×C3⋊D3—81no—
241C22×C3⋊D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246#638—24no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—81no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—81no—
268#624—81no—
269#624—81no—
270#624—81no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—91no—
277#485—91no—
278#482—91no—
279#476—91no—
280#474—31no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—31no—
288C4×D8—91no—
289#433—91no—
290C23×D3—61no—
291C23×D3—61no—
292C23×D3—121no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×D4—21no—
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C22×D311yescharacteristic
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—121no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305D3×D4—62no—
306D3×D4—62no—
307D3×D4—62no—
308D3×D4—62no—
309D3×D4—122no—
310D3×D4—122no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—121no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×Dic6—21no—
330C2×Dic6C22×D311yescharacteristic
331C3×SD16—62no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—31no—
348C3×C42—31no—
349C3×C42—61no—
350#217—21no—
351#217—21no—
352#215—62no—
353#214—22no—
354#213—62no—
355#213—62no—
356#213—122no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—121no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389C4×Dic3—21no—
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
399D24—62no—
400D24—62no—
401D24—122no—
402#204—62no—
403C22×C32—22no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32C22×D411yescharacteristic
407C2×C3⋊D3—21no—
408C2×C3⋊D3—21no—
409C2×C3⋊D3—22no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—84no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C22×D4—91no—
430C2×SD16—31no—
431C2×SD16—91no—
432C2×D8—91no—
433C2×D8—91no—
434C4⋊Q8—31no—
435#126—181no—
436#124—91no—
437#124—181no—
438#123—181no—
439C22⋊Q8—91no—
440C22⋊Q8—181no—
441#121—91no—
442C4×Q8—31no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—181no—
449C4×D4—181no—
450#117—91no—
451#117—91no—
452C2×C22⋊C4—181no—
453C2×C22⋊C4—181no—
454#107—31no—
455#107—31no—
456#106—31no—
457#106—91no—
458C4⋊C8—31no—
459C4⋊C8—91no—
460#103—31no—
461#103—91no—
462#102—31no—
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102D3211yescharacteristic
468C22⋊C8—91no—
469C22⋊C8—91no—
470#97—91no—
471C4×C8—31no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—41no—
475C22×D3—31no—
476C22×D3—31no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—64no—
481C22×D3—64no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—121no—
485C22×D3—124no—
486C22×D3—121no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3—242no—
492C22×D3—242no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—241no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—22no—
499C3×D4—41no—
500C3×D4#23512yes—
501C3×D4#23912yes—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—64no—
519#67—64no—
520#67—124no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—61no—
528C2×Dic3—81no—
529C2×Dic3—81no—
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534D12—32no—
535D12—32no—
536D12—62no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—121no—
544D12—121no—
545D12—121no—
546D12—241no—
547D12—241no—
548D12—242no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—121no—
554C4×D3—121no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561Dic6—21no—
562Dic6—21no—
563Dic6—81no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—121no—
574C2×C32—42no—
575C2×C32#52511yescharacteristic
576C2×C32#57611yescharacteristic
577C2×C32#57711yescharacteristic
578C3⋊D3—41no—
579C3⋊D3—42no—
580C3⋊D3—81no—
581C24—181no—
582C2×Q8—31no—
583C2×Q8—61no—
584C2×D4—91no—
585C2×D4—91no—
586C2×D4—181no—
587C2×D4—181no—
588C2×D4—182no—
589C2×D4—182no—
590C2×D4C2×D3211yescharacteristic
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—91no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597SD16—62no—
598SD16—182no—
599D8—182no—
600D8—182no—
601C2×C8—31no—
602C2×C8—31no—
603C2×C8—91no—
604C2×C8C2×D3211yescharacteristic
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4C2×D3211yescharacteristic
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—91no—
617C22⋊C4—91no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—31no—
627C42—31no—
628C42—61no—
629C42—181no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—42no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C2×D3—62no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—62no—
649C2×D3—61no—
650C2×D3—62no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—122no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—241no—
665C2×D3—241no—
666C2×D3—241no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3—248no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—81no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4C2×#23511yescharacteristic
686C3×C4C2×#23911yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4D3×#4111yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697Dic3—61no—
698Dic3—61no—
699Dic3—121no—
700C32#311811yescharacteristic, complemented, Sylow
701C23—21no—
702C23—91no—
703C23—184no—
704C23—181no—
705C23—181no—
706C23—721no—
707C23—721no—
708Q8—61no—
709Q8—61no—
710Q8—241no—
711D4—21no—
712D4—92no—
713D4—184no—
714D4—181no—
715D4—181no—
716D4—181no—
717D4—721no—
718D4#379912yes—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—241no—
732C2×C4—241no—
733C2×C4—721no—
734C2×C4—721no—
735C2×C4—721no—
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—61no—
739C8—61no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—42no—
745C2×C3—42no—
746C2×C3—82no—
747C2×C3#554711yescharacteristic
748C2×C3#562711yescharacteristic
749C2×C3#575711yescharacteristic
750C2×C3#576211yescharacteristic
751C2×C3#576911yescharacteristic
752C2×C3#577811yescharacteristic
753D3—122no—
754D3—121no—
755D3—122no—
756D3—121no—
757D3—122no—
758D3—242no—
759D3—241no—
760D3—241no—
761D3—481no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—181no—
766C22—182no—
767C22—181no—
768C22—181no—
769C22—361no—
770C22—361no—
771C22—361no—
772C22—361no—
773C22—361no—
774C22—724no—
775C22D32×D411yescharacteristic
776C4—41no—
777C4—61no—
778C4—61no—
779C4—61no—
780C4—61no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—181no—
786C4C2×#379911yescharacteristic
787C4#6431211yescharacteristic
788C3—21no—
789C3#7969611yescharacteristic, complemented
790C3#8095211yescharacteristic, complemented
791C2—42no—
792C2—361no—
793C2—362no—
794C2—721no—
795C2#1059406611yescharacteristic
796C2#1059473411yescharacteristic
797C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10592472C2
hypercenter#102D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595223C2semidirect
2. #10594352C2semidirect
4. C3×#4759C2semidirect
5. C3×#4758C2semidirect
6. #10591471C2semidirect
7. #10591467C2semidirect
8. #10591404C2semidirect
9. #10590770C2semidirect
10. #10590763C2semidirect
11. #10590715C2semidirect
12. #10590648C2semidirect
13. #10590466C2semidirect
14. #10590457C2semidirect
15. #10590451C2semidirect
25. C3×#888C22semidirect
26. C3×#887C22semidirect
34. #63894C22semidirect
40. #63864C22semidirect
47. C3×#818C22semidirect
48. C3×#816C22semidirect
49. C3×Dic3⋊C8C22semidirect
50. C3×C8×Dic3C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63574C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
60. #63554C22semidirect
88. #4759D3semidirect
89. #4758D3semidirect
182. #888C2×D3semidirect
183. #887C2×D3semidirect
216. #818C2×D3semidirect
217. #816C2×D3semidirect
220. Dic3⋊C8C2×D3semidirect
221. C8×Dic3C2×D3semidirect
231. #808C2×D3semidirect
232. #807C2×D3semidirect
700. C32#3118semidirect
789. C3#79696semidirect
790. C3#80952semidirect

Maximal subgroups

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

subgroupindex
#105952232
#105943522
#105924722
C3×#47592
C3×#47582
#105914712
#105914672
#105914042
#105907702
#105907632
#105907152
#105906482
#105904662
#105904572
#105904512
#809523
#796963