Finite Group Databasebeta

← #11870436

Subgroups — #11870436

Order 1152.

1083 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#624C211yesmaximal, characteristic, complemented
2#10594518C211yesmaximal, characteristic, complemented
3#10592472C211yesmaximal, characteristic, complemented
4C3×#4759C211yesmaximal, characteristic, complemented
5C3×#4756C211yesmaximal, characteristic, complemented
6#10591481C211yesmaximal, characteristic, complemented
7#10591456C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590765C211yesmaximal, characteristic, complemented
10#10590763C211yesmaximal, characteristic, complemented
11#10590650C211yesmaximal, characteristic, complemented
12#10590643C211yesmaximal, characteristic, complemented
13#10590464C211yesmaximal, characteristic, complemented
14#10590456C211yesmaximal, characteristic, complemented
15#10590442C211yesmaximal, characteristic, complemented
16#80948—31nomaximal
17#79590—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×#624—21no—
20C2×#3799—21no—
21C2×#3753C2211yescharacteristic
22C2×#3745C2211yescharacteristic
23#64104C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#893C2211yescharacteristic, complemented
28C3×#888C2211yescharacteristic, complemented
29#63974—21no—
30#63952—21no—
31#63952—21no—
32#63916C2211yescharacteristic
33#63911C2211yescharacteristic, complemented
34#63910—21no—
35#63907—21no—
36#63904—21no—
37#63900C2211yescharacteristic
38#63894C2211yescharacteristic
39#63894C2211yescharacteristic
40#63894C2211yescharacteristic, complemented
41C4×#624C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63647C2211yescharacteristic
45#63636C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#821C2211yescharacteristic, complemented
48C3×#818C2211yescharacteristic, complemented
49C3×Dic3⋊C8C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5725—31no—
62#5548—31no—
63C4×D3×D4—31no—
64C4×D3×D4—31no—
65C3×#474—31no—
66C3×C4×D8—31no—
67#5156—31no—
68#5150—31no—
69#5087—31no—
70#5015—31no—
71C4×#213—31no—
72C4×#213—31no—
73#4890—31no—
74#4882—31no—
75#4882—31no—
76#4882—31no—
77#4872—31no—
78#4872—31no—
79#4843—31no—
80#4833—31no—
81#4786—31no—
82#4774—31no—
83#4773—31no—
84#4773—31no—
85#4773—31no—
86#4773—61no—
87#4759D311yescharacteristic, complemented
88#4756—31no—
89#4756D311yescharacteristic, complemented
90C4×D24—31no—
91#4685—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×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×Dic6—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#624—21no—
110C2×#624—21no—
111C2×#624—21no—
112C2×#624—21no—
113C2×#624—44no—
114C2×#624D411yescharacteristic
115C2×#624D411yescharacteristic
116#3799—44no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3753—22no—
120#3752—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3745—22no—
123C3×#217—21no—
124C3×#217—21no—
125C3×#213—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32D411yescharacteristic
141Dic32D411yescharacteristic
142#3714—22no—
143#3100—91noSylow
144C2×#239—61no—
145C2×D3×D4—31no—
146C2×D3×D4—31no—
147C2×D3×D4—61no—
148C2×#235—61no—
149C22×C4×D3—61no—
150C22×C4×D3—61no—
151C2×C3×D8—31no—
152C3×C4⋊Q8—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156#947—61no—
157#940—31no—
158#938—31no—
159D4×Dic3C2×D311yescharacteristic
160D4×Dic3C2×D311yescharacteristic
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C2×#213—61no—
165C2×#213C2×D311yescharacteristic
166C4×#67—61no—
167C4×#67—61no—
168C4×#67—61no—
169C2×D24—31no—
170C2×D24—31no—
171C2×D24—31no—
172C2×D24—61no—
173#895—31no—
174#895—31no—
175#895—31no—
176#895—61no—
177#895—61no—
178#893—31no—
179#893—31no—
180#893—31no—
181#893—61no—
182#893C2×D311yescharacteristic, complemented
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185#888C2×D311yescharacteristic, complemented
186#885—61no—
187#884—61no—
188#67⋊C4—61no—
189#67⋊C4—61no—
190D3×C22⋊C4—61no—
191D3×C22⋊C4—61no—
192#874—31no—
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—31no—
196C42×D3—31no—
197C42×D3—31no—
198C3×#107—31no—
199C3×#107—31no—
200C3×#107—31no—
201C3×C4⋊C8—31no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102C2×D311yescharacteristic
206C3×#102C2×D311yescharacteristic
207C3×C4×C8—31no—
208#832—31no—
209#832C2×D311yescharacteristic
210#821—31no—
211#821—31no—
212#821—31no—
213#821C2×D311yescharacteristic, complemented
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#818C2×D311yescharacteristic, complemented
220Dic3⋊C8—31no—
221Dic3⋊C8C2×D311yescharacteristic, complemented
222C8×Dic3—31no—
223C8×Dic3C2×D311yescharacteristic, complemented
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—61no—
231#807—31no—
232#807—31no—
233#807C2×D311yescharacteristic, complemented
234#807C2×D311yescharacteristic, complemented
235C4⋊(C3⋊C8)—31no—
236C4×C3⋊C8—31no—
237C23×C32—21no—
238C22×C3⋊D3—24no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3—21no—
245C32×D4—21no—
246C32×D4#4112yescomplemented
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—24no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—42no—
255C4⋊(C3⋊D3)#4112yescomplemented
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×C4×D3—42no—
270C3×Dic6—42no—
271#626—42no—
272#626—42no—
273#626—42no—
274#624—41no—
275#624—42no—
276#624—42no—
277#624—42no—
278#624—42no—
279#624D814yescomplemented
280C32×C8—21no—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284#532—91no—
285C2×C4×D4—91no—
286#480—91no—
287#480—91no—
288#474—31no—
289#474—91no—
290#459—91no—
291#459—91no—
292#447—91no—
293#447—91no—
294C4×D8—31no—
295C4×D8—91no—
296C4×D8—91no—
297C4×D8—91no—
298#431—91no—
299C23×D3—61no—
300C23×D3—61no—
301C23×D3—121no—
302C2×C3×Q8—61no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—121no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318#239—124no—
319D3×D4—62no—
320D3×D4—62no—
321D3×D4—62no—
322D3×D4—62no—
323D3×D4—122no—
324D3×D4—122no—
325#235—124no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—121no—
338C2×D12C22×D311yescharacteristic
339C2×C4×D3—21no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—124no—
356C2×C4×D3—124no—
357C2×Dic6—21no—
358C3×D8—62no—
359C2×C3×C8—21no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8C22×D311yescharacteristic
363C2×C3×C8C22×D311yescharacteristic
364C3×C4⋊C4—21no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C42—31no—
375C3×C42—31no—
376#217—21no—
377#217—21no—
378#217—61no—
379#213—22no—
380#213—62no—
381#213—62no—
382#213—62no—
383#213—122no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—121no—
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398Dic3⋊C4—21no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3C22×D311yescharacteristic
406C4×Dic3C22×D311yescharacteristic
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D24—62no—
413D24—62no—
414D24—62no—
415D24—122no—
416C22×C32—22no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3—22no—
423C2×C3⋊D3—48no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3C2×D812yes—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4C2×#4111yescharacteristic
436C3⋊Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3C2×D812yes—
443C3×Dic3C2×D812yes—
444C2×#41—181no—
445C22×D4—91no—
446C23×C4—181no—
447C2×D8—31no—
448C2×D8—91no—
449C2×D8—91no—
450C2×D8—91no—
451C4⋊Q8—31no—
452#127—91no—
453#124—181no—
454#121—91no—
455#121—91no—
456#121—181no—
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—31no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—181no—
464C4×D4—181no—
465C4×D4—181no—
466C2×C4⋊C4—91no—
467C2×C22⋊C4—181no—
468C2×C42—91no—
469#107—31no—
470#107—31no—
471#107—31no—
472#107—91no—
473C4⋊C8—31no—
474C4⋊C8—91no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102D3211yescharacteristic
483C22⋊C8—91no—
484C22⋊C8—91no—
485C4×C8—31no—
486C4×C8—91no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—41no—
490C23×C3—61no—
491C22×D3—21no—
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—61no—
495C22×D3—64no—
496C22×D3—64no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—121no—
502C22×D3—124no—
503C22×D3—121no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—242no—
509C22×D3—242no—
510C3×Q8—122no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—22no—
514C3×D4—41no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4#23512yescomplemented
518C3×D4#23912yescomplemented
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—122no—
531C2×C3×C4—122no—
532C2×C3×C4—122no—
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535#67—64no—
536#67—64no—
537#67—124no—
538#67—122no—
539#67—122no—
540#67—122no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—42no—
547C2×Dic3—42no—
548C2×Dic3—61no—
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553D12—21no—
554D12—21no—
555D12—32no—
556D12—32no—
557D12—62no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—121no—
565D12—121no—
566D12—121no—
567D12—122no—
568D12—122no—
569D12—122no—
570D12—122no—
571D12—122no—
572D12—242no—
573C4×D3—34no—
574C4×D3—34no—
575C4×D3—42no—
576C4×D3—61no—
577C4×D3—61no—
578C4×D3—61no—
579C4×D3—61no—
580C4×D3—121no—
581C4×D3—121no—
582C4×D3—121no—
583C4×D3—121no—
584C4×D3—122no—
585C4×D3—122no—
586C4×D3—122no—
587C4×D3—122no—
588C4×D3—122no—
589C4×D3—122no—
590C4×D3—122no—
591C4×D3—122no—
592Dic6—42no—
593C3×C8—21no—
594C3×C8—21no—
595C3×C8—41no—
596C3×C8—61no—
597C3×C8—61no—
598C3⋊C8—21no—
599C3⋊C8—21no—
600C3⋊C8—61no—
601C3⋊C8—61no—
602C3⋊C8—121no—
603C2×C32—42no—
604C2×C32#52511yescharacteristic
605C2×C32C22×D811yescharacteristic
606C2×C32#57511yescharacteristic
607C3⋊D3—22no—
608C3⋊D3—42no—
609C3⋊D3—81no—
610C3×D3—81no—
611C24—181no—
612#41—364no—
613C2×Q8—61no—
614C2×D4—31no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—181no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—182no—
623C2×D4—182no—
624C2×D4C2×D3211yescharacteristic
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—91no—
629C22×C4—91no—
630C22×C4—91no—
631C22×C4—181no—
632C22×C4—181no—
633C22×C4—181no—
634C22×C4—181no—
635C22×C4—364no—
636D8—62no—
637D8—182no—
638D8—182no—
639D8—182no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—91no—
643C2×C8C2×D3211yescharacteristic
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—61no—
648C4⋊C4—181no—
649C4⋊C4C2×D3211yescharacteristic
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C42—31no—
659C42—31no—
660C42—91no—
661C42—91no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—21no—
665C22×C3—42no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3C2×D3×D411yescharacteristic
676C22×C3C2×D3×D411yescharacteristic
677C2×D3—32no—
678C2×D3—32no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—62no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—62no—
688C2×D3—62no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—122no—
692C2×D3—128no—
693C2×D3—128no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—248no—
705C2×D3—241no—
706C2×D3—241no—
707C2×D3—241no—
708C2×D3—241no—
709C2×D3—241no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—32no—
713C3×C4—32no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—81no—
719C3×C4—121no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4C2×#23511yescharacteristic
723C3×C4C2×#23911yescharacteristic
724C3×C4D3×#4111yescharacteristic
725C3×C4D3×#4111yescharacteristic
726Dic3—21no—
727Dic3—21no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731Dic3—61no—
732Dic3—61no—
733Dic3—121no—
734Dic3D3×D812yes—
735Dic3D3×D812yes—
736C32#310011yescharacteristic, complemented, Sylow
737C23—21no—
738C23—61no—
739C23—91no—
740C23—184no—
741C23—181no—
742C23—181no—
743C23—362no—
744C23—362no—
745Q8—122no—
746D4—21no—
747D4—61no—
748D4—61no—
749D4—92no—
750D4—184no—
751D4—181no—
752D4—181no—
753D4—181no—
754D4—362no—
755D4—362no—
756D4—362no—
757D4—362no—
758D4#379912yescomplemented
759C2×C4—21no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—94no—
768C2×C4—91no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4—181no—
773C2×C4—181no—
774C2×C4—362no—
775C2×C4—362no—
776C2×C4—362no—
777C2×C4—361no—
778C2×C4—362no—
779C2×C4C22×D3211yescharacteristic
780C8—21no—
781C8—61no—
782C8—61no—
783C8—181no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—42no—
788C2×C3—42no—
789C2×C3—82no—
790C2×C3—241no—
791C2×C3#554711yescharacteristic
792C2×C3#562711yescharacteristic
793C2×C3C2×D3×D811yescharacteristic
794C2×C3C2×D3×D811yescharacteristic
795C2×C3#576811yescharacteristic
796C2×C3#577711yescharacteristic
797D3—62no—
798D3—62no—
799D3—81no—
800D3—122no—
801D3—122no—
802D3—122no—
803D3—242no—
804D3—241no—
805D3—241no—
806D3—481no—
807C22—22no—
808C22—41no—
809C22—41no—
810C22—92no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—181no—
815C22—181no—
816C22—182no—
817C22—368no—
818C22—361no—
819C22—361no—
820C22—361no—
821C22—361no—
822C22—361no—
823C22D32×D411yescharacteristic
824C4—32no—
825C4—32no—
826C4—41no—
827C4—61no—
828C4—61no—
829C4—121no—
830C4—121no—
831C4—121no—
832C4—181no—
833C4C2×#379911yescharacteristic
834C4#6431211yescharacteristic
835C3—21no—
836C3#7959011yescharacteristic, complemented
837C3#8094811yescharacteristic, complemented
838C2—42no—
839C2—182no—
840C2—241no—
841C2—362no—
842C2—721no—
843C2#1059406611yescharacteristic
844C2D32×D811yescharacteristic
845C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3100
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. D4×#624C2semidirect
2. #10594518C2semidirect
3. #10592472C2semidirect
4. C3×#4759C2semidirect
5. C3×#4756C2semidirect
6. #10591481C2semidirect
7. #10591456C2semidirect
8. #10591400C2semidirect
9. #10590765C2semidirect
10. #10590763C2semidirect
11. #10590650C2semidirect
12. #10590643C2semidirect
13. #10590464C2semidirect
14. #10590456C2semidirect
15. #10590442C2semidirect
27. C3×#893C22semidirect
28. C3×#888C22semidirect
33. #63911C22semidirect
40. #63894C22semidirect
47. C3×#821C22semidirect
48. C3×#818C22semidirect
49. C3×Dic3⋊C8C22semidirect
50. C3×C8×Dic3C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
87. #4759D3semidirect
89. #4756D3semidirect
182. #893C2×D3semidirect
185. #888C2×D3semidirect
213. #821C2×D3semidirect
219. #818C2×D3semidirect
221. Dic3⋊C8C2×D3semidirect
223. C8×Dic3C2×D3semidirect
233. #807C2×D3semidirect
234. #807C2×D3semidirect
246. C32×D4#41semidirect
255. C4⋊(C3⋊D3)#41semidirect
279. #624D8semidirect
517. C3×D4#235semidirect
518. C3×D4#239semidirect
736. C32#3100semidirect
758. D4#3799semidirect
836. C3#79590semidirect
837. C3#80948semidirect

Maximal subgroups

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

subgroupindex
D4×#6242
#105945182
#105924722
C3×#47592
C3×#47562
#105914812
#105914562
#105914002
#105907652
#105907632
#105906502
#105906432
#105904642
#105904562
#105904422
#809483
#795903