Finite Group Databasebeta

← #11870878

Subgroups — #11870878

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595191C211yesmaximal, characteristic, complemented
2D4×#624C211yesmaximal, characteristic, complemented
3#10592855C211yesmaximal, characteristic
4C3×#5153C211yesmaximal, characteristic, complemented
5C3×Dic3×D8C211yesmaximal, characteristic, complemented
6#10591467C211yesmaximal, characteristic, complemented
7Dic3×#214C211yesmaximal, characteristic, complemented
8#10591432C211yesmaximal, characteristic, complemented
9#10591419C211yesmaximal, characteristic, complemented
10#10591409C211yesmaximal, characteristic, complemented
11#10591400C211yesmaximal, characteristic, complemented
12#10590792C211yesmaximal, characteristic, complemented
13#10590774C211yesmaximal, characteristic, complemented
14#10590689C211yesmaximal, characteristic, complemented
15#10590643C211yesmaximal, characteristic, complemented
16#80505—31nomaximal
17#79592—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×#624—21no—
20C2×C32×D8C2211yescharacteristic
21#64147C2211yescharacteristic
22C2×#3753C2211yescharacteristic
23C3×#936C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic, complemented
27C2×C3×#214C2211yescharacteristic
28#63975—21no—
29#63974—21no—
30#63956—21no—
31#63955—21no—
32#63952—21no—
33#63952—21no—
34#63952—21no—
35#63900C2211yescharacteristic
36#63894C2211yescharacteristic
37#63894C2211yescharacteristic
38C4×#624C2211yescharacteristic
39#63871C2211yescharacteristic
40#63869C2211yescharacteristic, complemented
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43#63659C2211yescharacteristic
44#63648C2211yescharacteristic
45#63647C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#818C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5680—31no—
62#5557—31no—
63C4×D3×D4—31no—
64C4×D3×D4—31no—
65C3×#463—31no—
66C3×C4×D8—31no—
67#5169—31no—
68Dic3×SD16—31no—
69#5156—31no—
70#5156—31no—
71#5156—61no—
72#5153D311yescharacteristic, complemented
73Dic3×D8D311yescharacteristic, complemented
74#5057—31no—
75C4×#214—31no—
76C4×#213—31no—
77#5009—31no—
78#4891—31no—
79#4884—31no—
80#4847—31no—
81#4833—31no—
82#4811—31no—
83#4788—31no—
84#4787—31no—
85#4777—31no—
86#4777—31no—
87#4776—31no—
88#4763—31no—
89#4756—31no—
90C4×#204—31no—
91#4685—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3—22no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#624—21no—
106C2×#624—21no—
107C2×#624—21no—
108C2×#624—44no—
109C2×#624D411yescharacteristic
110C2×#624D411yescharacteristic
111C32×D8—22no—
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114#3753—22no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#214—22no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138Dic32—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141#3717—22no—
142#3105—91noSylow
143C2×D3×D4—31no—
144C2×D3×D4—31no—
145C2×D3×D4—61no—
146C22×C4×D3—61no—
147C22×C4×D3—61no—
148C2×C3×SD16—31no—
149C2×C3×D8—21no—
150C2×C3×D8C2×D311yescharacteristic
151C2×C3×D8C2×D311yescharacteristic
152C3×#124—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156#946—31no—
157Q8×Dic3—31no—
158C2×#215—31no—
159#938—31no—
160#938—31no—
161#938—61no—
162#936C2×D311yescharacteristic, complemented
163D4×Dic3C2×D311yescharacteristic
164D4×Dic3C2×D311yescharacteristic
165D4×Dic3C2×D311yescharacteristic, complemented
166C2×#214C2×D311yescharacteristic
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—61no—
170C4×#67—61no—
171C4×#67—61no—
172C4×#67—61no—
173#926—61no—
174C2×#204—31no—
175#897—31no—
176#893—31no—
177#893—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—31no—
180#890—31no—
181#883—61no—
182#883—61no—
183#67⋊C4—61no—
184#67⋊C4—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#879—61no—
189#879—61no—
190#877—61no—
191C4×D12—31no—
192C4×D12—31no—
193C42×D3—31no—
194C42×D3—31no—
195#870—31no—
196C4×Dic6—31no—
197C3×#107—31no—
198C3×C4⋊C8—31no—
199C3×#103—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×C4×C8—31no—
204#835—31no—
205#832—31no—
206#832—31no—
207#832—61no—
208#832C2×D311yescharacteristic
209#832C2×D311yescharacteristic, complemented
210#832C2×D311yescharacteristic, complemented
211#821—31no—
212#821—31no—
213#821—31no—
214#821—61no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220#818C2×D311yescharacteristic, complemented
221#817—31no—
222#817—31no—
223#816C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8C2×D311yescharacteristic, complemented
226C8×Dic3—31no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#810—31no—
229#809—31no—
230#808—31no—
231#808—31no—
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C4×C3⋊C8—31no—
236C23×C32—21no—
237C23×C32—21no—
238C22×C3⋊D3—24no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—42no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4C2411yescharacteristic
248#638—24no—
249#638—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)#4112yes—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
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×Dic6—21no—
268C3×Dic6—21no—
269#624—22no—
270#624—22no—
271#624—42no—
272#624—42no—
273#624—42no—
274C32×C8—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#529—91no—
279C2×C4×D4—91no—
280#484—91no—
281#481—91no—
282#478—91no—
283#478—91no—
284#463—31no—
285#463—91no—
286#450—91no—
287#447—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×D8—31no—
291C4×D8—91no—
292#431—91no—
293C23×D3—61no—
294C23×D3—61no—
295C23×D3—121no—
296C2×C3×Q8—31no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—121no—
311C2×#67—121no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315D3×D4—62no—
316D3×D4—62no—
317D3×D4—62no—
318D3×D4—62no—
319D3×D4—122no—
320D3×D4—122no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—124no—
338C2×C4×D3—124no—
339C2×Dic6C22×D311yescharacteristic
340C3×SD16—62no—
341C3×D8—22no—
342C3×D8—22no—
343C3×D8—42no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358C3×C42—31no—
359#217—21no—
360#217—21no—
361#217—21no—
362#217—21no—
363#217—21no—
364#217—61no—
365#217—61no—
366#217—121no—
367#215—62no—
368#214—22no—
369#213—62no—
370#213—62no—
371#213—122no—
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—61no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407#204—62no—
408C22×C32—22no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3—48no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3#13512yes—
422C32×C4C2×#4111yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—21no—
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3AGL(1,ℤ/8)12yes—
434C22×D4—91no—
435C23×C4—181no—
436C2×SD16—31no—
437C2×SD16—91no—
438C2×D8—91no—
439C2×D8D3211yescharacteristic
440#126—181no—
441#125—91no—
442#124—31no—
443#123—181no—
444C22⋊Q8—91no—
445#121—91no—
446C4×Q8—91no—
447C4×D4—31no—
448C4×D4—31no—
449C4×D4—31no—
450C4×D4—91no—
451C4×D4—91no—
452C4×D4—181no—
453C4×D4—181no—
454C4×D4—181no—
455#117—181no—
456C2×C4⋊C4—91no—
457C2×C22⋊C4—181no—
458C2×C42—91no—
459#107—31no—
460#107—91no—
461#106—91no—
462#106—91no—
463C4⋊C8—31no—
464C4⋊C8—91no—
465#103—31no—
466#103—91no—
467#102—31no—
468#102—31no—
469#102—31no—
470#102—91no—
471#102—91no—
472#102—91no—
473C22⋊C8—91no—
474C22⋊C8—91no—
475C4×C8—31no—
476C4×C8—91no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—41no—
482C23×C3—41no—
483C22×D3—31no—
484C22×D3—31no—
485C22×D3—61no—
486C22×D3—64no—
487C22×D3—64no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3—124no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—242no—
497C22×D3—242no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—41no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4#23512yes—
511C3×D4#23712yes—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—122no—
522C2×C3×C4—122no—
523C2×C3×C4—122no—
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—64no—
527#67—64no—
528#67—124no—
529#67—122no—
530#67—122no—
531#67—242no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—42no—
539C2×Dic3—42no—
540C2×Dic3—42no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—121no—
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547C2×Dic3D3×D411yescharacteristic
548C2×Dic3D3×D411yescharacteristic
549D12—32no—
550D12—32no—
551D12—62no—
552D12—61no—
553D12—61no—
554D12—121no—
555C4×D3—62no—
556C4×D3—62no—
557C4×D3—62no—
558C4×D3—61no—
559C4×D3—61no—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—62no—
563C4×D3—121no—
564C4×D3—121no—
565C4×D3—122no—
566C4×D3—122no—
567C4×D3—122no—
568C4×D3—122no—
569C4×D3—122no—
570C4×D3—122no—
571Dic6—21no—
572Dic6—21no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32—42no—
584C2×C32—81no—
585C2×C32#52511yescharacteristic
586C2×C32C2×#13511yescharacteristic
587C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
588C3⋊D3—22no—
589C3⋊D3—42no—
590C24—181no—
591C2×Q8—31no—
592C2×D4—91no—
593C2×D4—181no—
594C2×D4—182no—
595C2×D4—182no—
596C2×D4—181no—
597C2×D4C2×D3211yescharacteristic
598C2×D4C2×D3211yescharacteristic
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—91no—
603C22×C4—91no—
604C22×C4—91no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—364no—
609SD16—62no—
610SD16—182no—
611D8—22no—
612D8—182no—
613C2×C8—31no—
614C2×C8—31no—
615C2×C8—91no—
616C2×C8C2×D3211yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—91no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C42—31no—
636C42—31no—
637C42—91no—
638C42—91no—
639C42—181no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—21no—
643C22×C3—42no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—32no—
662C2×D3—32no—
663C2×D3—62no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—122no—
673C2×D3—128no—
674C2×D3—128no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—248no—
680C2×D3—241no—
681C2×D3—241no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—32no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4C2×#23511yescharacteristic
693C3×C4C2×#23711yescharacteristic
694C3×C4D3×#4111yescharacteristic
695C3×C4D3×#4111yescharacteristic
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—41no—
703Dic3—61no—
704Dic3—61no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—241no—
709Dic3#91112yes—
710C32#310511yescharacteristic, complemented, Sylow
711C23—21no—
712C23—21no—
713C23—91no—
714C23—184no—
715C23—181no—
716C23—362no—
717C23—362no—
718Q8—61no—
719Q8—61no—
720D4—21no—
721D4—21no—
722D4—21no—
723D4—92no—
724D4—184no—
725D4—181no—
726D4—362no—
727D4#380412yes—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—91no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—182no—
741C2×C4—182no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—362no—
746C2×C4—362no—
747C2×C4—362no—
748C2×C4C22×D3211yescharacteristic
749C8—21no—
750C8—61no—
751C8—61no—
752C8—181no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—42no—
757C2×C3—42no—
758C2×C3—82no—
759C2×C3—81no—
760C2×C3—81no—
761C2×C3—161no—
762C2×C3#554711yescharacteristic
763C2×C3#560611yescharacteristic
764C2×C3C2×#91111yescharacteristic
765C2×C3D3×#13511yescharacteristic
766C2×C3D3×#13511yescharacteristic
767C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
768D3—62no—
769D3—62no—
770D3—122no—
771D3—122no—
772D3—122no—
773D3—242no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—92no—
781C22—181no—
782C22—181no—
783C22—182no—
784C22—368no—
785C22—361no—
786C22—361no—
787C22D32×D411yescharacteristic
788C4—32no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—121no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—181no—
797C4—361no—
798C4#6431211yescharacteristic
799C4C2×#380411yescharacteristic
800C3—21no—
801C3#7959211yescharacteristic, complemented
802C3#8050511yescharacteristic, complemented
803C2—42no—
804C2—81no—
805C2—182no—
806C2—362no—
807C2D3×#91111yescharacteristic
808C2#1059473011yescharacteristic
809C2#1059513811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radical#10592855C2
hypercenterC2×D8D32
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595191C2semidirect
2. D4×#624C2semidirect
4. C3×#5153C2semidirect
5. C3×Dic3×D8C2semidirect
6. #10591467C2semidirect
7. Dic3×#214C2semidirect
8. #10591432C2semidirect
9. #10591419C2semidirect
10. #10591409C2semidirect
11. #10591400C2semidirect
12. #10590792C2semidirect
13. #10590774C2semidirect
14. #10590689C2semidirect
15. #10590643C2semidirect
23. C3×#936C22semidirect
26. C3×D4×Dic3C22semidirect
40. #63869C22semidirect
41. Dic3×Dic6C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#818C22semidirect
50. C3×#816C22semidirect
51. C3×Dic3⋊C8C22semidirect
52. C3×C8×Dic3C22semidirect
53. #63576C22semidirect
54. #63573C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
72. #5153D3semidirect
73. Dic3×D8D3semidirect
162. #936C2×D3semidirect
165. D4×Dic3C2×D3semidirect
209. #832C2×D3semidirect
210. #832C2×D3semidirect
220. #818C2×D3semidirect
223. #816C2×D3semidirect
225. Dic3⋊C8C2×D3semidirect
227. C8×Dic3C2×D3semidirect
710. C32#3105semidirect
801. C3#79592semidirect
802. C3#80505semidirect

Maximal subgroups

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

subgroupindex
#105951912
D4×#6242
#105928552
C3×#51532
C3×Dic3×D82
#105914672
Dic3×#2142
#105914322
#105914192
#105914092
#105914002
#105907922
#105907742
#105906892
#105906432
#805053
#795923