Finite Group Databasebeta

← #11889768

Subgroups — #11889768

Order 1152.

870 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595228C211yesmaximal, characteristic
2#10594532C211yesmaximal, characteristic, complemented
3#10592464C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×#4774C211yesmaximal, characteristic, complemented
6#10591502C211yesmaximal, characteristic, complemented
7#10591443C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590960C211yesmaximal, characteristic, complemented
10#10590779C211yesmaximal, characteristic, complemented
11#10590725C211yesmaximal, characteristic, complemented
12#10590684C211yesmaximal, characteristic, complemented
13#10590607C211yesmaximal, characteristic, complemented
14#10590579C211yesmaximal, characteristic, complemented
15#10590471C211yesmaximal, characteristic, complemented
16#81289—31nomaximal
17#80163—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64145C2211yescharacteristic
21#64097C2211yescharacteristic, complemented
22C3×#938C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic, complemented
27#63976—21no—
28#63970—21no—
29#63969—21no—
30D3×#217—21no—
31C4×#625C2211yescharacteristic
32#63898C2211yescharacteristic
33#63896—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63879—21no—
36#63857—21no—
37#63857C2211yescharacteristic
38#63856C2211yescharacteristic, complemented
39#63847—21no—
40#63843C2211yescharacteristic, complemented
41C2×#3719C2211yescharacteristic, complemented
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47#63642C2211yescharacteristic, complemented
48#63637C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5806—31no—
62#5635—31no—
63#5612—31no—
64#5511—31no—
65C3×#480—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5174—31no—
69#5173—31no—
70#5166—31no—
71#5164—31no—
72#5051—31no—
73#5042—31no—
74#4966—31no—
75#4890—31no—
76#4889—31no—
77#4887—31no—
78#4884—31no—
79#4776D311yescharacteristic, complemented
80#4774D311yescharacteristic, complemented
81#4771—31no—
82D3×#102—31no—
83#4767—31no—
84#4765—31no—
85#4765—31no—
86#4765—61no—
87#4759—31no—
88#4733—31no—
89#4730—31no—
90#4728—31no—
91#4722—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#634—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×D3×D4—22no—
99C3×D3×D4—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#625—21no—
106C2×#625D411yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3757—21no—
115#3757—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#214—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×#204—22no—
130#3724—21no—
131#3724D411yescharacteristic
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3719—41no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235—31no—
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C3×C22⋊Q8—31no—
152C3×#121—31no—
153C2×C3×C4⋊C4—31no—
154#953—61no—
155C2×#217—61no—
156#946—31no—
157Q8×Dic3—31no—
158C2×#216—31no—
159#939—61no—
160#938—61no—
161#938C2×D311yescharacteristic
162#937—61no—
163#936—31no—
164#936—31no—
165#936—61no—
166#935—61no—
167D4×Dic3—31no—
168C2×#214C2×D311yescharacteristic
169C4×#67—31no—
170C4×#67—31no—
171C4×#67—61no—
172C2×C4⋊Dic3—31no—
173#924—31no—
174#924—31no—
175#924—61no—
176C2×#208—31no—
177C22×C3⋊C8—31no—
178C2×Dic12—31no—
179C2×#204C2×D311yescharacteristic
180C2×ΓL(1,𝔽25)—31no—
181C2×D3×C8—31no—
182#897—31no—
183#897—61no—
184#897C2×D311yescharacteristic
185#896—61no—
186#893—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4C2×D311yescharacteristic, complemented
189#889—61no—
190#889—61no—
191#888—31no—
192#888—31no—
193#888—61no—
194#887—31no—
195#883—61no—
196#67⋊C4—61no—
197D3×C22⋊C4—61no—
198#878—61no—
199C3×#107—31no—
200C3×#107—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102C2×D311yescharacteristic
205C3×#102C2×D311yescharacteristic
206C3×C22⋊C8—31no—
207C3×C22⋊C8—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic
215#821—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217(C2×D3)⋊C8C2×D311yescharacteristic, complemented
218#818—31no—
219#818C2×D311yescharacteristic, complemented
220#816—31no—
221#816—31no—
222#816—31no—
223#816—61no—
224#815—31no—
225#815—31no—
226#815—61no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—31no—
233#810—61no—
234#809—31no—
235#809C2×D311yescharacteristic
236#807—31no—
237#807C2×D311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253#634—21no—
254#634—21no—
255#634—81no—
256C3×#67—42no—
257C3×#67—81no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#625—22no—
273#625—42no—
274D3×Dic3—42no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—31no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—31no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—31no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4—121no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—21no—
312C2×#67—31no—
313C2×#67—31no—
314C2×#67—61no—
315C2×#67—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319#237—62no—
320#237—121no—
321D3×D4—22no—
322D3×D4—41no—
323#235—62no—
324#235—121no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—121no—
338C2×Dic6C22×D311yescharacteristic
339C3×SD16—62no—
340C3×SD16—121no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355#217—21no—
356#217—31no—
357#217—31no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—121no—
366#217—121no—
367#216—121no—
368#214—41no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375C4⋊Dic3—21no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—121no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400#208—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407Dic12—121no—
408#204—22no—
409ΓL(1,𝔽25)—121no—
410D3×C8—121no—
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—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—84no—
424C2×C3×D3#13712yes—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—31no—
441C2×SD16—31no—
442C2×M16—91no—
443C22×C8—91no—
444C4⋊Q8—91no—
445#125—181no—
446#124—91no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453#121—31no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—31no—
464#107—31no—
465#107—91no—
466C4⋊C8—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102D3211yescharacteristic
477C22⋊C8—31no—
478C22⋊C8—31no—
479#97—91no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3—241no—
489C22×D3—21no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3—81no—
493C22×D3D3×D411yescharacteristic
494C22×D3D3×D411yescharacteristic
495C3×Q8—61no—
496C3×Q8—61no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—32no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—61no—
505C3×D4—122no—
506C3×D4—241no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—241no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—42no—
524#67—62no—
525#67—62no—
526#67—81no—
527#67—122no—
528#67—122no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—122no—
545C2×Dic3—241no—
546C2×Dic3—241no—
547C2×Dic3D3×D411yescharacteristic
548C2×Dic3D3×D411yescharacteristic
549D12—21no—
550D12#23712yes—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—81no—
556C4×D3—122no—
557C4×D3—241no—
558C4×D3—241no—
559Dic6—21no—
560Dic6—21no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—121no—
566Dic6—121no—
567Dic6—241no—
568Dic6—241no—
569Dic6—242no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—41no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—121no—
580C2×C32—81no—
581C2×C32#54611yescharacteristic
582C2×C32C2×#13711yescharacteristic
583C2×C32#57611yescharacteristic
584C3×D3—22no—
585C3×D3—41no—
586C3×D3—42no—
587C24—61no—
588#41—182no—
589#41—361no—
590C2×Q8—31no—
591C2×Q8—91no—
592C2×Q8—181no—
593C2×D4—31no—
594C2×D4—61no—
595C2×D4—62no—
596C2×D4—61no—
597C2×D4—91no—
598C2×D4—121no—
599C2×D4—181no—
600C2×D4C2×D3211yescharacteristic
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4—181no—
607Q16—361no—
608SD16—62no—
609SD16—121no—
610M16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—361no—
615C2×C8C2×D3211yescharacteristic
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—91no—
621C4⋊C4—91no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4C2×D3211yescharacteristic
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—91no—
631C22⋊C4—91no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C42—91no—
638C42—181no—
639C22×C3—21no—
640C22×C3—32no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—62no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—244no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—84no—
670C2×D3#91512yes—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—81no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4C2×#23711yescharacteristic
682C3×C4#100411yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4#100911yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—61no—
691Dic3—61no—
692Dic3—61no—
693Dic3—61no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701Dic3—241no—
702C32#331411yescharacteristic, complemented, Sylow
703C23—21no—
704C23—31no—
705C23—31no—
706C23—61no—
707C23—122no—
708C23—122no—
709C23—241no—
710Q8—61no—
711Q8—61no—
712Q8—181no—
713Q8—181no—
714Q8—721no—
715D4—21no—
716D4—21no—
717D4—32no—
718D4—61no—
719D4—122no—
720D4—182no—
721D4—241no—
722D4—362no—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—241no—
738C2×C4—362no—
739C2×C4—721no—
740C2×C4—721no—
741C2×C4C22×D3211yescharacteristic
742C8—21no—
743C8—61no—
744C8—61no—
745C8—181no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—62no—
750C2×C3—81no—
751C2×C3—81no—
752C2×C3—121no—
753C2×C3—122no—
754C2×C3—161no—
755C2×C3#559111yescharacteristic
756C2×C3#565411yescharacteristic
757C2×C3#575711yescharacteristic
758C2×C3C2×#91511yescharacteristic
759C2×C3#577411yescharacteristic
760C2×C3D3×#13711yescharacteristic
761D3—22no—
762D3—42no—
763D3—41no—
764C22—32no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—62no—
774C22—121no—
775C22—121no—
776C22—244no—
777C22D32×D411yescharacteristic
778C4—41no—
779C4—61no—
780C4—61no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—181no—
785C4—181no—
786C4—361no—
787C4—361no—
788C4#6430711yescharacteristic
789C4D3×#23711yescharacteristic
790C3—21no—
791C3#8016311yescharacteristic, complemented
792C3#8128911yescharacteristic, complemented
793C2—62no—
794C2—81no—
795C2—121no—
796C2—122no—
797C2#1059427411yescharacteristic
798C2#1059473211yescharacteristic
799C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595228C2
hypercenter#102D32
hypocenterC32#3314
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
2. #10594532C2semidirect
3. #10592464C2semidirect
4. C3×#4776C2semidirect
5. C3×#4774C2semidirect
6. #10591502C2semidirect
7. #10591443C2semidirect
8. D3×#832C2semidirect
9. #10590960C2semidirect
10. #10590779C2semidirect
11. #10590725C2semidirect
12. #10590684C2semidirect
13. #10590607C2semidirect
14. #10590579C2semidirect
15. #10590471C2semidirect
21. #64097C22semidirect
26. C3×D3×C4⋊C4C22semidirect
38. #63856C22semidirect
40. #63843C22semidirect
41. C2×#3719C22semidirect
42. C2×#3711C22semidirect
46. #63643C22semidirect
47. #63642C22semidirect
48. #63637C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#818C22semidirect
54. C3×#807C22semidirect
55. #63575C22semidirect
56. #63572C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
79. #4776D3semidirect
80. #4774D3semidirect
188. D3×C4⋊C4C2×D3semidirect
217. (C2×D3)⋊C8C2×D3semidirect
219. #818C2×D3semidirect
237. #807C2×D3semidirect
702. C32#3314semidirect
791. C3#80163semidirect
792. C3#81289semidirect

Maximal subgroups

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

subgroupindex
#105952282
#105945322
#105924642
C3×#47762
C3×#47742
#105915022
#105914432
D3×#8322
#105909602
#105907792
#105907252
#105906842
#105906072
#105905792
#105904712
#812893
#801633