Finite Group Databasebeta

← #11889757

Subgroups — #11889757

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595371C211yesmaximal, characteristic, complemented
2#10595229C211yesmaximal, characteristic
3#10592873C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic, complemented
5C3×#5166C211yesmaximal, characteristic, complemented
6#10591656C211yesmaximal, characteristic, complemented
7#10591635C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10591488C211yesmaximal, characteristic, complemented
10#10591417C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic, complemented
12#10590957C211yesmaximal, characteristic, complemented
13#10590907C211yesmaximal, characteristic, complemented
14#10590762C211yesmaximal, characteristic, complemented
15#10590682C211yesmaximal, characteristic, complemented
16#80619—31nomaximal
17#80163—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21#64155C2211yescharacteristic, complemented
22#64147C2211yescharacteristic
23C2×#3743C2211yescharacteristic, complemented
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#936C2211yescharacteristic
29#63977—21no—
30#63971—21no—
31#63969—21no—
32D3×#217—21no—
33#63918C2211yescharacteristic, complemented
34C4×#626C2211yescharacteristic
35#63900C2211yescharacteristic, complemented
36#63899—21no—
37#63895—21no—
38Dic3×D12C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63880—21no—
41#63867—21no—
42#63856C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic, complemented
45#63659C2211yescharacteristic
46#63645C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#5806—31no—
62#5676—31no—
63#5635—31no—
64#5579—31no—
65C3×#464—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5188—31no—
69#5187—31no—
70#5174—31no—
71#5174—31no—
72#5174—61no—
73#5173—31no—
74#5169D311yescharacteristic, complemented
75#5166D311yescharacteristic, complemented
76#5164—31no—
77#5055—31no—
78#5051—31no—
79#5026—31no—
80#4846—31no—
81#4836—31no—
82#4811—31no—
83#4803—31no—
84#4774—31no—
85#4774—31no—
86#4771—31no—
87D3×#102—31no—
88#4765—31no—
89#4759—31no—
90#4730—31no—
91#4722—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×#67—21no—
98C3×D3×D4—22no—
99C3×D3×D4—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626D411yescharacteristic
106C2×#624—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796—41no—
112C32×SD16—41no—
113C2×C32×C8C2311yescharacteristic
114#3757—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3743—41no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#216—41no—
124C3×#215—22no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3D411yescharacteristic
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—21no—
151C2×C3×SD16—31no—
152C2×C3×SD16C2×D311yescharacteristic
153C2×C3×SD16C2×D311yescharacteristic
154C3×#124—31no—
155C3×C22⋊Q8—31no—
156C3×C4×Q8—31no—
157#953—61no—
158C2×#217—61no—
159#946—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163#946C2×D311yescharacteristic
164Q8×Dic3C2×D311yescharacteristic, complemented
165C2×#216C2×D311yescharacteristic, complemented
166C2×#215C2×D311yescharacteristic
167#939—61no—
168#938—31no—
169#938—31no—
170#938—61no—
171#936C2×D311yescharacteristic
172#935—61no—
173D4×Dic3—31no—
174C4×#67—31no—
175C2×C4⋊Dic3—31no—
176#924—31no—
177C22×C3⋊C8—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×ΓL(1,𝔽25)—61no—
181C2×D3×C8—31no—
182#897—61no—
183#896—61no—
184#896—61no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188#889—61no—
189#888—31no—
190#884—61no—
191#883—61no—
192#882—61no—
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195#878—61no—
196C4×D12—31no—
197C4×D12—31no—
198C4×D12—61no—
199#870—61no—
200#869—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—61no—
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#821—31no—
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8C2×D311yescharacteristic
224#818—31no—
225#818—31no—
226#818—31no—
227#818—31no—
228#818—61no—
229#816—31no—
230#816C2×D311yescharacteristic, complemented
231#815—31no—
232Dic3⋊C8C2×D311yescharacteristic, complemented
233#810—31no—
234#809—31no—
235#807—31no—
236#807—31no—
237#803—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251#638—81no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#627—81no—
271#626—22no—
272#626—42no—
273#624—81no—
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—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—31no—
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—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C2×C3×D4—62no—
306C2×C3×D4—121no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—31no—
310C2×#67—21no—
311C2×#67—31no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—121no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319#239—62no—
320#239—121no—
321#237—62no—
322#237—121no—
323D3×D4—22no—
324D3×D4—41no—
325C2×D12—31no—
326C2×D12—61no—
327C2×D12C22×D311yescharacteristic
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×D3C22×D311yescharacteristic
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6C22×D311yescharacteristic
340C3×Q16—121no—
341C3×SD16—41no—
342C3×SD16—41no—
343C3×SD16—42no—
344C3×SD16—62no—
345C2×C3×C8—21no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358C3×C42—61no—
359#217—21no—
360#217—21no—
361#217—31no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—121no—
367#216—41no—
368#215—22no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
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—21no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—121no—
401C4×Dic3—21no—
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409ΓL(1,𝔽25)—121no—
410ΓL(1,𝔽25)—121no—
411ΓL(1,𝔽25)—122no—
412D3×C8—121no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—84no—
426C2×C3×D3#13712yes—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—31no—
441C2×Q16—31no—
442C2×SD16—31no—
443C2×SD16D3211yescharacteristic
444C2×M16—91no—
445C22×C8—91no—
446C4⋊Q8—91no—
447#125—181no—
448#124—31no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—31no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465#107—91no—
466#107—91no—
467#107—91no—
468C4⋊C8—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3—61no—
487C23×C3—122no—
488C23×C3—122no—
489C23×C3—241no—
490C22×D3—21no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—61no—
496C22×D3—81no—
497C22×D3D3×D411yescharacteristic
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—41no—
503C3×Q8—41no—
504C3×Q8—61no—
505C3×Q8—61no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—32no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—61no—
514C3×D4—122no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—42no—
530#67—62no—
531#67—122no—
532#67—241no—
533#67—241no—
534#67—242no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—122no—
548C2×Dic3—241no—
549C2×Dic3—241no—
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553D12—21no—
554D12—62no—
555D12—122no—
556D12#23712yes—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—61no—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—61no—
563C4×D3—121no—
564C4×D3—121no—
565C4×D3—122no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570Dic6—21no—
571Dic6—21no—
572Dic6—241no—
573Dic6—241no—
574C3×C8—22no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C2×C32—81no—
585C2×C32#54611yescharacteristic
586C2×C32C2×#13711yescharacteristic
587C2×C32#57611yescharacteristic
588C3⋊D3—41no—
589C3×D3—22no—
590C3×D3—42no—
591C24—61no—
592#41—182no—
593#41—361no—
594C2×Q8—31no—
595C2×Q8—181no—
596C2×Q8C2×D3211yescharacteristic
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—62no—
600C2×D4—91no—
601C2×D4—121no—
602C2×D4—181no—
603C2×D4—181no—
604C2×D4C2×D3211yescharacteristic
605C22×C4—31no—
606C22×C4—91no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611Q16—121no—
612SD16—41no—
613SD16—62no—
614M16—361no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—91no—
618C2×C8—361no—
619C2×C8C2×D3211yescharacteristic
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—61no—
643C22×C3—21no—
644C22×C3—32no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—62no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—244no—
660C22×C3C2×D3×D411yescharacteristic
661C22×C3C2×D3×D411yescharacteristic
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—22no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—84no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3#91512yes—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C2×#23711yescharacteristic
690C3×C4#100411yescharacteristic
691C3×C4#100411yescharacteristic
692C3×C4D3×#4111yescharacteristic
693Dic3—21no—
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—61no—
700Dic3—61no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707Dic3—241no—
708C32#331411yescharacteristic, complemented, Sylow
709C23—21no—
710C23—31no—
711C23—61no—
712C23—91no—
713C23—122no—
714C23—122no—
715C23—241no—
716Q8—21no—
717Q8—21no—
718Q8—61no—
719Q8—61no—
720Q8—721no—
721D4—21no—
722D4—21no—
723D4—32no—
724D4—61no—
725D4—122no—
726D4—182no—
727D4—362no—
728D4—721no—
729C2×C4—21no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—91no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—362no—
744C2×C4—721no—
745C2×C4—721no—
746C2×C4—721no—
747C2×C4C22×D3211yescharacteristic
748C8—21no—
749C8—61no—
750C8—61no—
751C8—181no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—62no—
756C2×C3—81no—
757C2×C3—81no—
758C2×C3—122no—
759C2×C3—161no—
760C2×C3#559111yescharacteristic
761C2×C3#561211yescharacteristic
762C2×C3C2×#91511yescharacteristic
763C2×C3#576911yescharacteristic
764C2×C3#577411yescharacteristic
765C2×C3D3×#13711yescharacteristic
766D3—22no—
767D3—42no—
768D3—121no—
769D3—121no—
770D3—241no—
771C22—32no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—61no—
776C22—61no—
777C22—62no—
778C22—121no—
779C22—121no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—244no—
784C22D32×D411yescharacteristic
785C4—41no—
786C4—61no—
787C4—61no—
788C4—61no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—181no—
793C4—361no—
794C4—361no—
795C4D3×#23711yescharacteristic
796C4#6433011yescharacteristic
797C3—21no—
798C3#8016311yescharacteristic, complemented
799C3#8061911yescharacteristic, complemented
800C2—62no—
801C2—81no—
802C2—122no—
803C2—361no—
804C2D3×#91511yescharacteristic
805C2#1059475511yescharacteristic
806C2#1059529411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595229C2
hypercenterC2×SD16D32
hypocenterC32#3314
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. #10595371C2semidirect
3. #10592873C2semidirect
4. C3×#5169C2semidirect
5. C3×#5166C2semidirect
6. #10591656C2semidirect
7. #10591635C2semidirect
8. #10591566C2semidirect
9. #10591488C2semidirect
10. #10591417C2semidirect
11. D3×#832C2semidirect
12. #10590957C2semidirect
13. #10590907C2semidirect
14. #10590762C2semidirect
15. #10590682C2semidirect
21. #64155C22semidirect
23. C2×#3743C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
33. #63918C22semidirect
35. #63900C22semidirect
44. #63662C22semidirect
46. #63645C22semidirect
51. C3×#816C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63575C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
59. #63557C22semidirect
60. #63554C22semidirect
74. #5169D3semidirect
75. #5166D3semidirect
164. Q8×Dic3C2×D3semidirect
165. C2×#216C2×D3semidirect
230. #816C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
708. C32#3314semidirect
798. C3#80163semidirect
799. C3#80619semidirect

Maximal subgroups

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

subgroupindex
#105953712
#105952292
#105928732
C3×#51692
C3×#51662
#105916562
#105916352
#105915662
#105914882
#105914172
D3×#8322
#105909572
#105909072
#105907622
#105906822
#806193
#801633