Finite Group Databasebeta

← #11889735

Subgroups — #11889735

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595427C211yesmaximal, characteristic
2#10594531C211yesmaximal, characteristic, complemented
3#10592497C211yesmaximal, characteristic, complemented
4C3×#4811C211yesmaximal, characteristic, complemented
5C3×#4803C211yesmaximal, characteristic, complemented
6#10591632C211yesmaximal, characteristic, complemented
7#10591599C211yesmaximal, characteristic, complemented
8#10591596C211yesmaximal, characteristic, complemented
9#10590946C211yesmaximal, characteristic, complemented
10#10590838C211yesmaximal, characteristic, complemented
11#10590778C211yesmaximal, characteristic, complemented
12#10590724C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590422C211yesmaximal, characteristic, complemented
16#81486—31nomaximal
17#78898—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20#64156C2211yescharacteristic
21C2×#3756C2211yescharacteristic, complemented
22C2×#3744C2211yescharacteristic
23#64096C2211yescharacteristic, complemented
24C3×#946C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28#63922—21no—
29D3×(C2×D3)⋊C4—21no—
30#63919C2211yescharacteristic, complemented
31#63909C2211yescharacteristic
32C4×#625—21no—
33C4×#625C2211yescharacteristic
34#63898C2211yescharacteristic
35#63886—21no—
36#63870—21no—
37#63857C2211yescharacteristic
38#63857C2211yescharacteristic, complemented
39#63851—21no—
40#63851—21no—
41#63850—21no—
42C2×#3716C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63641C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#5829—31no—
62#5630—31no—
63#5511—31no—
64#5511—31no—
65C3×#484—31no—
66C3×#417—31no—
67#5239—31no—
68#5134—31no—
69#5127—31no—
70#5051—31no—
71#4967—31no—
72C2×#809—31no—
73#4890—31no—
74#4889—31no—
75#4886—31no—
76#4882—31no—
77#4813—31no—
78#4811D311yescharacteristic, complemented
79#4808—31no—
80#4803D311yescharacteristic, complemented
81#4798—31no—
82#4798—31no—
83#4798—61no—
84#4794—31no—
85#4794—31no—
86#4776—31no—
87D3×#102—31no—
88#4759—31no—
89#4757—31no—
90#4731—31no—
91#4730—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C3×#239—22no—
97C3×#239—41no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#627—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#625D411yescharacteristic
109C2×D3×Dic3—21no—
110D3×D12—22no—
111D3×D12—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3756—41no—
115#3752—21no—
116#3752—21no—
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3744—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×ΓL(1,𝔽25)—41no—
132#3724—21no—
133#3724D411yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3716—22no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×D3×D4—31no—
148C22×D12—31no—
149C2×C3×M16—31no—
150C3×C22⋊Q8—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153#947—31no—
154#947—31no—
155#947—61no—
156#946C2×D311yescharacteristic
157C2×#216—31no—
158C2×#216—31no—
159C2×#216—61no—
160#939—61no—
161#937—61no—
162D4×Dic3—31no—
163C2×#214—31no—
164#930—31no—
165#929—61no—
166C4×#67—31no—
167C4×#67—31no—
168C4×#67—61no—
169C4×#67—61no—
170C2×(C2×D3)⋊C4—61no—
171#924—31no—
172#924—31no—
173#924—61no—
174#924—61no—
175C22×C3⋊C8—31no—
176C2×#204—31no—
177C2×#204—31no—
178C2×#204—31no—
179C2×#204—61no—
180C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
181C2×D3×C8—31no—
182#897—31no—
183#897—31no—
184#896—61no—
185#896—61no—
186#895—31no—
187#895—61no—
188#894—61no—
189#893—31no—
190D3×C4⋊C4C2×D311yescharacteristic
191D3×C4⋊C4C2×D311yescharacteristic, complemented
192#889—61no—
193#889—61no—
194#888—31no—
195#888—31no—
196#887—31no—
197#887—31no—
198#887—61no—
199#882—61no—
200D3×C22⋊C4—61no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic, complemented
207C3×#103C2×D311yescharacteristic, complemented
208C3×#102—31no—
209C3×#102—31no—
210C3×C22⋊C8—31no—
211#835C2×D311yescharacteristic, complemented
212#835C2×D311yescharacteristic, complemented
213#832—31no—
214#830—31no—
215#821—31no—
216#821—31no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic
220#818C2×D311yescharacteristic, complemented
221#816—31no—
222#815—31no—
223#815—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227#810—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic
235#807—31no—
236#807—31no—
237#807C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255#634—21no—
256#634—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—42no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270C3×C4×D3—81no—
271C3×C4×D3—81no—
272#627—81no—
273#626—42no—
274#626—81no—
275#625—22no—
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—31no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—31no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C3×#41—62no—
299C3×#41—121no—
300C2×C3×Q8—21no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—31no—
311C2×#67—31no—
312C2×#67—61no—
313C2×#67—61no—
314C22×Dic3—61no—
315#239—22no—
316#239—41no—
317D3×D4—62no—
318D3×D4—121no—
319C2×D12—21no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—62no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—121no—
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C3×M16—121no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—61no—
355#217—31no—
356#217—31no—
357#217—61no—
358#217—61no—
359#217—61no—
360#216—121no—
361#216—121no—
362#216—122no—
363#214—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
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—121no—
377(C2×D3)⋊C4—121no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
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—
400C4×Dic3—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
407#204—62no—
408#204—121no—
409#204—121no—
410#204—122no—
411ΓL(1,𝔽25)—41no—
412D3×C8—121no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—22no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3#13712yes—
426D32—84no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—21no—
432C3⋊Dic3—21no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—31no—
440C22×D4—91no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×M16—31no—
445C22×C8—91no—
446C4⋊Q8—91no—
447#125—181no—
448#124—91no—
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—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—181no—
465#107—31no—
466#107—31no—
467#107—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103D3211yescharacteristic, complemented
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—61no—
485C22×D3—21no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—121no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—241no—
494C22×D3—241no—
495C22×D3D3×D411yescharacteristic
496C22×D3D3×D411yescharacteristic
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—41no—
502C3×Q8—41no—
503C3×D4—32no—
504C3×D4—61no—
505C3×D4—122no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—122no—
523C2×C3×C4—241no—
524C2×C3×C4—241no—
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—62no—
528#67—62no—
529#67—122no—
530#67—241no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—121no—
543C2×Dic3—241no—
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546D12—21no—
547D12—42no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—121no—
553D12—121no—
554D12—122no—
555D12—241no—
556D12#23512yes—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—42no—
562C4×D3—81no—
563C4×D3—81no—
564C4×D3—241no—
565Dic6—62no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—121no—
571Dic6—241no—
572Dic6—241no—
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#54611yescharacteristic
584C2×C32C2×#13711yescharacteristic
585C2×C32#57611yescharacteristic
586C3⋊D3—81no—
587C3×D3—22no—
588C3×D3—42no—
589C3×D3—41no—
590C24—181no—
591#41—62no—
592#41—121no—
593C2×Q8—91no—
594C2×Q8—181no—
595C2×Q8C2×D3211yescharacteristic
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—182no—
602C2×D4—181no—
603C2×D4—361no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—181no—
610Q16—361no—
611SD16—182no—
612SD16—361no—
613M16—121no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—361no—
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—91no—
641C42—181no—
642C22×C3—21no—
643C22×C3—32no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—62no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—22no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—241no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—244no—
672C2×D3—244no—
673C2×D3#91812yes—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—81no—
683C3×C4—81no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4C2×#23511yescharacteristic
688C3×C4#100411yescharacteristic
689C3×C4D3×#4111yescharacteristic
690C3×C4#100911yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—121no—
701Dic3—121no—
702Dic3—122no—
703Dic3—121no—
704Dic3—121no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—31no—
707C23—31no—
708C23—61no—
709C23—181no—
710C23—362no—
711C23—362no—
712C23—721no—
713Q8—21no—
714Q8—21no—
715Q8—181no—
716Q8—181no—
717Q8—721no—
718D4—32no—
719D4—61no—
720D4—122no—
721D4—182no—
722D4—181no—
723D4—181no—
724D4—362no—
725D4—721no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—91no—
738C2×C4—91no—
739C2×C4—122no—
740C2×C4—181no—
741C2×C4—241no—
742C2×C4—241no—
743C2×C4—721no—
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—61no—
747C8—61no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—62no—
753C2×C3—122no—
754C2×C3—121no—
755C2×C3#549011yescharacteristic
756C2×C3#565411yescharacteristic
757C2×C3C2×#91811yescharacteristic
758C2×C3#577411yescharacteristic
759C2×C3#577411yescharacteristic
760C2×C3D3×#13711yescharacteristic
761D3—22no—
762D3—41no—
763D3—42no—
764D3—241no—
765D3—241no—
766D3—481no—
767C22—32no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—62no—
774C22—121no—
775C22—121no—
776C22—361no—
777C22—361no—
778C22—361no—
779C22—724no—
780C22D32×D411yescharacteristic
781C4—41no—
782C4—41no—
783C4—61no—
784C4—61no—
785C4—121no—
786C4—121no—
787C4—121no—
788C4—181no—
789C4—181no—
790C4—361no—
791C4D3×#23511yescharacteristic
792C4#6431411yescharacteristic
793C3—21no—
794C3#7889811yescharacteristic, complemented
795C3#8148611yescharacteristic, complemented
796C2—62no—
797C2—121no—
798C2—122no—
799C2—721no—
800C2#1059427211yescharacteristic
801C2#1059475011yescharacteristic
802C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595427C2
hypercenter#103D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594531C2semidirect
3. #10592497C2semidirect
4. C3×#4811C2semidirect
5. C3×#4803C2semidirect
6. #10591632C2semidirect
7. #10591599C2semidirect
8. #10591596C2semidirect
9. #10590946C2semidirect
10. #10590838C2semidirect
11. #10590778C2semidirect
12. #10590724C2semidirect
13. D3×#809C2semidirect
14. #10590461C2semidirect
15. #10590422C2semidirect
21. C2×#3756C22semidirect
23. #64096C22semidirect
25. C2×C3×ΓL(1,𝔽25)C22semidirect
27. C3×D3×C4⋊C4C22semidirect
30. #63919C22semidirect
38. #63857C22semidirect
44. C32×#103C22semidirect
45. #63641C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. C3×#818C22semidirect
53. C3×#807C22semidirect
54. #63576C22semidirect
55. #63567C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63555C22semidirect
78. #4811D3semidirect
80. #4803D3semidirect
180. C2×ΓL(1,𝔽25)C2×D3semidirect
191. D3×C4⋊C4C2×D3semidirect
206. C3×#103C2×D3semidirect
207. C3×#103C2×D3semidirect
211. #835C2×D3semidirect
212. #835C2×D3semidirect
220. #818C2×D3semidirect
237. #807C2×D3semidirect
472. #103D32semidirect
705. C32#3314semidirect
794. C3#78898semidirect
795. C3#81486semidirect

Maximal subgroups

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

subgroupindex
#105954272
#105945312
#105924972
C3×#48112
C3×#48032
#105916322
#105915992
#105915962
#105909462
#105908382
#105907782
#105907242
D3×#8092
#105904612
#105904222
#814863
#788983