Finite Group Databasebeta

← #11889089

Subgroups — #11889089

Order 1152.

951 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#625C211yesmaximal, characteristic
2#10594456C211yesmaximal, characteristic, complemented
3#10592465C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×#4770C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591446C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590876C211yesmaximal, characteristic, complemented
10#10590833C211yesmaximal, characteristic, complemented
11#10590724C211yesmaximal, characteristic, complemented
12#10590680C211yesmaximal, characteristic, complemented
13#10590554C211yesmaximal, characteristic, complemented
14#10590505C211yesmaximal, characteristic, complemented
15#10590501C211yesmaximal, characteristic, complemented
16#80160—31nomaximal
17#78934—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×#625—21no—
21D4×C3⋊Dic3C2211yescharacteristic
22#64099C2211yescharacteristic, complemented
23C2×C3×#214C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic, complemented
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
26C3×#897C2211yescharacteristic, complemented
27C3×#892C2211yescharacteristic, complemented
28#63980—21no—
29#63976—21no—
30#63976—21no—
31#63914C2211yescharacteristic
32#63908C2211yescharacteristic
33#63908C2211yescharacteristic
34C4×#625C2211yescharacteristic
35#63891—21no—
36D3×C4⋊Dic3C2211yescharacteristic, complemented
37#63877—21no—
38#63869—21no—
39#63858—21no—
40#63856C2211yescharacteristic, complemented
41#63843C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63645C2211yescharacteristic, complemented
47#63641C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61D4×#67—31no—
62D4×#67—31no—
63#5642—31no—
64#5529—31no—
65C3×#450—31no—
66C3×#418—31no—
67#5218—31no—
68C2×#832—31no—
69#5174—31no—
70#5169—31no—
71#5164—31no—
72#5163—31no—
73#5134—31no—
74#5127—31no—
75#5048—31no—
76#5003—31no—
77#4784—31no—
78#4778—31no—
79#4776D311yescharacteristic, complemented
80#4774—31no—
81#4770D311yescharacteristic, complemented
82D3×#102—31no—
83#4766—31no—
84#4766—31no—
85#4766—61no—
86#4764—31no—
87#4764—31no—
88#4762—31no—
89#4757—31no—
90#4736—31no—
91#4730—31no—
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C3×D3×D4—41no—
101C3×D3×D4—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#625—21no—
108C2×#625—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×#625—44no—
112C2×#625D411yescharacteristic
113C2×D3×Dic3—21no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3757—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#214—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—41no—
132C3×ΓL(1,𝔽25)—41no—
133#3724—21no—
134#3724D411yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3715—41no—
144D3×C3⋊C8—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×#67—61no—
149C22×#67—61no—
150C2×D3×D4C2×D311yescharacteristic
151C2×D3×D4C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C2×C3×M16—31no—
155C3×C22⋊Q8—31no—
156C3×#117—31no—
157#953—61no—
158#953—61no—
159#946—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162#940—31no—
163#940—31no—
164#939—61no—
165#939—61no—
166#938—31no—
167#938—31no—
168#937—61no—
169#937—61no—
170D4×Dic3—31no—
171D4×Dic3—31no—
172D4×Dic3—61no—
173C2×#214—31no—
174C2×#214C2×D311yescharacteristic
175#930—31no—
176#930—31no—
177C4×#67—31no—
178C4×#67—31no—
179C2×C4⋊Dic3—31no—
180#924—31no—
181C22×C3⋊C8—31no—
182C2×#204C2×D311yescharacteristic, complemented
183C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
184C2×D3×C8—31no—
185#898—61no—
186#897C2×D311yescharacteristic, complemented
187#892C2×D311yescharacteristic, complemented
188D3×C4⋊C4—31no—
189#890—31no—
190#890—31no—
191#890—61no—
192#890—61no—
193#887—31no—
194#886—61no—
195#883—61no—
196#879—61no—
197#877—61no—
198#872—61no—
199#870—61no—
200C3×#102—21no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102C2×D311yescharacteristic
206C3×#102C2×D311yescharacteristic
207C3×C22⋊C8—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216#830—31no—
217#821—31no—
218#821—31no—
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8C2×D311yescharacteristic, complemented
222#818—31no—
223#818—31no—
224#818—31no—
225#818—61no—
226#816—31no—
227#815—31no—
228#815—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—61no—
232#809—31no—
233#809C2×D311yescharacteristic, complemented
234#809C2×D311yescharacteristic, complemented
235#808—31no—
236#808—31no—
237#808—61no—
238#807—31no—
239C23×C32—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—81no—
247C22×C3×D3—81no—
248C22×C3×D3C2×D411yescharacteristic
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—42no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C3×#67—42no—
260C3×#67—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#625—22no—
276#625—42no—
277#625—42no—
278#625—42no—
279#625—81no—
280D3×Dic3—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—31no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—31no—
299C2×#102—91no—
300C24×C3—61no—
301C24×C3—61no—
302C23×D3—21no—
303C23×D3—21no—
304C2×C3×Q8—31no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—62no—
311C2×C3×D4—62no—
312C2×C3×D4—121no—
313C2×C3×D4—121no—
314C2×C3×D4C22×D311yescharacteristic
315C2×C3×D4C22×D311yescharacteristic
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—31no—
321C2×#67—31no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—124no—
331C2×#67—124no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—121no—
336D3×D4—22no—
337D3×D4—22no—
338D3×D4—41no—
339D3×D4—41no—
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—61no—
343C2×C4×D3C22×D311yescharacteristic
344C2×C4×D3C22×D311yescharacteristic
345C2×Dic6C22×D311yescharacteristic
346C3×SD16—62no—
347C3×SD16—121no—
348C3×M16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—61no—
362#217—31no—
363#217—31no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—121no—
370#215—121no—
371#214—22no—
372#214—121no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380C4⋊Dic3—21no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—121no—
392C4⋊Dic3C22×D311yescharacteristic
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—121no—
402C4×Dic3—21no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8—121no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414#204—41no—
415ΓL(1,𝔽25)—41no—
416D3×C8—121no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—84no—
433C2×C3×D3—84no—
434C2×C3×D3AGL(1,ℤ/8)12yes—
435C32×C4—41no—
436C32×C4C2×#4111yescharacteristic
437C32×C4H(5,𝔽2)11yescharacteristic
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3⋊Dic3—41no—
441C3⋊Dic3—41no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—31no—
447C22×D4—31no—
448C22×D4—181no—
449C2×SD16—31no—
450C2×SD16—31no—
451C2×SD16—91no—
452C2×M16—31no—
453C22×C8—91no—
454#127—91no—
455#126—181no—
456#125—91no—
457#125—181no—
458#123—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461#121—91no—
462#121—91no—
463#121—181no—
464#120—181no—
465#120—181no—
466C4×Q8—91no—
467C4×D4—91no—
468C4×D4—91no—
469#117—31no—
470#117—181no—
471C2×C4⋊C4—91no—
472#107—91no—
473#107—91no—
474#106—91no—
475C4⋊C8—91no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102D3211yescharacteristic
486C22⋊C8—31no—
487C22⋊C8—91no—
488#97—91no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—31no—
492C23×C3—31no—
493C23×C3—41no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—122no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—122no—
500C23×C3—241no—
501C23×C3—241no—
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3—42no—
507C22×D3—42no—
508C22×D3—81no—
509C22×D3—81no—
510C22×D3D3×D411yescharacteristic
511C22×D3D3×D411yescharacteristic
512C3×Q8—61no—
513C3×Q8—61no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—22no—
517C3×D4—41no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—122no—
523C3×D4—122no—
524C3×D4#23512yes—
525C3×D4#23712yes—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—42no—
541#67—42no—
542#67—62no—
543#67—62no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—122no—
549#67—122no—
550#67—241no—
551#67—241no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—122no—
567C2×Dic3—122no—
568C2×Dic3—122no—
569C2×Dic3—242no—
570C2×Dic3D3×D411yescharacteristic
571C2×Dic3D3×D411yescharacteristic
572D12—21no—
573D12—21no—
574D12—21no—
575D12—21no—
576C4×D3—21no—
577C4×D3—21no—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—122no—
581Dic6—21no—
582Dic6—21no—
583C3×C8—21no—
584C3×C8—21no—
585C3×C8—41no—
586C3×C8—61no—
587C3×C8—61no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—121no—
593C2×C32—42no—
594C2×C32#54611yescharacteristic
595C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
596C2×C32#57711yescharacteristic
597C3×D3—22no—
598C3×D3—41no—
599C3×D3—81no—
600C3×D3—81no—
601C24—61no—
602C24—61no—
603C2×Q8—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—62no—
609C2×D4—62no—
610C2×D4—91no—
611C2×D4—121no—
612C2×D4—121no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—364no—
618C2×D4C2×D3211yescharacteristic
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—181no—
622C22×C4—181no—
623SD16—62no—
624SD16—121no—
625SD16—361no—
626M16—121no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—91no—
630C2×C8—361no—
631C2×C8C2×D3211yescharacteristic
632C4⋊C4—31no—
633C4⋊C4—61no—
634C4⋊C4—91no—
635C4⋊C4—91no—
636C4⋊C4—91no—
637C4⋊C4—181no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4C2×D3211yescharacteristic
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—91no—
646C22⋊C4—91no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C42—61no—
652C42—91no—
653C42—181no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—32no—
658C22×C3—42no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—244no—
677C22×C3—244no—
678C22×C3C2×D3×D411yescharacteristic
679C22×C3C2×D3×D411yescharacteristic
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—84no—
692C2×D3—84no—
693C2×D3#91412yes—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—81no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4C2×#23511yescharacteristic
704C3×C4C2×#23711yescharacteristic
705C3×C4#100411yescharacteristic
706C3×C4#100411yescharacteristic
707Dic3—21no—
708Dic3—21no—
709Dic3—41no—
710Dic3—41no—
711Dic3—61no—
712Dic3—61no—
713Dic3—61no—
714Dic3—61no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—121no—
719Dic3—121no—
720Dic3—121no—
721Dic3—241no—
722Dic3—241no—
723C32#331011yescharacteristic, complemented, Sylow
724C23—21no—
725C23—31no—
726C23—31no—
727C23—61no—
728C23—61no—
729C23—122no—
730C23—122no—
731C23—122no—
732C23—122no—
733C23—241no—
734C23—241no—
735Q8—61no—
736Q8—61no—
737D4—21no—
738D4—61no—
739D4—61no—
740D4—61no—
741D4—61no—
742D4—122no—
743D4—122no—
744D4—182no—
745D4—362no—
746D4—362no—
747D4—362no—
748D4—721no—
749D4#379512yes—
750C2×C4—21no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—91no—
760C2×C4—91no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—362no—
764C2×C4—362no—
765C2×C4C22×D3211yescharacteristic
766C8—21no—
767C8—61no—
768C8—61no—
769C8—181no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—42no—
774C2×C3—42no—
775C2×C3—62no—
776C2×C3—82no—
777C2×C3—121no—
778C2×C3—241no—
779C2×C3—241no—
780C2×C3#549011yescharacteristic
781C2×C3#559111yescharacteristic
782C2×C3C2×#91411yescharacteristic
783C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
784C2×C3#577511yescharacteristic
785C2×C3#577511yescharacteristic
786D3—22no—
787D3—41no—
788D3—81no—
789D3—81no—
790C22—22no—
791C22—32no—
792C22—41no—
793C22—41no—
794C22—61no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—244no—
806C22—244no—
807C22D32×D411yescharacteristic
808C4—41no—
809C4—61no—
810C4—61no—
811C4—121no—
812C4—121no—
813C4—181no—
814C4—181no—
815C4—361no—
816C4—361no—
817C4C2×#379511yescharacteristic
818C4#6431311yescharacteristic
819C3—21no—
820C3#7893411yescharacteristic, complemented
821C3#8016011yescharacteristic, complemented
822C2—42no—
823C2—62no—
824C2—121no—
825C2—241no—
826C2—241no—
827C2#1059418411yescharacteristic
828C2#1059473311yescharacteristic
829C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalD4×#625C2
hypercenter#102D32
hypocenterC32#3310
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. #10594456C2semidirect
3. #10592465C2semidirect
4. C3×#4776C2semidirect
5. C3×#4770C2semidirect
6. #10591458C2semidirect
7. #10591446C2semidirect
8. D3×#832C2semidirect
9. #10590876C2semidirect
10. #10590833C2semidirect
11. #10590724C2semidirect
12. #10590680C2semidirect
13. #10590554C2semidirect
14. #10590505C2semidirect
15. #10590501C2semidirect
22. #64099C22semidirect
24. C2×C3×#204C22semidirect
25. C2×C3×ΓL(1,𝔽25)C22semidirect
26. C3×#897C22semidirect
27. C3×#892C22semidirect
36. D3×C4⋊Dic3C22semidirect
40. #63856C22semidirect
41. #63843C22semidirect
42. C2×#3715C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63645C22semidirect
47. #63641C22semidirect
48. #63635C22semidirect
50. C3×#821C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#809C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63555C22semidirect
79. #4776D3semidirect
81. #4770D3semidirect
182. C2×#204C2×D3semidirect
183. C2×ΓL(1,𝔽25)C2×D3semidirect
186. #897C2×D3semidirect
187. #892C2×D3semidirect
219. #821C2×D3semidirect
221. (C2×D3)⋊C8C2×D3semidirect
233. #809C2×D3semidirect
234. #809C2×D3semidirect
723. C32#3310semidirect
820. C3#78934semidirect
821. C3#80160semidirect

Maximal subgroups

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

subgroupindex
D4×#6252
#105944562
#105924652
C3×#47762
C3×#47702
#105914582
#105914462
D3×#8322
#105908762
#105908332
#105907242
#105906802
#105905542
#105905052
#105905012
#801603
#789343