Finite Group Databasebeta

← #11889153

Subgroups — #11889153

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
1#10594618C211yesmaximal, characteristic
2#10594551C211yesmaximal, characteristic, complemented
3#10592590C211yesmaximal, characteristic, complemented
4C3×#4886C211yesmaximal, characteristic, complemented
5C3×#4882C211yesmaximal, characteristic, complemented
6#10590942C211yesmaximal, characteristic, complemented
7#10590939C211yesmaximal, characteristic, complemented
8#10590876C211yesmaximal, characteristic, complemented
9#10590724C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590554C211yesmaximal, characteristic, complemented
13#10590514C211yesmaximal, characteristic, complemented
14#10590484C211yesmaximal, characteristic, complemented
15#10590446C211yesmaximal, characteristic, complemented
16#81303—31nomaximal
17#80821—31nomaximal
18C2×#3802—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21#64102C2211yescharacteristic
22#64099C2211yescharacteristic, complemented
23C2×C3×#204C2211yescharacteristic, complemented
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
25C3×#897C2211yescharacteristic, complemented
26C3×#895C2211yescharacteristic
27C3×#895C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29#63922—21no—
30#63922—21no—
31#63914C2211yescharacteristic
32#63912—21no—
33#63905—21no—
34C4×#625C2211yescharacteristic
35#63861—21no—
36#63856C2211yescharacteristic, complemented
37#63847—21no—
38#63843C2211yescharacteristic, complemented
39#63841—21no—
40#63841C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3715C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63641C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48#63635C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#5639—31no—
62#5609—31no—
63#5609—31no—
64#5513—31no—
65C3×#480—31no—
66C3×#468—31no—
67#5169—31no—
68#5163—31no—
69#5131—31no—
70#5127—31no—
71#5046—31no—
72#5041—31no—
73#5035—31no—
74C2×#809—31no—
75#4891—31no—
76#4891—31no—
77#4891—61no—
78#4889—31no—
79#4886D311yescharacteristic, complemented
80#4885—31no—
81#4882D311yescharacteristic, complemented
82#4817—31no—
83#4807—31no—
84#4776—31no—
85#4770—31no—
86D3×#102—31no—
87#4764—31no—
88#4764—31no—
89#4762—31no—
90#4731—31no—
91#4730—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12—21no—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×#625D411yescharacteristic
109#3802—44no—
110D3×D12—22no—
111D3×D12—22no—
112D3×D12—41no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3752—21no—
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—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—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142#3717—22no—
143#3715—41no—
144D3×C3⋊C8—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12—31no—
152C2×C3×SD16—31no—
153C2×C3×M16—31no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C3×#121—31no—
157C2×C3×C4⋊C4—31no—
158#946—31no—
159Q8×Dic3—31no—
160C2×#215—31no—
161C2×#215—31no—
162#940—31no—
163#940—31no—
164#937—61no—
165#937—61no—
166C2×#214—31no—
167#929—61no—
168C4×#67—31no—
169C4×#67—31no—
170#926—31no—
171#926—61no—
172#924—31no—
173C22×C3⋊C8—31no—
174C2×#204—31no—
175C2×#204C2×D311yescharacteristic, complemented
176C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
177C2×D3×C8—31no—
178#898—61no—
179#897C2×D311yescharacteristic, complemented
180#895C2×D311yescharacteristic
181#895C2×D311yescharacteristic
182#893—31no—
183#893—31no—
184#893—61no—
185#892—31no—
186#892—61no—
187D3×C4⋊C4C2×D311yescharacteristic, complemented
188#890—31no—
189#890—31no—
190#890—61no—
191#889—61no—
192#889—61no—
193#887—31no—
194#884—61no—
195#884—61no—
196#883—61no—
197#882—61no—
198#882—61no—
199#879—61no—
200C3×#107—21no—
201C3×#107—31no—
202C3×#107C2×D311yescharacteristic, complemented
203C3×#107C2×D311yescharacteristic, complemented
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#830—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8C2×D311yescharacteristic, complemented
222#815—31no—
223#815—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#809C2×D311yescharacteristic, complemented
234#809C2×D311yescharacteristic, complemented
235#808—31no—
236#808—31no—
237#808—61no—
238#807C2×D311yescharacteristic, complemented
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)#4112yes—
258C4×C3⋊D3—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—42no—
268C3×D12—42no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—42no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#626—42no—
277#626—42no—
278#625—22no—
279#625—42no—
280#625—81no—
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—31no—
290#478—91no—
291#468—31no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C2×#67—31no—
313C2×#67—31no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320D3×D4—62no—
321D3×D4—62no—
322D3×D4—121no—
323D3×D4—121no—
324D3×D4—124no—
325D3×D4—124no—
326C2×D12—21no—
327C2×D12—21no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—62no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—121no—
336C2×D12—121no—
337C2×D12C22×D311yescharacteristic
338C2×D12C22×D311yescharacteristic
339C2×C4×D3—21no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—121no—
343C2×C4×D3C22×D311yescharacteristic
344C2×C4×D3C22×D311yescharacteristic
345C2×Dic6C22×D311yescharacteristic
346C3×SD16—121no—
347C3×M16—121no—
348C2×C3×C8—21no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365#217—31no—
366#217—31no—
367#217—61no—
368#217—61no—
369#215—62no—
370#215—121no—
371#214—121no—
372(C2×D3)⋊C4—21no—
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—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—121no—
382C4⋊Dic3—21no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—121no—
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—31no—
393Dic3⋊C4—31no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—121no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—41no—
414#204—62no—
415ΓL(1,𝔽25)—41no—
416D3×C8—121no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
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×D3AGL(1,ℤ/8)12yes—
433D32—84no—
434D32—84no—
435C32×C4—41no—
436C32×C4—41no—
437C32×C4C2×#4111yescharacteristic
438C32×C4H(5,𝔽2)11yescharacteristic
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—41no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—91no—
447C22×D4—91no—
448C22×D4—181no—
449C2×SD16—31no—
450C2×SD16—91no—
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—31no—
462#121—31no—
463#121—181no—
464#120—181no—
465#120—181no—
466C4×Q8—91no—
467C4×D4—91no—
468C4×D4—91no—
469#117—91no—
470#117—181no—
471C2×C4⋊C4—31no—
472#107—31no—
473#107D3211yescharacteristic, complemented
474#106—91no—
475C4⋊C8—91no—
476#103—31no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486C22⋊C8—31no—
487C22⋊C8—91no—
488#97—91no—
489C23×C3—31no—
490C23×C3—31no—
491C23×C3—61no—
492C23×C3—61no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—121no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—241no—
507C22×D3—241no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3D3×D411yescharacteristic
511C22×D3D3×D411yescharacteristic
512C3×Q8—61no—
513C3×Q8—61no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—122no—
519C3×D4—122no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—122no—
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538#67—62no—
539#67—62no—
540#67—122no—
541#67—122no—
542#67—122no—
543#67—122no—
544#67—241no—
545#67—241no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—121no—
557C2×Dic3D3×D411yescharacteristic
558C2×Dic3D3×D411yescharacteristic
559D12—21no—
560D12—21no—
561D12—21no—
562D12—21no—
563D12—32no—
564D12—32no—
565D12—42no—
566D12—42no—
567D12—62no—
568D12—61no—
569D12—61no—
570D12—121no—
571D12—122no—
572D12—122no—
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—42no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—242no—
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#54611yescharacteristic
594C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
595C2×C32#57711yescharacteristic
596C3⋊D3—42no—
597C3×D3—22no—
598C3×D3—41no—
599C3×D3—81no—
600C3×D3—81no—
601C24—181no—
602C24—181no—
603C2×Q8—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—91no—
609C2×D4—91no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4—182no—
613C2×D4—182no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—361no—
617C2×D4—361no—
618C2×D4—364no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—61no—
622C22×C4—181no—
623SD16—121no—
624SD16—182no—
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—61no—
635C4⋊C4—91no—
636C4⋊C4—91no—
637C4⋊C4—181no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4C2×D3211yescharacteristic
642C4⋊C4C2×D3211yescharacteristic
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—91no—
647C22⋊C4—91no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C42—91no—
652C42—181no—
653C42—181no—
654C22×C3—21no—
655C22×C3—32no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3C2×D3×D411yescharacteristic
668C22×C3C2×D3×D411yescharacteristic
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—122no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—244no—
690C2×D3—244no—
691C2×D3—244no—
692C2×D3—244no—
693C2×D3#91112yes—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—81no—
703C3×C4—81no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4#100411yescharacteristic
707C3×C4D3×#4111yescharacteristic
708C3×C4D3×#4111yescharacteristic
709C3×C4#100911yescharacteristic
710Dic3—21no—
711Dic3—21no—
712Dic3—41no—
713Dic3—41no—
714Dic3—61no—
715Dic3—61no—
716Dic3—61no—
717Dic3—61no—
718Dic3—121no—
719Dic3—121no—
720Dic3—121no—
721Dic3—121no—
722Dic3—241no—
723C32#331011yescharacteristic, complemented, Sylow
724C23—31no—
725C23—31no—
726C23—61no—
727C23—61no—
728C23—181no—
729C23—362no—
730C23—362no—
731C23—362no—
732C23—362no—
733C23—721no—
734C23—721no—
735Q8—61no—
736Q8—61no—
737D4—61no—
738D4—61no—
739D4—61no—
740D4—61no—
741D4—92no—
742D4—122no—
743D4—122no—
744D4—182no—
745D4—181no—
746D4—362no—
747D4—362no—
748D4—362no—
749D4—721no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—91no—
761C2×C4—91no—
762C2×C4—122no—
763C2×C4—181no—
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—62no—
774C2×C3—121no—
775C2×C3—241no—
776C2×C3—241no—
777C2×C3#561011yescharacteristic
778C2×C3#565411yescharacteristic
779C2×C3C2×#91111yescharacteristic
780C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
781C2×C3#577811yescharacteristic
782C2×C3#577811yescharacteristic
783D3—22no—
784D3—41no—
785D3—81no—
786D3—81no—
787D3—122no—
788D3—122no—
789D3—242no—
790C22—32no—
791C22—61no—
792C22—61no—
793C22—61no—
794C22—61no—
795C22—61no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—182no—
803C22—361no—
804C22—361no—
805C22—724no—
806C22—724no—
807C22D32×D411yescharacteristic
808C4—41no—
809C4—41no—
810C4—61no—
811C4—61no—
812C4—121no—
813C4—121no—
814C4—181no—
815C4—181no—
816C4—361no—
817C4#6430711yescharacteristic
818C4#6431911yescharacteristic
819C3—21no—
820C3#8082111yescharacteristic, complemented
821C3#8130311yescharacteristic, complemented
822C2—62no—
823C2—121no—
824C2—241no—
825C2—241no—
826C2—362no—
827C2#1059461711yescharacteristic
828C2D3×#91111yescharacteristic
829C2#1059476711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594618C2
hypercenter#107D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594551C2semidirect
3. #10592590C2semidirect
4. C3×#4886C2semidirect
5. C3×#4882C2semidirect
6. #10590942C2semidirect
7. #10590939C2semidirect
8. #10590876C2semidirect
9. #10590724C2semidirect
10. #10590596C2semidirect
11. D3×#809C2semidirect
12. #10590554C2semidirect
13. #10590514C2semidirect
14. #10590484C2semidirect
15. #10590446C2semidirect
22. #64099C22semidirect
23. C2×C3×#204C22semidirect
24. C2×C3×ΓL(1,𝔽25)C22semidirect
25. C3×#897C22semidirect
28. C3×D3×C4⋊C4C22semidirect
36. #63856C22semidirect
38. #63843C22semidirect
40. #63841C22semidirect
42. C2×#3715C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#107C22semidirect
46. #63641C22semidirect
48. #63635C22semidirect
49. C3×#821C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#810C22semidirect
52. C3×#809C22semidirect
53. C3×#809C22semidirect
54. C3×#807C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63555C22semidirect
79. #4886D3semidirect
81. #4882D3semidirect
175. C2×#204C2×D3semidirect
176. C2×ΓL(1,𝔽25)C2×D3semidirect
179. #897C2×D3semidirect
187. D3×C4⋊C4C2×D3semidirect
202. C3×#107C2×D3semidirect
203. C3×#107C2×D3semidirect
219. #821C2×D3semidirect
221. (C2×D3)⋊C8C2×D3semidirect
227. #810C2×D3semidirect
233. #809C2×D3semidirect
234. #809C2×D3semidirect
238. #807C2×D3semidirect
473. #107D32semidirect
723. C32#3310semidirect
820. C3#80821semidirect
821. C3#81303semidirect

Maximal subgroups

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

subgroupindex
#105946182
#105945512
#105925902
C3×#48862
C3×#48822
#105909422
#105909392
#105908762
#105907242
#105905962
D3×#8092
#105905542
#105905142
#105904842
#105904462
#813033
#808213