Finite Group Databasebeta

← #11889162

Subgroups — #11889162

Order 1152.

960 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595380C211yesmaximal, characteristic, complemented
2#10594618C211yesmaximal, characteristic
3#10592516C211yesmaximal, characteristic, complemented
4C3×#4812C211yesmaximal, characteristic, complemented
5C3×#4807C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591651C211yesmaximal, characteristic, complemented
8#10591622C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10D3×#821C211yesmaximal, characteristic, complemented
11#10590888C211yesmaximal, characteristic, complemented
12#10590722C211yesmaximal, characteristic, complemented
13#10590449C211yesmaximal, characteristic, complemented
14#10590438C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16#80821—31nomaximal
17#80685—31nomaximal
18C2×#3802—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23#64102C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C3×#946C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#895C2211yescharacteristic
32#63922—21no—
33#63922—21no—
34#63914C2211yescharacteristic
35#63912—21no—
36C4×#625C2211yescharacteristic
37#63891—21no—
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63878—21no—
40#63872C2211yescharacteristic, complemented
41#63862—21no—
42#63845—21no—
43#63841C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63642C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63563C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5642—31no—
62#5639—31no—
63#5609—31no—
64#5609—31no—
65C3×#468—31no—
66C3×#465—31no—
67#5169—31no—
68#5169—31no—
69#5163—31no—
70#5163—31no—
71#5131—31no—
72#5127—31no—
73C2×#821—31no—
74#5111—31no—
75#5046—31no—
76#5046—31no—
77#5035—31no—
78#5033—31no—
79#4891—31no—
80#4882—31no—
81#4871—31no—
82#4866—31no—
83#4817—31no—
84#4817—31no—
85#4817—61no—
86#4812D311yescharacteristic, complemented
87#4807D311yescharacteristic, complemented
88#4770—31no—
89D3×#102—31no—
90#4764—31no—
91#4764—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×#626—21no—
104C2×#626—21no—
105C2×#625—21no—
106C2×#625—21no—
107C2×#625D411yescharacteristic
108C2×D3×Dic3—21no—
109#3802—44no—
110D3×D12—22no—
111D3×D12—22no—
112D3×D12—41no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3755—22no—
117#3752—21no—
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#215—41no—
124C3×#215—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×ΓL(1,𝔽25)—41no—
136C3×D3×C8—41no—
137#3724D411yescharacteristic
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143(C2×D3)⋊Dic3D411yescharacteristic
144Dic32—21no—
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×SD16—31no—
154C2×C3×M16—31no—
155C22×C3×C8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×#121—31no—
159C3×#121—31no—
160#946C2×D311yescharacteristic, complemented
161#946C2×D311yescharacteristic, complemented
162Q8×Dic3—31no—
163Q8×Dic3—31no—
164Q8×Dic3—61no—
165C2×#215—31no—
166C2×#215—31no—
167C2×#215—61no—
168C2×#215C2×D311yescharacteristic, complemented
169C2×#215C2×D311yescharacteristic, complemented
170#940—31no—
171#940—31no—
172#937—61no—
173#937—61no—
174C4×#67—31no—
175C4×#67—31no—
176#926—31no—
177C2×C4⋊Dic3—31no—
178C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
179C2×D3×C8C2×D311yescharacteristic, complemented
180#898—61no—
181#895C2×D311yescharacteristic
182#895C2×D311yescharacteristic
183#893—31no—
184#893—31no—
185#893—61no—
186#892—31no—
187#892—61no—
188D3×C4⋊C4—31no—
189#890—31no—
190#890—31no—
191#890—61no—
192#889—61no—
193#886—61no—
194#884—61no—
195#884—61no—
196#883—61no—
197#882—61no—
198#882—61no—
199#879—61no—
200#877—61no—
201C3×#107—31no—
202C3×#106—31no—
203C3×#103—21no—
204C3×#103C2×D311yescharacteristic, complemented
205C3×#103C2×D311yescharacteristic, complemented
206C3×#102—31no—
207C3×#102—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#830—31no—
213#830—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#821C2×D311yescharacteristic, complemented
222#821C2×D311yescharacteristic, complemented
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#815—31no—
226#815—31no—
227#815—61no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237#807—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—
250C32×Q8—21no—
251C32×Q8—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)#4112yes—
260C4×C3⋊D3—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×D12—42no—
270C3×D12—42no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275#626—42no—
276#626—42no—
277#625—22no—
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—31no—
292#465—31no—
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—21no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C2×#67—31no—
314C2×#67—31no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C22×Dic3—61no—
322D3×D4—62no—
323D3×D4—62no—
324D3×D4—121no—
325D3×D4—121no—
326D3×D4—124no—
327D3×D4—124no—
328C2×D12—21no—
329C2×D12—21no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—61no—
333C2×D12—62no—
334C2×D12—62no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—121no—
338C2×D12—121no—
339C2×D12C22×D311yescharacteristic
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—121no—
345C2×C4×D3C22×D311yescharacteristic
346C2×C4×D3C22×D311yescharacteristic
347C3×SD16—121no—
348C3×SD16—121no—
349C3×M16—121no—
350C2×C3×C8—21no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—121no—
354C2×C3×C8C22×D311yescharacteristic
355C2×C3×C8C22×D311yescharacteristic
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367#217—31no—
368#217—31no—
369#217—61no—
370#215—41no—
371#215—41no—
372#215—62no—
373#215—62no—
374#215—64no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—121no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—121no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—31no—
399Dic3⋊C4—31no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—121no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416ΓL(1,𝔽25)—41no—
417D3×C8—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3AGL(1,ℤ/8)12yes—
434D32—84no—
435D32—84no—
436C32×C4—41no—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C22×D4—91no—
448C22×D4—91no—
449C22×D4—181no—
450C2×SD16—31no—
451C2×SD16—31no—
452C2×SD16—91no—
453C2×M16—31no—
454C22×C8—31no—
455#127—91no—
456#126—181no—
457#125—91no—
458#125—181no—
459#123—181no—
460C22⋊Q8—31no—
461C22⋊Q8—31no—
462#121—31no—
463#121—31no—
464#121—181no—
465#120—181no—
466#120—181no—
467C4×Q8—91no—
468C4×D4—91no—
469C4×D4—91no—
470#117—91no—
471#117—181no—
472C2×C4⋊C4—91no—
473#107—31no—
474#107—91no—
475#106—31no—
476C4⋊C8—91no—
477#103D3211yescharacteristic, complemented
478#102—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487C22⋊C8—91no—
488C22⋊C8—91no—
489#97—91no—
490C23×C3—31no—
491C23×C3—31no—
492C23×C3—61no—
493C23×C3—61no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—121no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—241no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3—241no—
511C22×D3D3×D411yescharacteristic
512C22×D3D3×D411yescharacteristic
513C3×Q8—22no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—21no—
517C3×Q8—21no—
518C3×Q8—41no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—122no—
524C3×D4—122no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542#67—62no—
543#67—62no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—241no—
549#67—241no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—121no—
561C2×Dic3—122no—
562C2×Dic3D3×D411yescharacteristic
563C2×Dic3D3×D411yescharacteristic
564D12—21no—
565D12—21no—
566D12—21no—
567D12—21no—
568D12—32no—
569D12—32no—
570D12—42no—
571D12—42no—
572D12—62no—
573D12—61no—
574D12—61no—
575D12—121no—
576D12—122no—
577D12—122no—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—122no—
583C4×D3—122no—
584C4×D3—122no—
585C4×D3—242no—
586C3×C8—21no—
587C3×C8—21no—
588C3×C8—41no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C3⋊C8—62no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C2×C32#54611yescharacteristic
597C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
598C2×C32#57711yescharacteristic
599C3⋊D3—42no—
600C3×D3—22no—
601C3×D3—41no—
602C3×D3—81no—
603C3×D3—81no—
604C24—181no—
605C24—181no—
606C2×Q8C2×D3211yescharacteristic
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—91no—
612C2×D4—91no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—182no—
616C2×D4—182no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—361no—
620C2×D4—361no—
621C2×D4—364no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—181no—
625C22×C4—181no—
626SD16—121no—
627SD16—121no—
628SD16—182no—
629M16—121no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—121no—
634C2×C8C2×D3211yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4—181no—
645C4⋊C4C2×D3211yescharacteristic
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C42—91no—
655C42—181no—
656C42—181no—
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—62no—
684C2×D3—62no—
685C2×D3—122no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—241no—
691C2×D3—241no—
692C2×D3—244no—
693C2×D3—244no—
694C2×D3—244no—
695C2×D3—244no—
696C2×D3#91412yes—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—42no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—81no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4#100411yescharacteristic
710C3×C4#100411yescharacteristic
711C3×C4D3×#4111yescharacteristic
712C3×C4D3×#4111yescharacteristic
713Dic3—21no—
714Dic3—21no—
715Dic3—41no—
716Dic3—41no—
717Dic3—61no—
718Dic3—61no—
719Dic3—61no—
720Dic3—61no—
721Dic3—121no—
722Dic3—121no—
723Dic3—121no—
724Dic3—121no—
725Dic3—241no—
726C32#331011yescharacteristic, complemented, Sylow
727C23—31no—
728C23—31no—
729C23—61no—
730C23—61no—
731C23—181no—
732C23—362no—
733C23—362no—
734C23—362no—
735C23—362no—
736C23—721no—
737C23—721no—
738Q8—21no—
739Q8—21no—
740D4—61no—
741D4—61no—
742D4—61no—
743D4—61no—
744D4—92no—
745D4—122no—
746D4—122no—
747D4—182no—
748D4—181no—
749D4—362no—
750D4—362no—
751D4—362no—
752D4—721no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—181no—
766C2×C4—362no—
767C2×C4—362no—
768C2×C4C22×D3211yescharacteristic
769C8—21no—
770C8—61no—
771C8—61no—
772C8—181no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—62no—
777C2×C3—121no—
778C2×C3—241no—
779C2×C3—241no—
780C2×C3#561011yescharacteristic
781C2×C3#561011yescharacteristic
782C2×C3C2×#91411yescharacteristic
783C2×C3#577011yescharacteristic
784C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
785C2×C3#577811yescharacteristic
786D3—22no—
787D3—41no—
788D3—81no—
789D3—81no—
790D3—122no—
791D3—122no—
792D3—242no—
793C22—32no—
794C22—61no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—182no—
806C22—361no—
807C22—361no—
808C22—724no—
809C22—724no—
810C22D32×D411yescharacteristic
811C4—41no—
812C4—41no—
813C4—61no—
814C4—61no—
815C4—121no—
816C4—121no—
817C4—181no—
818C4—181no—
819C4—361no—
820C4#6430611yescharacteristic
821C4#6431311yescharacteristic
822C3—21no—
823C3#8068511yescharacteristic, complemented
824C3#8082111yescharacteristic, complemented
825C2—62no—
826C2—121no—
827C2—241no—
828C2—241no—
829C2—362no—
830C2#1059427611yescharacteristic
831C2D3×#91411yescharacteristic
832C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594618C2
hypercenter#103D32
hypocenterC32#3310
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
1. #10595380C2semidirect
3. #10592516C2semidirect
4. C3×#4812C2semidirect
5. C3×#4807C2semidirect
6. #10591651C2semidirect
7. #10591651C2semidirect
8. #10591622C2semidirect
9. #10590939C2semidirect
10. D3×#821C2semidirect
11. #10590888C2semidirect
12. #10590722C2semidirect
13. #10590449C2semidirect
14. #10590438C2semidirect
15. #10590435C2semidirect
21. Q8×C3⋊Dic3C22semidirect
24. C3×#946C22semidirect
25. C3×#946C22semidirect
26. C2×C3×#215C22semidirect
27. C2×C3×#215C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
29. C2×C3×D3×C8C22semidirect
38. D3×C4⋊Dic3C22semidirect
40. #63872C22semidirect
43. #63841C22semidirect
44. C32×#103C22semidirect
46. #63642C22semidirect
47. #63634C22semidirect
48. C3×#821C22semidirect
49. C3×#821C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. #63572C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
86. #4812D3semidirect
87. #4807D3semidirect
160. #946C2×D3semidirect
161. #946C2×D3semidirect
168. C2×#215C2×D3semidirect
169. C2×#215C2×D3semidirect
178. C2×ΓL(1,𝔽25)C2×D3semidirect
179. C2×D3×C8C2×D3semidirect
204. C3×#103C2×D3semidirect
205. C3×#103C2×D3semidirect
221. #821C2×D3semidirect
222. #821C2×D3semidirect
234. #808C2×D3semidirect
238. #807C2×D3semidirect
477. #103D32semidirect
726. C32#3310semidirect
823. C3#80685semidirect
824. C3#80821semidirect

Maximal subgroups

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

subgroupindex
#105953802
#105946182
#105925162
C3×#48122
C3×#48072
#105916512
#105916222
#105909392
D3×#8212
#105908882
#105907222
#105904492
#105904382
#105904352
#808213
#806853