Finite Group Databasebeta

← #11887165

Subgroups — #11887165

Order 1152.

978 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594618C211yesmaximal, characteristic
2#10594532C211yesmaximal, characteristic, complemented
3#10592569C211yesmaximal, characteristic, complemented
4C3×#4864C211yesmaximal, characteristic, complemented
5C3×#4863C211yesmaximal, characteristic, complemented
6#10590942C211yesmaximal, characteristic, complemented
7D3×#821C211yesmaximal, characteristic, complemented
8#10590876C211yesmaximal, characteristic, complemented
9#10590717C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590552C211yesmaximal, characteristic, complemented
13#10590514C211yesmaximal, characteristic, complemented
14#10590483C211yesmaximal, characteristic, complemented
15#10590441C211yesmaximal, characteristic, complemented
16#81342—31nomaximal
17#80680—31nomaximal
18C2×#3802—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21#64102C2211yescharacteristic
22#64097C2211yescharacteristic, complemented
23C2×C3×#204C2211yescharacteristic, complemented
24C2×C3×D3×C8C2211yescharacteristic, complemented
25C3×#897C2211yescharacteristic, complemented
26C3×#895C2211yescharacteristic
27C3×#895C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29#63922—21no—
30#63922—21no—
31#63914C2211yescharacteristic
32#63912—21no—
33C4×#625C2211yescharacteristic
34#63896—21no—
35D3×C4⋊Dic3C2211yescharacteristic, complemented
36#63879—21no—
37#63857—21no—
38#63856C2211yescharacteristic, complemented
39#63847—21no—
40#63843C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3715C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, 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×#808C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5635—31no—
62#5609—31no—
63#5609—31no—
64#5511—31no—
65C3×#481—31no—
66C3×#465—31no—
67#5169—31no—
68#5163—31no—
69C2×#821—31no—
70C8×#67—31no—
71#5046—31no—
72#5041—31no—
73#5034—31no—
74C2×#809—31no—
75#4870—31no—
76#4870—31no—
77#4870—61no—
78#4864D311yescharacteristic, complemented
79#4863—31no—
80#4863D311yescharacteristic, complemented
81#4852—31no—
82#4807—31no—
83#4788—31no—
84#4776—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4762—31no—
88#4760—31no—
89#4760—31no—
90#4731—31no—
91#67⋊C8—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634—21no—
97C2×C3×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×#625—21no—
109C2×#625D411yescharacteristic
110C2×D3×Dic3—21no—
111#3802—44no—
112D3×D12—22no—
113D3×D12—22no—
114D3×D12—41no—
115D3×D12—41no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3752—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×#204—41no—
133C3×D3×C8—41no—
134#3724—21no—
135#3724D411yescharacteristic
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3717—22no—
143#3715—41no—
144D3×C3⋊C8—41no—
145#3295—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—
153C22×C3×C8—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—
167C4×#67—31no—
168C4×#67—31no—
169C4×#67—61no—
170C2×C4⋊Dic3—31no—
171#924—31no—
172#924—61no—
173C22×C3⋊C8—31no—
174C2×#204—31no—
175C2×#204C2×D311yescharacteristic, complemented
176C2×D3×C8—31no—
177C2×D3×C8C2×D311yescharacteristic, complemented
178#897—61no—
179#897C2×D311yescharacteristic, complemented
180#896—61no—
181#895C2×D311yescharacteristic
182#895C2×D311yescharacteristic
183#893—31no—
184#893—31no—
185#893—61no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4C2×D311yescharacteristic, complemented
188#889—61no—
189#889—61no—
190#888—31no—
191#888—31no—
192#888—61no—
193#887—31no—
194#884—61no—
195#884—61no—
196#882—61no—
197#882—61no—
198#67⋊C4—61no—
199#878—61no—
200C3×#106—21no—
201C3×#106—31no—
202C3×#106C2×D311yescharacteristic, complemented
203C3×#106C2×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
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—61no—
225C8×Dic3—31no—
226C8×Dic3—31no—
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#808C2×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—
259#634—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×D12—42no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—81no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277#626—42no—
278#626—42no—
279#625—42no—
280#625—81no—
281#625SD1614yescomplemented
282D3×Dic3—81no—
283C32×C8—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—91no—
288D42—91no—
289#486—91no—
290#481—31no—
291#481—91no—
292#476—91no—
293#465—31no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—91no—
301C2×#102—91no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×Q8—31no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C2×#67—31no—
315C2×#67—31no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C22×Dic3—61no—
323D3×D4—62no—
324D3×D4—62no—
325D3×D4—121no—
326D3×D4—121no—
327D3×D4—124no—
328D3×D4—124no—
329C2×D12—21no—
330C2×D12—21no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—61no—
334C2×D12—62no—
335C2×D12—62no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—121no—
339C2×D12—121no—
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—121no—
347C2×C4×D3C22×D311yescharacteristic
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—61no—
350C2×Dic6—61no—
351C2×Dic6—121no—
352C2×Dic6C22×D311yescharacteristic
353C3×SD16—121no—
354C2×C3×C8—21no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8—121no—
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372#217—31no—
373#217—31no—
374#217—61no—
375#215—62no—
376#215—121no—
377#214—121no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—121no—
387C4⋊Dic3—21no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—31no—
396Dic3⋊C4—31no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—121no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—121no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415#204—41no—
416#204—62no—
417D3×C8—41no—
418D3×C8—121no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—22no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
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×D3C2×SD1612yes—
434C2×C3×D3C2×SD1612yes—
435D32—84no—
436D32—84no—
437C32×C4—41no—
438C32×C4—41no—
439C32×C4C2×#4111yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—21no—
442C3⋊Dic3—41no—
443C3⋊Dic3C2×SD1612yes—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—91no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—91no—
453C2×SD16—91no—
454C22×C8—31no—
455C22×C8—91no—
456C4⋊Q8—91no—
457#127—91no—
458#125—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461C22⋊Q8—181no—
462C22⋊Q8—181no—
463#121—31no—
464#121—31no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—91no—
469C4×D4—91no—
470C4×D4—91no—
471C4×D4—181no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—91no—
474#106—31no—
475#106—91no—
476#106D3211yescharacteristic, complemented
477C4⋊C8—91no—
478#103—31no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—31no—
489C22⋊C8—91no—
490C4×C8—91no—
491C23×C3—31no—
492C23×C3—31no—
493C23×C3—61no—
494C23×C3—61no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—121no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3—241no—
511C22×D3—241no—
512C22×D3D3×D411yescharacteristic
513C22×D3D3×D411yescharacteristic
514C3×Q8—61no—
515C3×Q8—61no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—122no—
521C3×D4—122no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—241no—
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—34no—
541#67—34no—
542#67—122no—
543#67—122no—
544#67—122no—
545#67—122no—
546#67—241no—
547#67—241no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—121no—
559C2×Dic3—241no—
560C2×Dic3D3×D411yescharacteristic
561C2×Dic3D3×D411yescharacteristic
562D12—21no—
563D12—21no—
564D12—21no—
565D12—21no—
566D12—32no—
567D12—32no—
568D12—42no—
569D12—42no—
570D12—62no—
571D12—61no—
572D12—61no—
573D12—121no—
574D12—122no—
575D12—122no—
576C4×D3—21no—
577C4×D3—21no—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—81no—
581C4×D3—122no—
582C4×D3—122no—
583C4×D3—242no—
584C4×D3—241no—
585Dic6—21no—
586Dic6—21no—
587Dic6—241no—
588Dic6—241no—
589Dic6—242no—
590C3×C8—21no—
591C3×C8—21no—
592C3×C8—41no—
593C3×C8—61no—
594C3×C8—61no—
595C3⋊C8—21no—
596C3⋊C8—21no—
597C3⋊C8—61no—
598C3⋊C8—61no—
599C3⋊C8—121no—
600C2×C32#54611yescharacteristic
601C2×C32C22×SD1611yescharacteristic
602C2×C32#57611yescharacteristic
603C3⋊D3—42no—
604C3×D3—22no—
605C3×D3—22no—
606C3×D3—81no—
607C3×D3—81no—
608C24—181no—
609C24—181no—
610C2×Q8—31no—
611C2×Q8—181no—
612C2×D4—31no—
613C2×D4—31no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—91no—
617C2×D4—91no—
618C2×D4—181no—
619C2×D4—181no—
620C2×D4—182no—
621C2×D4—182no—
622C2×D4—181no—
623C2×D4—181no—
624C2×D4—361no—
625C2×D4—361no—
626C2×D4—364no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—61no—
630C22×C4—181no—
631C22×C4—181no—
632SD16—121no—
633SD16—182no—
634SD16—361no—
635C2×C8—31no—
636C2×C8—31no—
637C2×C8—91no—
638C2×C8—121no—
639C2×C8—361no—
640C2×C8C2×D3211yescharacteristic
641C4⋊C4—31no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—91no—
645C4⋊C4—91no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C4⋊C4C2×D3211yescharacteristic
651C4⋊C4C2×D3211yescharacteristic
652C22⋊C4—61no—
653C22⋊C4—61no—
654C22⋊C4—61no—
655C22⋊C4—91no—
656C22⋊C4—91no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C42—91no—
660C42—181no—
661C22×C3—21no—
662C22×C3—32no—
663C22×C3—32no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3C2×D3×D411yescharacteristic
675C22×C3C2×D3×D411yescharacteristic
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—62no—
687C2×D3—62no—
688C2×D3—122no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—241no—
694C2×D3—241no—
695C2×D3—244no—
696C2×D3—244no—
697C2×D3—244no—
698C2×D3—244no—
699C2×D3D3×SD1612yes—
700C2×D3D3×SD1612yes—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—81no—
710C3×C4—81no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4#100411yescharacteristic
714C3×C4D3×#4111yescharacteristic
715C3×C4D3×#4111yescharacteristic
716C3×C4#100911yescharacteristic
717Dic3—21no—
718Dic3—21no—
719Dic3—32no—
720Dic3—32no—
721Dic3—41no—
722Dic3—41no—
723Dic3—62no—
724Dic3—61no—
725Dic3—61no—
726Dic3—121no—
727Dic3—121no—
728Dic3—121no—
729Dic3—241no—
730C32#329511yescharacteristic, complemented, Sylow
731C23—31no—
732C23—31no—
733C23—61no—
734C23—61no—
735C23—181no—
736C23—362no—
737C23—362no—
738C23—362no—
739C23—362no—
740C23—721no—
741C23—721no—
742Q8—61no—
743Q8—61no—
744Q8—721no—
745D4—61no—
746D4—61no—
747D4—61no—
748D4—61no—
749D4—94no—
750D4—92no—
751D4—122no—
752D4—122no—
753D4—181no—
754D4—362no—
755D4—362no—
756D4—362no—
757D4—721no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—91no—
769C2×C4—91no—
770C2×C4—181no—
771C2×C4—241no—
772C2×C4—362no—
773C2×C4—721no—
774C2×C4C22×D3211yescharacteristic
775C8—21no—
776C8—61no—
777C8—61no—
778C8—181no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—62no—
783C2×C3—62no—
784C2×C3—241no—
785C2×C3—241no—
786C2×C3#561011yescharacteristic
787C2×C3#565411yescharacteristic
788C2×C3C2×D3×SD1611yescharacteristic
789C2×C3C2×D3×SD1611yescharacteristic
790C2×C3#576911yescharacteristic
791C2×C3#577411yescharacteristic
792D3—22no—
793D3—22no—
794D3—81no—
795D3—81no—
796D3—122no—
797D3—122no—
798D3—242no—
799C22—32no—
800C22—32no—
801C22—61no—
802C22—61no—
803C22—61no—
804C22—61no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—182no—
812C22—361no—
813C22—361no—
814C22—724no—
815C22—724no—
816C22D32×D411yescharacteristic
817C4—41no—
818C4—41no—
819C4—61no—
820C4—61no—
821C4—92no—
822C4—121no—
823C4—121no—
824C4—181no—
825C4—361no—
826C4#6430711yescharacteristic
827C4#6431911yescharacteristic
828C3—21no—
829C3#8068011yescharacteristic, complemented
830C3#8134211yescharacteristic, complemented
831C2—62no—
832C2—62no—
833C2—241no—
834C2—241no—
835C2—362no—
836C2#1059461711yescharacteristic
837C2D32×SD1611yescharacteristic
838C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594618C2
hypercenter#106D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594532C2semidirect
3. #10592569C2semidirect
4. C3×#4864C2semidirect
5. C3×#4863C2semidirect
6. #10590942C2semidirect
7. D3×#821C2semidirect
8. #10590876C2semidirect
9. #10590717C2semidirect
10. #10590596C2semidirect
11. D3×#809C2semidirect
12. #10590552C2semidirect
13. #10590514C2semidirect
14. #10590483C2semidirect
15. #10590441C2semidirect
22. #64097C22semidirect
23. C2×C3×#204C22semidirect
24. C2×C3×D3×C8C22semidirect
25. C3×#897C22semidirect
28. C3×D3×C4⋊C4C22semidirect
35. D3×C4⋊Dic3C22semidirect
38. #63856C22semidirect
40. #63843C22semidirect
42. C2×#3715C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#106C22semidirect
46. #63641C22semidirect
48. #63635C22semidirect
49. C3×#821C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#810C22semidirect
52. C3×#809C22semidirect
53. C3×#809C22semidirect
54. C3×#808C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63553C22semidirect
78. #4864D3semidirect
80. #4863D3semidirect
175. C2×#204C2×D3semidirect
177. C2×D3×C8C2×D3semidirect
179. #897C2×D3semidirect
187. D3×C4⋊C4C2×D3semidirect
202. C3×#106C2×D3semidirect
203. C3×#106C2×D3semidirect
219. #821C2×D3semidirect
221. (C2×D3)⋊C8C2×D3semidirect
227. #810C2×D3semidirect
233. #809C2×D3semidirect
234. #809C2×D3semidirect
238. #808C2×D3semidirect
281. #625SD16semidirect
476. #106D32semidirect
730. C32#3295semidirect
829. C3#80680semidirect
830. C3#81342semidirect

Maximal subgroups

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

subgroupindex
#105946182
#105945322
#105925692
C3×#48642
C3×#48632
#105909422
D3×#8212
#105908762
#105907172
#105905962
D3×#8092
#105905522
#105905142
#105904832
#105904412
#813423
#806803