Finite Group Databasebeta

← #11887149

Subgroups — #11887149

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595288C211yesmaximal, characteristic
2#10594532C211yesmaximal, characteristic, complemented
3#10592459C211yesmaximal, characteristic, complemented
4C3×#4778C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591444C211yesmaximal, characteristic, complemented
8#10591415C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590847C211yesmaximal, characteristic, complemented
11#10590742C211yesmaximal, characteristic, complemented
12C8×#625C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590472C211yesmaximal, characteristic, complemented
15#10590423C211yesmaximal, characteristic, complemented
16#80680—31nomaximal
17#78758—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21#64149C2211yescharacteristic
22#64097C2211yescharacteristic, complemented
23C3×#938C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic, complemented
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×#897C2211yescharacteristic, complemented
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29#63983—21no—
30#63977—21no—
31#63971—21no—
32#63909C2211yescharacteristic
33C4×#625C2211yescharacteristic
34#63898C2211yescharacteristic
35#63896—21no—
36D3×C4⋊Dic3C2211yescharacteristic, complemented
37#63879—21no—
38#63857—21no—
39#63856C2211yescharacteristic, complemented
40#63847—21no—
41#63843C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic
44C32×#102C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63648C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48#63636C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61D4×#67—31no—
62#5635—31no—
63#5609—31no—
64#5511—31no—
65C3×#465—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5169—31no—
69#5163—31no—
70#5114—31no—
71C2×#821—31no—
72C8×#67—31no—
73C8×#67—31no—
74#5046—31no—
75#5034—31no—
76#4968—31no—
77#4870—31no—
78#4863—31no—
79#4807—31no—
80#4788—31no—
81#4778D311yescharacteristic, complemented
82#4777—31no—
83#4776—31no—
84D3×#102—31no—
85D3×#102D311yescharacteristic, complemented
86#4762—31no—
87#4761—31no—
88#4760—31no—
89#4760—31no—
90#4760—61no—
91#4758—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108D3×#67—44no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#625D411yescharacteristic
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114D3×D12—22no—
115D3×D12—41no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#214—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132C3×D3×C8—41no—
133#3724—21no—
134#3724D411yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3717—41no—
144#3715—22no—
145#3295—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C2×D3×D4C2×D311yescharacteristic
151C22×D12—31no—
152C2×C3×SD16—31no—
153C22×C3×C8—31no—
154C22×C3×C8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C2×C3×C4⋊C4—31no—
158#953—61no—
159#946—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162C2×#215—31no—
163#940—31no—
164#940—31no—
165#940—61no—
166#939—61no—
167#938C2×D311yescharacteristic
168#937—61no—
169#937—61no—
170D4×Dic3—31no—
171C2×#214—31no—
172C2×#214C2×D311yescharacteristic, complemented
173#930—31no—
174C4×#67—31no—
175C4×#67—31no—
176C4×#67—61no—
177C2×C4⋊Dic3—31no—
178#924—31no—
179#924—61no—
180C2×#204—31no—
181C2×D3×C8C2×D311yescharacteristic, complemented
182C2×D3×C8C2×D311yescharacteristic, complemented
183#897—61no—
184#897C2×D311yescharacteristic, complemented
185#896—61no—
186#895—31no—
187#893—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4C2×D311yescharacteristic, complemented
190#889—61no—
191#889—61no—
192#888—31no—
193#888—31no—
194#888—61no—
195#887—31no—
196#884—61no—
197#882—61no—
198#67⋊C4—61no—
199#878—61no—
200C3×#106—31no—
201C3×#103—31no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic, complemented
207C3×#102C2×D311yescharacteristic, complemented
208#832—31no—
209#832—31no—
210#832—31no—
211#832—61no—
212#832C2×D311yescharacteristic, complemented
213#830—31no—
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223#817—31no—
224#816C2×D311yescharacteristic, complemented
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—61no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic
235#808—31no—
236#808—31no—
237#808—31no—
238#808C2×D311yescharacteristic, complemented
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×D4—21no—
251C32×D4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255#638—81no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261#634—81no—
262C3×#67—42no—
263C3×#67—42no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12#4112yes—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—81no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278#626—42no—
279#626—42no—
280#625SD1614yescomplemented
281D3×Dic3—42no—
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—91no—
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—31no—
301C2×#102—91no—
302C24×C3—61no—
303C23×D3—21no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×Q8—31no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C2×C3×D4—62no—
311C2×C3×D4—61no—
312C2×C3×D4—121no—
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C22×D311yescharacteristic
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—61no—
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—121no—
329C2×#67—121no—
330C2×#67—124no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333D3×D4—22no—
334D3×D4—41no—
335D3×D4—62no—
336D3×D4—121no—
337D3×D4—124no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—61no—
341C2×D12—62no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—121no—
345C2×D12C22×D311yescharacteristic
346C2×C4×D3—21no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3C22×D311yescharacteristic
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6—61no—
352C2×Dic6—61no—
353C2×Dic6—121no—
354C2×Dic6C22×D311yescharacteristic
355C3×SD16—121no—
356C2×C3×C8—21no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8—121no—
360C2×C3×C8—121no—
361C2×C3×C8C22×D311yescharacteristic
362C2×C3×C8C22×D311yescharacteristic
363C3×C4⋊C4—21no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372#217—21no—
373#217—31no—
374#217—31no—
375#217—61no—
376#217—61no—
377#215—62no—
378#215—121no—
379#214—41no—
380#214—62no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388C4⋊Dic3—21no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—31no—
398Dic3⋊C4—31no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—121no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416#204—121no—
417D3×C8—41no—
418D3×C8—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—22no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—84no—
434C2×C3×D3C2×SD1612yes—
435C2×C3×D3C2×SD1612yes—
436D32—84no—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—41no—
442C3⋊Dic3C2×SD1612yes—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—31no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—91no—
453C2×SD16—91no—
454C22×C8—31no—
455C22×C8—31no—
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—91no—
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#106—91no—
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#102D3211yescharacteristic, complemented
488C22⋊C8—91no—
489C22⋊C8—91no—
490C4×C8—91no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—31no—
494C23×C3—31no—
495C23×C3—41no—
496C23×C3—61no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—241no—
500C22×D3—21no—
501C22×D3—42no—
502C22×D3—42no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—81no—
506C22×D3—121no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—241no—
512C22×D3—241no—
513C22×D3D3×D411yescharacteristic
514C22×D3D3×D411yescharacteristic
515C3×Q8—61no—
516C3×Q8—61no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—21no—
520C3×D4—21no—
521C3×D4—32no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—61no—
525C3×D4—122no—
526C3×D4—122no—
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—61no—
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×C4—241no—
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543#67—34no—
544#67—34no—
545#67—42no—
546#67—42no—
547#67—122no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—242no—
552#67—241no—
553#67—241no—
554#67—242no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—121no—
567C2×Dic3—122no—
568C2×Dic3—241no—
569C2×Dic3D3×D411yescharacteristic
570C2×Dic3D3×D411yescharacteristic
571D12—21no—
572D12—61no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—121no—
577D12—121no—
578D12—122no—
579D12—122no—
580D12#23512yes—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—21no—
584C4×D3—21no—
585C4×D3—81no—
586C4×D3—122no—
587C4×D3—241no—
588Dic6—21no—
589Dic6—21no—
590Dic6—241no—
591Dic6—241no—
592Dic6—242no—
593C3×C8—21no—
594C3×C8—21no—
595C3×C8—41no—
596C3×C8—61no—
597C3×C8—61no—
598C3⋊C8—21no—
599C3⋊C8—21no—
600C3⋊C8—61no—
601C3⋊C8—61no—
602C3⋊C8—121no—
603C2×C32—81no—
604C2×C32#54611yescharacteristic
605C2×C32C22×SD1611yescharacteristic
606C2×C32#57611yescharacteristic
607C3⋊D3—81no—
608C3×D3—22no—
609C3×D3—22no—
610C3×D3—42no—
611C24—61no—
612C24—181no—
613C2×Q8—31no—
614C2×Q8—181no—
615C2×D4—31no—
616C2×D4—61no—
617C2×D4—62no—
618C2×D4—61no—
619C2×D4—91no—
620C2×D4—91no—
621C2×D4—121no—
622C2×D4—181no—
623C2×D4—182no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—181no—
627C2×D4—361no—
628C2×D4—364no—
629C2×D4C2×D3211yescharacteristic
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—61no—
633C22×C4—181no—
634C22×C4—181no—
635SD16—121no—
636SD16—182no—
637SD16—361no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—91no—
641C2×C8—121no—
642C2×C8—121no—
643C2×C8C2×D3211yescharacteristic
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—91no—
649C4⋊C4—91no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4C2×D3211yescharacteristic
655C22⋊C4—61no—
656C22⋊C4—61no—
657C22⋊C4—91no—
658C22⋊C4—91no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C42—91no—
663C42—181no—
664C22×C3—21no—
665C22×C3—32no—
666C22×C3—32no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—62no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—244no—
684C22×C3C2×D3×D411yescharacteristic
685C22×C3C2×D3×D411yescharacteristic
686C2×D3—21no—
687C2×D3—21no—
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—22no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—84no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—241no—
701C2×D3—241no—
702C2×D3—241no—
703C2×D3—244no—
704C2×D3—244no—
705C2×D3D3×SD1612yes—
706C2×D3D3×SD1612yes—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—61no—
712C3×C4—61no—
713C3×C4—81no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4—121no—
717C3×C4C2×#23511yescharacteristic
718C3×C4#100411yescharacteristic
719C3×C4#100411yescharacteristic
720C3×C4D3×#4111yescharacteristic
721Dic3—21no—
722Dic3—21no—
723Dic3—32no—
724Dic3—32no—
725Dic3—41no—
726Dic3—41no—
727Dic3—41no—
728Dic3—62no—
729Dic3—62no—
730Dic3—61no—
731Dic3—61no—
732Dic3—121no—
733Dic3—121no—
734Dic3—241no—
735C32#329511yescharacteristic, complemented, Sylow
736C23—21no—
737C23—31no—
738C23—31no—
739C23—61no—
740C23—122no—
741C23—122no—
742C23—181no—
743C23—241no—
744C23—362no—
745C23—362no—
746C23—721no—
747Q8—61no—
748Q8—61no—
749Q8—721no—
750D4—21no—
751D4—21no—
752D4—32no—
753D4—61no—
754D4—94no—
755D4—122no—
756D4—122no—
757D4—181no—
758D4—181no—
759D4—362no—
760D4—362no—
761D4—362no—
762D4—721no—
763C2×C4—21no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—181no—
776C2×C4—241no—
777C2×C4—362no—
778C2×C4—721no—
779C2×C4C22×D3211yescharacteristic
780C8—21no—
781C8—61no—
782C8—61no—
783C8—181no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—62no—
788C2×C3—62no—
789C2×C3—81no—
790C2×C3—81no—
791C2×C3—122no—
792C2×C3—161no—
793C2×C3#549011yescharacteristic
794C2×C3#561011yescharacteristic
795C2×C3#575711yescharacteristic
796C2×C3C2×D3×SD1611yescharacteristic
797C2×C3C2×D3×SD1611yescharacteristic
798C2×C3#576911yescharacteristic
799D3—22no—
800D3—22no—
801D3—42no—
802D3—241no—
803D3—241no—
804D3—481no—
805C22—32no—
806C22—32no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—62no—
815C22—121no—
816C22—121no—
817C22—244no—
818C22—361no—
819C22—361no—
820C22—361no—
821C22—724no—
822C22D32×D411yescharacteristic
823C4—41no—
824C4—61no—
825C4—61no—
826C4—92no—
827C4—121no—
828C4—121no—
829C4—121no—
830C4—181no—
831C4—361no—
832C4D3×#23511yescharacteristic
833C4#6431311yescharacteristic
834C3—21no—
835C3#7875811yescharacteristic, complemented
836C3#8068011yescharacteristic, complemented
837C2—62no—
838C2—62no—
839C2—81no—
840C2—122no—
841C2—721no—
842C2#1059427311yescharacteristic
843C2#1059473411yescharacteristic
844C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595288C2
hypercenter#102D32
hypocenterC32#3295
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. #10594532C2semidirect
3. #10592459C2semidirect
4. C3×#4778C2semidirect
5. C3×D3×#102C2semidirect
6. #10591458C2semidirect
7. #10591444C2semidirect
8. #10591415C2semidirect
9. D3×#821C2semidirect
10. #10590847C2semidirect
11. #10590742C2semidirect
12. C8×#625C2semidirect
13. #10590596C2semidirect
14. #10590472C2semidirect
15. #10590423C2semidirect
22. #64097C22semidirect
24. C2×C3×#214C22semidirect
25. C2×C3×D3×C8C22semidirect
26. C2×C3×D3×C8C22semidirect
27. C3×#897C22semidirect
28. C3×D3×C4⋊C4C22semidirect
36. D3×C4⋊Dic3C22semidirect
39. #63856C22semidirect
41. #63843C22semidirect
42. C2×#3717C22semidirect
44. C32×#102C22semidirect
45. #63659C22semidirect
46. #63648C22semidirect
47. C8×C3⋊Dic3C22semidirect
48. #63636C22semidirect
49. C3×#832C22semidirect
51. C3×#816C22semidirect
53. C3×#808C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63564C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
81. #4778D3semidirect
85. D3×#102D3semidirect
172. C2×#214C2×D3semidirect
181. C2×D3×C8C2×D3semidirect
182. C2×D3×C8C2×D3semidirect
184. #897C2×D3semidirect
189. D3×C4⋊C4C2×D3semidirect
206. C3×#102C2×D3semidirect
207. C3×#102C2×D3semidirect
212. #832C2×D3semidirect
224. #816C2×D3semidirect
238. #808C2×D3semidirect
280. #625SD16semidirect
487. #102D32semidirect
735. C32#3295semidirect
835. C3#78758semidirect
836. C3#80680semidirect

Maximal subgroups

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

subgroupindex
#105952882
#105945322
#105924592
C3×#47782
C3×D3×#1022
#105914582
#105914442
#105914152
D3×#8212
#105908472
#105907422
C8×#6252
#105905962
#105904722
#105904232
#806803
#787583