Finite Group Databasebeta

← #11887145

Subgroups — #11887145

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595293C211yesmaximal, characteristic
2#10594536C211yesmaximal, characteristic, complemented
3#10592476C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4762C211yesmaximal, characteristic, complemented
6#10591487C211yesmaximal, characteristic, complemented
7#10591465C211yesmaximal, characteristic, complemented
8#10591458C211yesmaximal, characteristic, complemented
9#10590943C211yesmaximal, characteristic, complemented
10#10590829C211yesmaximal, characteristic, complemented
11#10590757C211yesmaximal, characteristic, complemented
12#10590720C211yesmaximal, characteristic, complemented
13#10590593C211yesmaximal, characteristic, complemented
14#10590500C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#80395—31nomaximal
17#78758—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21#64147C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
23C3×#940C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic, complemented
25C2×C3×#204C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28C3×#887C2211yescharacteristic, complemented
29#63983—21no—
30#63976—21no—
31#63970—21no—
32#63918C2211yescharacteristic, complemented
33#63908C2211yescharacteristic
34C4×#626—21no—
35C4×#626C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63871C2211yescharacteristic, complemented
38#63867—21no—
39#63865—21no—
40#63856C2211yescharacteristic, complemented
41#63851—21no—
42C2×#3715C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63647C2211yescharacteristic, complemented
47#63644C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61D4×#67—31no—
62#5717—31no—
63#5579—31no—
64#5511—31no—
65C3×#460—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5171—31no—
69#5171—31no—
70#5169—31no—
71#5169—31no—
72#5114—31no—
73C8×#67—31no—
74#5070—31no—
75C4×#215—31no—
76#4968—31no—
77#4842—31no—
78#4834—31no—
79#4778—31no—
80#4777—31no—
81#4777—31no—
82#4777—31no—
83#4777—61no—
84#4776—31no—
85D3×#102—31no—
86D3×#102—31no—
87D3×#102D311yescharacteristic, complemented
88#4762D311yescharacteristic, complemented
89#4761—31no—
90#4760—31no—
91#4758—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108D3×#67—44no—
109C2×#627—21no—
110C2×#626D411yescharacteristic
111C2×#625—21no—
112C2×#625—21no—
113C2×D3×Dic3—21no—
114#3802—22no—
115#3802—41no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3757—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#214—41no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—41no—
132C3×D3×C8—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143#3715—22no—
144#3710—41no—
145#3295—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×#127—31no—
156C3×C4×Q8—31no—
157C2×C3×C4⋊C4—31no—
158#953—61no—
159#946—31no—
160#946—31no—
161C2×#215—31no—
162#940C2×D311yescharacteristic
163#939—61no—
164#938—31no—
165#938—31no—
166#938—31no—
167#938—61no—
168#938—61no—
169#937—61no—
170#937—61no—
171#937—61no—
172D4×Dic3—31no—
173C2×#214—31no—
174C2×#214C2×D311yescharacteristic, complemented
175#930—31no—
176C4×#67—31no—
177C4×#67—61no—
178#924—31no—
179#924—61no—
180C2×#204C2×D311yescharacteristic, complemented
181C2×D3×C8—31no—
182C2×D3×C8—31no—
183C2×D3×C8C2×D311yescharacteristic, complemented
184#897—31no—
185#896—61no—
186#896—61no—
187#896—61no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—61no—
191D3×C4⋊C4C2×D311yescharacteristic, complemented
192#889—61no—
193#888—31no—
194#887C2×D311yescharacteristic, complemented
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198#870—61no—
199#869—31no—
200C3×C4⋊C8—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic, complemented
207C3×#102C2×D311yescharacteristic, complemented
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic, complemented
216#830—31no—
217#821—31no—
218#821—31no—
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—61no—
224#817—31no—
225#817—31no—
226#817—31no—
227#817—61no—
228#816—31no—
229Dic3⋊C8C2×D311yescharacteristic, complemented
230C8×Dic3—31no—
231#809—31no—
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic, complemented
234#808—31no—
235#808—31no—
236#808—31no—
237#808—61no—
238C4×C3⋊C8—31no—
239C23×C32—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
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—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260C4×C3⋊D3—81no—
261C3×#67—42no—
262C3×#67—42no—
263C3×#67—81no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12#4112yes—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—81no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278#627—81no—
279#626SD1614yescomplemented
280#625—42no—
281#625—42no—
282D3×Dic3—42no—
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—91no—
294#465—91no—
295#460—31no—
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—31no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C2×C3×D4—62no—
314C2×C3×D4—121no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C2×#67—21no—
320C2×#67—21no—
321C2×#67—21no—
322C2×#67—31no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—121no—
330C2×#67—124no—
331C22×Dic3—61no—
332D3×D4—22no—
333D3×D4—41no—
334D3×D4—62no—
335D3×D4—62no—
336D3×D4—121no—
337D3×D4—121no—
338D3×D4—124no—
339C2×D12—31no—
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—121no—
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6—61no—
352C2×Dic6—61no—
353C2×Dic6C22×D311yescharacteristic
354C3×SD16—121no—
355C3×SD16—121no—
356C2×C3×C8—21no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8—121no—
360C2×C3×C8C22×D311yescharacteristic
361C2×C3×C8C22×D311yescharacteristic
362C3×C4⋊C4—21no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C42—31no—
369C3×C42—61no—
370#217—31no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—121no—
377#215—62no—
378#214—41no—
379#214—62no—
380(C2×D3)⋊C4—31no—
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—61no—
387(C2×D3)⋊C4—61no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—31no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—121no—
408C4×Dic3—21no—
409C4×Dic3C22×D311yescharacteristic
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415#204—41no—
416D3×C8—41no—
417D3×C8—121no—
418D3×C8—121no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3C2×SD1612yes—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—84no—
435C2×C3×D3C2×SD1612yes—
436D32—84no—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3C2×SD1612yes—
448C22×D4—31no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—31no—
453C2×SD16—91no—
454C22×C8—31no—
455C22×C8—91no—
456C4⋊Q8—91no—
457#127—31no—
458#125—181no—
459C22⋊Q8—91no—
460C22⋊Q8—91no—
461C22⋊Q8—181no—
462C22⋊Q8—181no—
463#121—91no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—31no—
469C4×D4—91no—
470C4×D4—91no—
471C4×D4—181no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—91no—
474#106—91no—
475#106—91no—
476#106—91no—
477C4⋊C8—31no—
478#103—91no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—31no—
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—41no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—241no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—31no—
503C22×D3—31no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3—61no—
507C22×D3—81no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—241no—
513C22×D3—241no—
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—61no—
526C3×D4—61no—
527C3×D4—122no—
528C3×D4—122no—
529C3×D4—241no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—41no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—241no—
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544#67—34no—
545#67—42no—
546#67—42no—
547#67—81no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—242no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—31no—
558C2×Dic3—31no—
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×Dic3D3×D411yescharacteristic
568C2×Dic3D3×D411yescharacteristic
569C2×Dic3D3×D411yescharacteristic
570D12—21no—
571D12—21no—
572D12—21no—
573D12—34no—
574D12#23512yes—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—61no—
578C4×D3—61no—
579C4×D3—61no—
580C4×D3—61no—
581C4×D3—81no—
582C4×D3—121no—
583C4×D3—121no—
584C4×D3—122no—
585C4×D3—241no—
586C4×D3—241no—
587C4×D3—242no—
588Dic6—21no—
589Dic6—21no—
590Dic6—241no—
591Dic6—241no—
592C3×C8—21no—
593C3×C8—21no—
594C3×C8—41no—
595C3×C8—61no—
596C3×C8—61no—
597C3⋊C8—21no—
598C3⋊C8—21no—
599C3⋊C8—61no—
600C3⋊C8—61no—
601C3⋊C8—121no—
602C2×C32—81no—
603C2×C32#54611yescharacteristic
604C2×C32C22×SD1611yescharacteristic
605C2×C32#57611yescharacteristic
606C3⋊D3—22no—
607C3×D3—22no—
608C3×D3—42no—
609C3×D3—81no—
610C24—61no—
611C24—181no—
612C2×Q8—31no—
613C2×Q8—181no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—62no—
620C2×D4—91no—
621C2×D4—121no—
622C2×D4—181no—
623C2×D4—182no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—361no—
627C2×D4—364no—
628C2×D4C2×D3211yescharacteristic
629C22×C4—31no—
630C22×C4—61no—
631C22×C4—91no—
632C22×C4—181no—
633C22×C4—181no—
634SD16—121no—
635SD16—121no—
636SD16—182no—
637C2×C8—31no—
638C2×C8—31no—
639C2×C8—91no—
640C2×C8—121no—
641C2×C8—361no—
642C2×C8C2×D3211yescharacteristic
643C4⋊C4—31no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—91no—
647C4⋊C4—91no—
648C4⋊C4—91no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4C2×D3211yescharacteristic
654C22⋊C4—91no—
655C22⋊C4—91no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C42—31no—
662C42—61no—
663C22×C3—21no—
664C22×C3—32no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—62no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—244no—
683C22×C3C2×D3×D411yescharacteristic
684C22×C3C2×D3×D411yescharacteristic
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—22no—
688C2×D3—32no—
689C2×D3—32no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—62no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—61no—
700C2×D3—84no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—244no—
704C2×D3—244no—
705C2×D3D3×SD1612yes—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—32no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—61no—
712C3×C4—61no—
713C3×C4—81no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4C2×#23511yescharacteristic
717C3×C4#100411yescharacteristic
718C3×C4#100411yescharacteristic
719C3×C4D3×#4111yescharacteristic
720Dic3—21no—
721Dic3—21no—
722Dic3—41no—
723Dic3—41no—
724Dic3—61no—
725Dic3—61no—
726Dic3—121no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—241no—
732Dic3—241no—
733Dic3D3×SD1612yes—
734C32#329511yescharacteristic, complemented, Sylow
735C23—21no—
736C23—31no—
737C23—61no—
738C23—61no—
739C23—91no—
740C23—122no—
741C23—122no—
742C23—241no—
743C23—362no—
744C23—362no—
745C23—721no—
746Q8—61no—
747Q8—61no—
748Q8—721no—
749D4—21no—
750D4—21no—
751D4—32no—
752D4—61no—
753D4—61no—
754D4—61no—
755D4—94no—
756D4—122no—
757D4—122no—
758D4—241no—
759D4—362no—
760D4—362no—
761D4—362no—
762C2×C4—21no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—91no—
771C2×C4—181no—
772C2×C4—181no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—241no—
776C2×C4—362no—
777C2×C4—721no—
778C2×C4C22×D3211yescharacteristic
779C8—21no—
780C8—61no—
781C8—61no—
782C8—181no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—62no—
787C2×C3—81no—
788C2×C3—81no—
789C2×C3—122no—
790C2×C3—161no—
791C2×C3—241no—
792C2×C3#549011yescharacteristic
793C2×C3#561211yescharacteristic
794C2×C3#575711yescharacteristic
795C2×C3C2×D3×SD1611yescharacteristic
796C2×C3C2×D3×SD1611yescharacteristic
797C2×C3#577411yescharacteristic
798D3—22no—
799D3—42no—
800D3—62no—
801D3—62no—
802D3—81no—
803D3—122no—
804C22—32no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—61no—
809C22—61no—
810C22—62no—
811C22—92no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—181no—
818C22—181no—
819C22—244no—
820C22—724no—
821C22D32×D411yescharacteristic
822C4—32no—
823C4—41no—
824C4—61no—
825C4—61no—
826C4—121no—
827C4—121no—
828C4—181no—
829C4—361no—
830C4—361no—
831C4D3×#23511yescharacteristic
832C4#6431311yescharacteristic
833C3—21no—
834C3#7875811yescharacteristic, complemented
835C3#8039511yescharacteristic, complemented
836C2—62no—
837C2—81no—
838C2—122no—
839C2—182no—
840C2—241no—
841C2#1059427811yescharacteristic
842C2#1059473211yescharacteristic
843C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595293C2
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. #10594536C2semidirect
3. #10592476C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4762C2semidirect
6. #10591487C2semidirect
7. #10591465C2semidirect
8. #10591458C2semidirect
9. #10590943C2semidirect
10. #10590829C2semidirect
11. #10590757C2semidirect
12. #10590720C2semidirect
13. #10590593C2semidirect
14. #10590500C2semidirect
15. #10590453C2semidirect
22. C4⋊C4×C3⋊D3C22semidirect
24. C2×C3×#214C22semidirect
25. C2×C3×#204C22semidirect
26. C2×C3×D3×C8C22semidirect
27. C3×D3×C4⋊C4C22semidirect
28. C3×#887C22semidirect
32. #63918C22semidirect
37. #63871C22semidirect
40. #63856C22semidirect
43. C2×#3710C22semidirect
44. C32×#102C22semidirect
45. #63659C22semidirect
46. #63647C22semidirect
47. #63644C22semidirect
48. #63635C22semidirect
49. C3×#832C22semidirect
51. C3×Dic3⋊C8C22semidirect
53. C3×#809C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
87. D3×#102D3semidirect
88. #4762D3semidirect
174. C2×#214C2×D3semidirect
180. C2×#204C2×D3semidirect
183. C2×D3×C8C2×D3semidirect
191. D3×C4⋊C4C2×D3semidirect
194. #887C2×D3semidirect
206. C3×#102C2×D3semidirect
207. C3×#102C2×D3semidirect
215. #832C2×D3semidirect
229. Dic3⋊C8C2×D3semidirect
233. #809C2×D3semidirect
279. #626SD16semidirect
487. #102D32semidirect
734. C32#3295semidirect
834. C3#78758semidirect
835. C3#80395semidirect

Maximal subgroups

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

subgroupindex
#105952932
#105945362
#105924762
C3×D3×#1022
C3×#47622
#105914872
#105914652
#105914582
#105909432
#105908292
#105907572
#105907202
#105905932
#105905002
#105904532
#803953
#787583