Finite Group Databasebeta

← #11887121

Subgroups — #11887121

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
1D4×#625C211yesmaximal, characteristic
2#10594532C211yesmaximal, characteristic, complemented
3#10592460C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591445C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590876C211yesmaximal, characteristic, complemented
10#10590829C211yesmaximal, characteristic, complemented
11#10590717C211yesmaximal, characteristic, complemented
12#10590676C211yesmaximal, characteristic, complemented
13#10590552C211yesmaximal, characteristic, complemented
14#10590501C211yesmaximal, characteristic, complemented
15#10590500C211yesmaximal, characteristic, complemented
16#80158—31nomaximal
17#78758—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×#625—21no—
21D4×C3⋊Dic3C2211yescharacteristic
22#64097C2211yescharacteristic, complemented
23C2×C3×#214C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic, complemented
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×#897C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28#63980—21no—
29#63976—21no—
30#63976—21no—
31#63914C2211yescharacteristic
32#63908C2211yescharacteristic
33#63908C2211yescharacteristic
34C4×#625C2211yescharacteristic
35#63896—21no—
36D3×C4⋊Dic3C2211yescharacteristic, complemented
37#63879—21no—
38#63857—21no—
39#63856C2211yescharacteristic, complemented
40#63847—21no—
41#63843C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63644C2211yescharacteristic, complemented
47#63641C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61D4×#67—31no—
62D4×#67—31no—
63#5635—31no—
64#5511—31no—
65C3×#450—31no—
66C2×C3×#102—31no—
67#5218—31no—
68C2×#832—31no—
69#5171—31no—
70#5169—31no—
71#5163—31no—
72Dic3×SD16—31no—
73#5114—31no—
74C8×#67—31no—
75#5048—31no—
76#4968—31no—
77#4778—31no—
78#4777—31no—
79#4777—31no—
80#4776D311yescharacteristic, complemented
81D3×#102—31no—
82D3×#102D311yescharacteristic, complemented
83#4762—31no—
84#4761—31no—
85#4761—31no—
86#4761—61no—
87#4760—31no—
88#4760—31no—
89#4758—31no—
90#4735—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×#634—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#625—21no—
110C2×#625—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—44no—
114C2×#625D411yescharacteristic
115C2×D3×Dic3—21no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3757—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#214—22no—
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×D3×C8—41no—
133#3724—21no—
134#3724D411yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3715—41no—
144D3×C3⋊C8—41no—
145#3295—91noSylow
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×#67—61no—
149C22×#67—61no—
150C2×D3×D4C2×D311yescharacteristic
151C2×D3×D4C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×C22⋊Q8—31no—
156C2×C3×C4⋊C4—31no—
157#953—61no—
158#953—61no—
159#946—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162#940—31no—
163#940—31no—
164#939—61no—
165#939—61no—
166#938—31no—
167#938—31no—
168#937—61no—
169#937—61no—
170D4×Dic3—31no—
171D4×Dic3—31no—
172D4×Dic3—61no—
173C2×#214—31no—
174C2×#214C2×D311yescharacteristic
175#930—31no—
176#930—31no—
177C4×#67—31no—
178C4×#67—31no—
179C4×#67—61no—
180C2×C4⋊Dic3—31no—
181#924—31no—
182#924—61no—
183C22×C3⋊C8—31no—
184C2×#204C2×D311yescharacteristic, complemented
185C2×D3×C8—31no—
186C2×D3×C8C2×D311yescharacteristic, complemented
187#897—61no—
188#897C2×D311yescharacteristic, complemented
189#896—61no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4C2×D311yescharacteristic, complemented
192#889—61no—
193#889—61no—
194#888—31no—
195#888—31no—
196#888—61no—
197#887—31no—
198#67⋊C4—61no—
199#878—61no—
200C3×#102—21no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102C2×D311yescharacteristic
206C3×#102C2×D311yescharacteristic
207C3×C22⋊C8—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216#830—31no—
217#821—31no—
218#821—31no—
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8C2×D311yescharacteristic, complemented
222#817—31no—
223#817—31no—
224#817—31no—
225#817—61no—
226#816—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—61no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#809—31no—
233#809C2×D311yescharacteristic, complemented
234#809C2×D311yescharacteristic, complemented
235#808—31no—
236#808—31no—
237#808—31no—
238#808—61no—
239C23×C32—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—81no—
247C22×C3×D3—81no—
248C22×C3×D3C2×D411yescharacteristic
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—42no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259#634—81no—
260C3×#67—42no—
261C3×#67—42no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
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#625—42no—
278#625—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—91no—
291#481—91no—
292#476—91no—
293#465—91no—
294#465—91no—
295#460—91no—
296#450—31no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—31no—
301C2×#102—91no—
302C24×C3—61no—
303C24×C3—61no—
304C23×D3—21no—
305C23×D3—21no—
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—62no—
313C2×C3×D4—62no—
314C2×C3×D4—121no—
315C2×C3×D4—121no—
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C22×D311yescharacteristic
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—61no—
321C2×#67—21no—
322C2×#67—21no—
323C2×#67—31no—
324C2×#67—31no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—124no—
334C2×#67—124no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—121no—
339D3×D4—22no—
340D3×D4—22no—
341D3×D4—41no—
342D3×D4—41no—
343C2×D12C22×D311yescharacteristic
344C2×D12C22×D311yescharacteristic
345C2×C4×D3—21no—
346C2×C4×D3—61no—
347C2×C4×D3C22×D311yescharacteristic
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—61no—
350C2×Dic6—61no—
351C2×Dic6—121no—
352C2×Dic6C22×D311yescharacteristic
353C3×SD16—62no—
354C3×SD16—121no—
355C2×C3×C8—21no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8—121no—
359C2×C3×C8C22×D311yescharacteristic
360C2×C3×C8C22×D311yescharacteristic
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×C22⋊C4—61no—
368#217—31no—
369#217—31no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—121no—
376#215—121no—
377#214—22no—
378#214—121no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385C4⋊Dic3—21no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—31no—
397Dic3⋊C4—31no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—121no—
405C4×Dic3—31no—
406C4×Dic3—31no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—121no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416#204—41no—
417D3×C8—41no—
418D3×C8—121no—
419C22×C32—22no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
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×D3—84no—
434C2×C3×D3—84no—
435C2×C3×D3C2×SD1612yes—
436C2×C3×D3C2×SD1612yes—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3⋊Dic3C2×SD1612yes—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—31no—
449C22×D4—31no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—31no—
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—91no—
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—91no—
475#106—91no—
476#106—91no—
477C4⋊C8—91no—
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
488C22⋊C8—31no—
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—61no—
498C23×C3—122no—
499C23×C3—122no—
500C23×C3—122no—
501C23×C3—122no—
502C23×C3—241no—
503C23×C3—241no—
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—42no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—42no—
510C22×D3—81no—
511C22×D3—81no—
512C22×D3D3×D411yescharacteristic
513C22×D3D3×D411yescharacteristic
514C3×Q8—61no—
515C3×Q8—61no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—22no—
519C3×D4—41no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—122no—
525C3×D4—122no—
526C3×D4#23512yes—
527C3×D4#23712yes—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
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×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—122no—
552#67—122no—
553#67—241no—
554#67—241no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—121no—
568C2×Dic3—121no—
569C2×Dic3—122no—
570C2×Dic3—122no—
571C2×Dic3—242no—
572C2×Dic3—241no—
573C2×Dic3D3×D411yescharacteristic
574C2×Dic3D3×D411yescharacteristic
575D12—21no—
576D12—21no—
577D12—21no—
578D12—21no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—81no—
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—42no—
601C2×C32#54611yescharacteristic
602C2×C32C22×SD1611yescharacteristic
603C2×C32#57611yescharacteristic
604C3×D3—22no—
605C3×D3—22no—
606C3×D3—81no—
607C3×D3—81no—
608C24—61no—
609C24—61no—
610C2×Q8—31no—
611C2×Q8—181no—
612C2×D4—31no—
613C2×D4—31no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—62no—
617C2×D4—62no—
618C2×D4—91no—
619C2×D4—121no—
620C2×D4—121no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—181no—
624C2×D4—181no—
625C2×D4—364no—
626C2×D4C2×D3211yescharacteristic
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—61no—
630C22×C4—181no—
631C22×C4—181no—
632SD16—62no—
633SD16—121no—
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—91no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4C2×D3211yescharacteristic
652C22⋊C4—61no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C42—91no—
660C42—181no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—21no—
664C22×C3—32no—
665C22×C3—32no—
666C22×C3—42no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—244no—
684C22×C3—244no—
685C22×C3C2×D3×D411yescharacteristic
686C22×C3C2×D3×D411yescharacteristic
687C2×D3—21no—
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—84no—
698C2×D3—84no—
699C2×D3D3×SD1612yes—
700C2×D3D3×SD1612yes—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—61no—
706C3×C4—61no—
707C3×C4—81no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4C2×#23511yescharacteristic
711C3×C4C2×#23711yescharacteristic
712C3×C4#100411yescharacteristic
713C3×C4#100411yescharacteristic
714Dic3—21no—
715Dic3—21no—
716Dic3—32no—
717Dic3—32no—
718Dic3—41no—
719Dic3—41no—
720Dic3—62no—
721Dic3—61no—
722Dic3—61no—
723Dic3—121no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—121no—
728Dic3—241no—
729Dic3—241no—
730C32#329511yescharacteristic, complemented, Sylow
731C23—21no—
732C23—31no—
733C23—31no—
734C23—61no—
735C23—61no—
736C23—122no—
737C23—122no—
738C23—122no—
739C23—122no—
740C23—241no—
741C23—241no—
742Q8—61no—
743Q8—61no—
744Q8—721no—
745D4—21no—
746D4—61no—
747D4—61no—
748D4—61no—
749D4—61no—
750D4—94no—
751D4—122no—
752D4—122no—
753D4—362no—
754D4—362no—
755D4—362no—
756D4—721no—
757D4#379512yes—
758C2×C4—21no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—91no—
768C2×C4—91no—
769C2×C4—181no—
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—42no—
783C2×C3—42no—
784C2×C3—62no—
785C2×C3—62no—
786C2×C3—82no—
787C2×C3—241no—
788C2×C3—241no—
789C2×C3#549011yescharacteristic
790C2×C3#559111yescharacteristic
791C2×C3#575711yescharacteristic
792C2×C3C2×D3×SD1611yescharacteristic
793C2×C3C2×D3×SD1611yescharacteristic
794C2×C3#577411yescharacteristic
795D3—22no—
796D3—22no—
797D3—81no—
798D3—81no—
799C22—22no—
800C22—32no—
801C22—32no—
802C22—41no—
803C22—41no—
804C22—61no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—244no—
815C22—244no—
816C22D32×D411yescharacteristic
817C4—41no—
818C4—61no—
819C4—61no—
820C4—92no—
821C4—121no—
822C4—121no—
823C4—181no—
824C4—361no—
825C4—361no—
826C4C2×#379511yescharacteristic
827C4#6431311yescharacteristic
828C3—21no—
829C3#7875811yescharacteristic, complemented
830C3#8015811yescharacteristic, complemented
831C2—42no—
832C2—62no—
833C2—62no—
834C2—241no—
835C2—241no—
836C2#1059418411yescharacteristic
837C2#1059473211yescharacteristic
838C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalD4×#625C2
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. #10592460C2semidirect
4. C3×#4776C2semidirect
5. C3×D3×#102C2semidirect
6. #10591458C2semidirect
7. #10591445C2semidirect
8. D3×#832C2semidirect
9. #10590876C2semidirect
10. #10590829C2semidirect
11. #10590717C2semidirect
12. #10590676C2semidirect
13. #10590552C2semidirect
14. #10590501C2semidirect
15. #10590500C2semidirect
22. #64097C22semidirect
24. C2×C3×#204C22semidirect
25. C2×C3×D3×C8C22semidirect
26. C3×#897C22semidirect
27. C3×D3×C4⋊C4C22semidirect
36. D3×C4⋊Dic3C22semidirect
39. #63856C22semidirect
41. #63843C22semidirect
42. C2×#3715C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63644C22semidirect
47. #63641C22semidirect
48. #63635C22semidirect
50. C3×#821C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#809C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63553C22semidirect
80. #4776D3semidirect
82. D3×#102D3semidirect
184. C2×#204C2×D3semidirect
186. C2×D3×C8C2×D3semidirect
188. #897C2×D3semidirect
191. D3×C4⋊C4C2×D3semidirect
219. #821C2×D3semidirect
221. (C2×D3)⋊C8C2×D3semidirect
233. #809C2×D3semidirect
234. #809C2×D3semidirect
281. #625SD16semidirect
730. C32#3295semidirect
829. C3#78758semidirect
830. C3#80158semidirect

Maximal subgroups

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

subgroupindex
D4×#6252
#105945322
#105924602
C3×#47762
C3×D3×#1022
#105914582
#105914452
D3×#8322
#105908762
#105908292
#105907172
#105906762
#105905522
#105905012
#105905002
#801583
#787583