Finite Group Databasebeta

← #11889127

Subgroups — #11889127

Order 1152.

962 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#10594004C211yesmaximal, characteristic
2#10593947C211yesmaximal, characteristic, complemented
3#10592535C211yesmaximal, characteristic, complemented
4C3×#4848C211yesmaximal, characteristic, complemented
5C3×#4847C211yesmaximal, characteristic, complemented
6#10590943C211yesmaximal, characteristic, complemented
7#10590943C211yesmaximal, characteristic, complemented
8#10590941C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590845C211yesmaximal, characteristic, complemented
11#10590843C211yesmaximal, characteristic, complemented
12#10590652C211yesmaximal, characteristic, complemented
13#10590650C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590279C211yesmaximal, characteristic, complemented
16#81189—31nomaximal
17#80397—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×D3×D12—21no—
21C2×#3743C2211yescharacteristic, complemented
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic, complemented
25C2×C3×#204C2211yescharacteristic, complemented
26C3×#874C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28C3×#870C2211yescharacteristic, complemented
29C3×C4×Dic6C2211yescharacteristic, complemented
30#63922—21no—
31#63922—21no—
32#63916C2211yescharacteristic
33#63916C2211yescharacteristic
34#63908—21no—
35#63900C2211yescharacteristic, complemented
36#63897—21no—
37#63871C2211yescharacteristic, complemented
38#63871C2211yescharacteristic, complemented
39#63868—21no—
40#63849C2211yescharacteristic, complemented
41#63845—21no—
42#63836—21no—
43C2×#3715C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic, complemented
45#63647C2211yescharacteristic, complemented
46#63647C2211yescharacteristic, complemented
47#63630C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53C3×#817C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61#5717—31no—
62#5694—31no—
63#5581—31no—
64D4×D12—31no—
65C3×#478—31no—
66C3×#460—31no—
67#5174—31no—
68#5171—31no—
69#5169—31no—
70#5169—31no—
71#5071—31no—
72#5067—31no—
73#5026—31no—
74#5018—31no—
75#4886—31no—
76#4882—31no—
77#4866—31no—
78#4864—31no—
79#4848D311yescharacteristic, complemented
80#4847D311yescharacteristic, complemented
81#4836—31no—
82#4836—31no—
83#4836—61no—
84#4779—31no—
85#4776—31no—
86#4776—31no—
87#4774—31no—
88#4770—31no—
89#4770—31no—
90D3×#102—31no—
91D3×#102—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)D411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×#624—21no—
109#3802—22no—
110#3802—22no—
111#3802—41no—
112#3802—41no—
113D3×D12—44no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C32×C42C2311yescharacteristic
117#3752D411yescharacteristic
118#3752D411yescharacteristic
119C4⋊(C3⋊Dic3)D411yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3743—41no—
123C8×C3⋊D3—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C3×#204—41no—
134C3×#204—41no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144#3715—22no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C22×D12—61no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×#127—31no—
155C3×#125—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158#946—31no—
159#946—31no—
160C2×#215—31no—
161#938—31no—
162#938—31no—
163#938—61no—
164#937—61no—
165#937—61no—
166C2×#214—31no—
167#930—61no—
168C2×#204C2×D311yescharacteristic, complemented
169C2×#204C2×D311yescharacteristic, complemented
170C2×ΓL(1,𝔽25)—31no—
171C2×ΓL(1,𝔽25)—31no—
172C2×ΓL(1,𝔽25)—61no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8—61no—
176#898—61no—
177#897—31no—
178#897—31no—
179#895—31no—
180#895—31no—
181#894—61no—
182#894—61no—
183#892—31no—
184#892—31no—
185#892—61no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188#890—61no—
189#889—61no—
190#882—61no—
191#882—61no—
192#876—61no—
193#874C2×D311yescharacteristic
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197C4×D12C2×D311yescharacteristic
198#872—61no—
199#870C2×D311yescharacteristic, complemented
200C4×Dic6C2×D311yescharacteristic, complemented
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—21no—
204C3×C4⋊C8C2×D311yescharacteristic, complemented
205C3×C4⋊C8C2×D311yescharacteristic, complemented
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218#821C2×D311yescharacteristic, complemented
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—61no—
225(C2×D3)⋊C8—61no—
226#818C2×D311yescharacteristic, complemented
227#817C2×D311yescharacteristic, complemented
228#810—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#807—31no—
235#807—31no—
236#803—31no—
237#803—31no—
238#803—61no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4⋊(C3⋊D3)—22no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—42no—
271C3×D12—81no—
272C3×D12#4112yes—
273C3×C4×D3—42no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#626—42no—
277#626—42no—
278#625—42no—
279#625—42no—
280#624—42no—
281C32×C8—21no—
282C32×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—31no—
291#468—91no—
292#465—91no—
293#460—31no—
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—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C22×C3×C4—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317D3×D4—62no—
318D3×D4—62no—
319D3×D4—62no—
320D3×D4—62no—
321D3×D4—124no—
322D3×D4—121no—
323D3×D4—121no—
324D3×D4—121no—
325D3×D4—121no—
326C2×D12—21no—
327C2×D12—21no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—124no—
334C2×D12C22×D311yescharacteristic
335C2×D12C22×D311yescharacteristic
336C2×D12C22×D311yescharacteristic
337C2×C4×D3—21no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×Dic6C22×D311yescharacteristic
347C3×SD16—121no—
348C3×SD16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—21no—
364C3×C42—61no—
365C3×C42C22×D311yescharacteristic
366C3×C42C22×D311yescharacteristic
367#217—61no—
368#217—61no—
369#215—62no—
370#214—62no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402C4×Dic3—21no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—61no—
411#204—41no—
412#204—41no—
413ΓL(1,𝔽25)—121no—
414ΓL(1,𝔽25)—121no—
415ΓL(1,𝔽25)—122no—
416D3×C8—121no—
417D3×C8—121no—
418D3×C8—122no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3AGL(1,ℤ/8)12yes—
426C2×C3×D3—22no—
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—41no—
434C2×C3×D3—41no—
435D32—84no—
436D32—84no—
437C32×C4—21no—
438C32×C4—21no—
439C32×C4C2×#4111yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—91no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—31no—
453C2×SD16—91no—
454C2×M16—91no—
455C22×C8—91no—
456#127—31no—
457#126—181no—
458#125—31no—
459#125—181no—
460#123—181no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463#121—91no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—31no—
469C4×D4—31no—
470C4×D4—91no—
471#117—91no—
472#117—181no—
473C2×C4⋊C4—91no—
474#107—31no—
475#107—91no—
476#106—31no—
477C4⋊C8D3211yescharacteristic, complemented
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#102—91no—
488C22⋊C8—91no—
489C22⋊C8—91no—
490#97—91no—
491C23×C3—61no—
492C23×C3—61no—
493C23×C3—61no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—31no—
498C22×D3—31no—
499C22×D3—31no—
500C22×D3—31no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—241no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3—241no—
515C3×Q8—61no—
516C3×Q8—61no—
517C3×D4—32no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—122no—
524C3×D4—241no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—122no—
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—122no—
541#67—122no—
542#67—122no—
543#67—122no—
544#67—122no—
545#67—122no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557D12—21no—
558D12—21no—
559D12—21no—
560D12—21no—
561D12—21no—
562D12—42no—
563D12—62no—
564D12—62no—
565D12—81no—
566D12—122no—
567D12—122no—
568D12—122no—
569D12#23912yes—
570C4×D3—42no—
571C4×D3—61no—
572C4×D3—61no—
573C4×D3—61no—
574C4×D3—61no—
575C4×D3—61no—
576C4×D3—61no—
577C4×D3—61no—
578C4×D3—61no—
579C4×D3—121no—
580C4×D3—121no—
581C4×D3—121no—
582C4×D3—121no—
583C4×D3—122no—
584C4×D3—122no—
585Dic6—21no—
586Dic6—21no—
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—21no—
590C3×C8—21no—
591C3×C8—41no—
592C3×C8—41no—
593C3⋊C8—62no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—61no—
597C3⋊C8—61no—
598C3⋊C8—121no—
599C2×C32#54611yescharacteristic
600C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
601C2×C32#57711yescharacteristic
602C3⋊D3—22no—
603C3⋊D3—41no—
604C3×D3—42no—
605C3×D3—81no—
606C3×D3—81no—
607C24—181no—
608C24—181no—
609C2×Q8—31no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—91no—
616C2×D4—181no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—181no—
620C2×D4—182no—
621C2×D4—182no—
622C2×D4—364no—
623C2×D4—361no—
624C2×D4—361no—
625C22×C4—61no—
626C22×C4—91no—
627C22×C4—91no—
628C22×C4—181no—
629SD16—121no—
630SD16—121no—
631SD16—182no—
632M16—361no—
633C2×C8—91no—
634C2×C8—91no—
635C2×C8—361no—
636C2×C8C2×D3211yescharacteristic
637C2×C8C2×D3211yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—91no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C22⋊C4—61no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C42—61no—
658C42—181no—
659C42C2×D3211yescharacteristic
660C22×C3—21no—
661C22×C3—62no—
662C22×C3—121no—
663C22×C3—121no—
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—22no—
673C2×D3—32no—
674C2×D3—32no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—62no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—244no—
700C2×D3—244no—
701C2×D3—244no—
702C2×D3—244no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4#100411yescharacteristic
717C3×C4C2×#23911yescharacteristic
718C3×C4D3×#4111yescharacteristic
719C3×C4#100911yescharacteristic
720Dic3—41no—
721Dic3—41no—
722Dic3—41no—
723Dic3—41no—
724Dic3—41no—
725Dic3—61no—
726Dic3—61no—
727Dic3—61no—
728Dic3—61no—
729Dic3—121no—
730Dic3—121no—
731C32#331011yescharacteristic, complemented, Sylow
732C23—61no—
733C23—61no—
734C23—61no—
735C23—91no—
736C23—91no—
737C23—362no—
738C23—362no—
739C23—362no—
740C23—362no—
741C23—721no—
742C23—721no—
743Q8—61no—
744Q8—61no—
745D4—32no—
746D4—61no—
747D4—61no—
748D4—61no—
749D4—61no—
750D4—61no—
751D4—122no—
752D4—182no—
753D4—241no—
754D4—362no—
755D4—362no—
756D4—362no—
757D4—362no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—122no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—181no—
769C2×C4—181no—
770C2×C4—362no—
771C2×C4#380211yescharacteristic
772C2×C4#380211yescharacteristic
773C2×C4C22×D3211yescharacteristic
774C8—21no—
775C8—21no—
776C8—181no—
777C8—181no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—122no—
782C2×C3—241no—
783C2×C3—241no—
784C2×C3#561211yescharacteristic
785C2×C3#563011yescharacteristic
786C2×C3#576211yescharacteristic
787C2×C3#577011yescharacteristic
788C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
789C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
790D3—42no—
791D3—62no—
792D3—62no—
793D3—81no—
794D3—81no—
795D3—122no—
796D3—121no—
797D3—121no—
798D3—241no—
799C22—62no—
800C22—92no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—181no—
810C22—181no—
811C22—181no—
812C22—181no—
813C22—181no—
814C22—724no—
815C22—724no—
816C22C2×#380211yescharacteristic
817C4—21no—
818C4—21no—
819C4—121no—
820C4—121no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—181no—
825C4—181no—
826C4#6431411yescharacteristic
827C4D3×#23911yescharacteristic
828C3—21no—
829C3#8039711yescharacteristic, complemented
830C3#8118911yescharacteristic, complemented
831C2—122no—
832C2—182no—
833C2—241no—
834C2—241no—
835C2—361no—
836C2#1059463311yescharacteristic
837C2#1059468611yescharacteristic
838C2#1059471611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594004C2
hypercenterC4⋊C8D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593947C2semidirect
3. #10592535C2semidirect
4. C3×#4848C2semidirect
5. C3×#4847C2semidirect
6. #10590943C2semidirect
7. #10590943C2semidirect
8. #10590941C2semidirect
9. #10590940C2semidirect
10. #10590845C2semidirect
11. #10590843C2semidirect
12. #10590652C2semidirect
13. #10590650C2semidirect
14. #10590358C2semidirect
15. #10590279C2semidirect
21. C2×#3743C22semidirect
22. C2×C8×C3⋊D3C22semidirect
24. C2×C3×#204C22semidirect
25. C2×C3×#204C22semidirect
28. C3×#870C22semidirect
29. C3×C4×Dic6C22semidirect
35. #63900C22semidirect
37. #63871C22semidirect
38. #63871C22semidirect
40. #63849C22semidirect
44. C32×C4⋊C8C22semidirect
45. #63647C22semidirect
46. #63647C22semidirect
47. #63630C22semidirect
50. C3×#821C22semidirect
51. C3×#821C22semidirect
52. C3×#818C22semidirect
53. C3×#817C22semidirect
54. #63576C22semidirect
55. #63565C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
79. #4848D3semidirect
80. #4847D3semidirect
168. C2×#204C2×D3semidirect
169. C2×#204C2×D3semidirect
199. #870C2×D3semidirect
200. C4×Dic6C2×D3semidirect
204. C3×C4⋊C8C2×D3semidirect
205. C3×C4⋊C8C2×D3semidirect
218. #821C2×D3semidirect
219. #821C2×D3semidirect
226. #818C2×D3semidirect
227. #817C2×D3semidirect
477. C4⋊C8D32semidirect
731. C32#3310semidirect
829. C3#80397semidirect
830. C3#81189semidirect

Maximal subgroups

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

subgroupindex
#105940042
#105939472
#105925352
C3×#48482
C3×#48472
#105909432
#105909412
#105909402
#105908452
#105908432
#105906522
#105906502
#105903582
#105902792
#811893
#803973