Finite Group Databasebeta

← #11887111

Subgroups — #11887111

Order 1152.

991 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595069C211yesmaximal, characteristic
2#10594991C211yesmaximal, characteristic, complemented
3#10592424C211yesmaximal, characteristic, complemented
4C3×#4735C211yesmaximal, characteristic, complemented
5C3×#4731C211yesmaximal, characteristic, complemented
6#10591179C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590943C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590885C211yesmaximal, characteristic, complemented
11#10590876C211yesmaximal, characteristic, complemented
12#10590843C211yesmaximal, characteristic, complemented
13#10590776C211yesmaximal, characteristic, complemented
14#10590775C211yesmaximal, characteristic, complemented
15#10590649C211yesmaximal, characteristic, complemented
16#81342—31nomaximal
17#80158—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21C4×#638C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C2×C8×C3⋊D3C2211yescharacteristic, complemented
24C3×#930C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
26C3×#924C2211yescharacteristic, complemented
27C2×C3×#204C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic, complemented
29#63976—21no—
30#63964—21no—
31#63952—21no—
32#63922—21no—
33#63919C2211yescharacteristic, complemented
34#63916C2211yescharacteristic
35#63914C2211yescharacteristic
36#63900C2211yescharacteristic, complemented
37#63898C2211yescharacteristic
38#63895—21no—
39#63885—21no—
40#63871C2211yescharacteristic, complemented
41#63847—21no—
42#63843C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63647C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53C3×#817C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61D4×#67—31no—
62#5635—31no—
63#5609—31no—
64#5511—31no—
65C3×#481—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5171—31no—
69#5169—31no—
70#5163—31no—
71Dic3×SD16—31no—
72#5048—31no—
73#5041—31no—
74C2×#809—31no—
75#4870—31no—
76#4864—31no—
77#4863—31no—
78#4852—31no—
79#4777—31no—
80#4776—31no—
81D3×#102—31no—
82D3×#102—31no—
83#4762—31no—
84#4761—31no—
85#4760—31no—
86#4760—31no—
87#4735D311yescharacteristic, complemented
88#4731D311yescharacteristic, complemented
89#67⋊C8—31no—
90#67⋊C8—31no—
91#67⋊C8—61no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638D411yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C2×C3×D12—22no—
100C2×C3×D12—21no—
101C2×C3×D12—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106D3×#67—44no—
107C2×#627—21no—
108C2×#626—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×#625—21no—
112C2×#624—21no—
113C2×D3×Dic3—21no—
114#3802—22no—
115#3802—41no—
116C2×C32×C8C2311yescharacteristic
117C2×C32×C8C2311yescharacteristic
118#3757D411yescharacteristic
119#3752D411yescharacteristic
120#3750D411yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)—41no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C8×C3⋊D3—41no—
126C3×#217—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×#204—22no—
135C3×#204—41no—
136#3724—21no—
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144#3715—41no—
145#3295—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C22×D12C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C2×C3×C4⋊C4—31no—
157#953—61no—
158#946—31no—
159Q8×Dic3—31no—
160C2×#215—31no—
161#940—31no—
162#940—31no—
163#939—61no—
164#938—31no—
165#937—61no—
166#937—61no—
167D4×Dic3—31no—
168C2×#214—31no—
169#930C2×D311yescharacteristic
170C4×#67—31no—
171C4×#67—31no—
172C4×#67—61no—
173C4×#67—61no—
174C2×C4⋊Dic3C2×D311yescharacteristic, complemented
175#924—61no—
176#924C2×D311yescharacteristic, complemented
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—61no—
180C2×#204C2×D311yescharacteristic
181C2×#204C2×D311yescharacteristic, complemented
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184C2×D3×C8—61no—
185#897—31no—
186#897—61no—
187#896—61no—
188#895—31no—
189#893—31no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—31no—
192#889—61no—
193#889—61no—
194#888—31no—
195#888—31no—
196#887—31no—
197#884—61no—
198#882—61no—
199#67⋊C4—61no—
200#878—61no—
201C3×#106—31no—
202C3×#106—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—21no—
208C3×C22⋊C8C2×D311yescharacteristic, complemented
209C3×C22⋊C8C2×D311yescharacteristic, complemented
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic, complemented
218#821C2×D311yescharacteristic, complemented
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—61no—
223#817C2×D311yescharacteristic, complemented
224#817C2×D311yescharacteristic, complemented
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—61no—
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—61no—
231#810—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#808—31no—
238#808—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—81no—
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638SD1614yescomplemented
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260C3×#67—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—81no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—42no—
273C3×D12#4112yes—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#627—81no—
277#626—42no—
278#625—42no—
279#625—42no—
280#625—81no—
281#624—81no—
282D3×Dic3—42no—
283C32×C8—21no—
284C32×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—91no—
294#465—91no—
295#460—91no—
296#450—31no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—91no—
301C2×#102—91no—
302C24×C3—61no—
303C23×D3—21no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×Q8—31no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—62no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C2×C3×D4—121no—
314C22×C3×C4—21no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—21no—
319C2×#67—31no—
320C2×#67—31no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—124no—
330C22×Dic3—21no—
331C22×Dic3—61no—
332D3×D4—62no—
333D3×D4—62no—
334D3×D4—121no—
335D3×D4—121no—
336D3×D4—124no—
337C2×D12—22no—
338C2×D12—21no—
339C2×D12—41no—
340C2×D12—61no—
341C2×D12C22×D311yescharacteristic
342C2×D12C22×D311yescharacteristic
343C2×D12C22×D311yescharacteristic
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×Dic6—61no—
351C2×Dic6—61no—
352C2×Dic6C22×D311yescharacteristic
353C3×SD16—62no—
354C3×SD16—121no—
355C2×C3×C8—21no—
356C2×C3×C8—21no—
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C2×C3×C8C22×D311yescharacteristic
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369#217—21no—
370#217—31no—
371#217—31no—
372#217—61no—
373#217—61no—
374#217—61no—
375#215—121no—
376#214—121no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
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—
385C4⋊Dic3—21no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—121no—
414C2×C3⋊C8—121no—
415C2×C3⋊C8—122no—
416#204—22no—
417#204—41no—
418D3×C8—121no—
419D3×C8—121no—
420D3×C8—122no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32C2×SD1612yes—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3C2×SD1612yes—
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—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—84no—
438D32—84no—
439C32×C4—21no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3⋊Dic3—21no—
443C3⋊Dic3—21no—
444C3⋊Dic3C2×SD1612yes—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C22×D4—31no—
451C22×D4—91no—
452C22×D4—181no—
453C2×SD16—31no—
454C2×SD16—31no—
455C2×SD16—91no—
456C22×C8—91no—
457C22×C8—91no—
458C4⋊Q8—91no—
459#127—91no—
460#125—181no—
461C22⋊Q8—31no—
462C22⋊Q8—91no—
463C22⋊Q8—181no—
464C22⋊Q8—181no—
465#121—31no—
466#121—91no—
467#121—181no—
468#120—181no—
469#120—181no—
470C4×Q8—91no—
471C4×D4—91no—
472C4×D4—91no—
473C4×D4—181no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—91no—
476#106—31no—
477#106—31no—
478#106—91no—
479C4⋊C8—91no—
480#103—91no—
481#102—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—91no—
491C22⋊C8D3211yescharacteristic, complemented
492C4×C8—91no—
493C23×C3—21no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—241no—
500C23×C3D3×D411yescharacteristic
501C23×C3D3×D411yescharacteristic
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—21no—
505C22×D3—31no—
506C22×D3—31no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—61no—
510C22×D3—81no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—241no—
516C22×D3—241no—
517C3×Q8—61no—
518C3×Q8—61no—
519C3×D4—32no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—122no—
526C3×D4—122no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
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×C4D3×D411yescharacteristic
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—34no—
546#67—34no—
547#67—42no—
548#67—64no—
549#67—122no—
550#67—122no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—241no—
555#67—241no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—81no—
571C2×Dic3—122no—
572D12—21no—
573D12—21no—
574D12—21no—
575D12—21no—
576D12—21no—
577D12—42no—
578D12—122no—
579D12#23712yes—
580C4×D3—61no—
581C4×D3—61no—
582C4×D3—61no—
583C4×D3—61no—
584C4×D3—121no—
585C4×D3—121no—
586C4×D3—122no—
587C4×D3—241no—
588C4×D3—241no—
589Dic6—21no—
590Dic6—21no—
591Dic6—241no—
592Dic6—241no—
593C3×C8—21no—
594C3×C8—21no—
595C3×C8—21no—
596C3×C8—21no—
597C3×C8—41no—
598C3×C8—41no—
599C3⋊C8—62no—
600C3⋊C8—61no—
601C3⋊C8—61no—
602C3⋊C8—61no—
603C3⋊C8—61no—
604C3⋊C8—121no—
605C2×C32—22no—
606C2×C32#54611yescharacteristic
607C2×C32C22×SD1611yescharacteristic
608C2×C32#57611yescharacteristic
609C3⋊D3—22no—
610C3×D3—42no—
611C3×D3—81no—
612C3×D3—81no—
613C24—61no—
614C24—181no—
615C2×Q8—31no—
616C2×Q8—181no—
617C2×D4—31no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—62no—
621C2×D4—61no—
622C2×D4—61no—
623C2×D4—91no—
624C2×D4—121no—
625C2×D4—181no—
626C2×D4—181no—
627C2×D4—181no—
628C2×D4—181no—
629C2×D4—182no—
630C2×D4—361no—
631C2×D4—364no—
632C22×C4—61no—
633C22×C4—91no—
634C22×C4—181no—
635C22×C4—181no—
636C22×C4C2×D3211yescharacteristic
637SD16—62no—
638SD16—121no—
639SD16—361no—
640C2×C8—91no—
641C2×C8—91no—
642C2×C8—361no—
643C2×C8—361no—
644C2×C8C2×D3211yescharacteristic
645C2×C8C2×D3211yescharacteristic
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—31no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—91no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4—181no—
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—91no—
660C22⋊C4—91no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C42—91no—
665C42—181no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—22no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—62no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—244no—
684C22×C3D3×SD1612yes—
685C22×C3D3×SD1612yes—
686C22×C3C2×D3×D411yescharacteristic
687C22×C3C2×D3×D411yescharacteristic
688C2×D3—22no—
689C2×D3—32no—
690C2×D3—32no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—62no—
700C2×D3—61no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—84no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—244no—
708C2×D3—244no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—41no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4C2×#23711yescharacteristic
720C3×C4#100411yescharacteristic
721C3×C4D3×#4111yescharacteristic
722C3×C4#100911yescharacteristic
723Dic3—32no—
724Dic3—32no—
725Dic3—41no—
726Dic3—41no—
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—62no—
731Dic3—61no—
732Dic3—61no—
733Dic3—61no—
734Dic3—61no—
735Dic3—121no—
736Dic3—121no—
737C32#329511yescharacteristic, complemented, Sylow
738C23—61no—
739C23—61no—
740C23—61no—
741C23—91no—
742C23—122no—
743C23—122no—
744C23—241no—
745C23—362no—
746C23—362no—
747C23—721no—
748C23#380211yescharacteristic
749Q8—61no—
750Q8—61no—
751Q8—721no—
752D4—32no—
753D4—61no—
754D4—61no—
755D4—61no—
756D4—61no—
757D4—61no—
758D4—94no—
759D4—122no—
760D4—122no—
761D4—362no—
762D4—362no—
763D4—362no—
764D4—721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—241no—
778C2×C4—362no—
779C2×C4—721no—
780C2×C4#380211yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C8—21no—
783C8—21no—
784C8—181no—
785C8—181no—
786C2×C3—22no—
787C2×C3—22no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—42no—
792C2×C3—122no—
793C2×C3—241no—
794C2×C3—241no—
795C2×C3#559111yescharacteristic
796C2×C3#565411yescharacteristic
797C2×C3C2×D3×SD1611yescharacteristic
798C2×C3C2×D3×SD1611yescharacteristic
799C2×C3#577411yescharacteristic
800C2×C3#577411yescharacteristic
801D3—42no—
802D3—62no—
803D3—62no—
804D3—81no—
805D3—81no—
806D3—122no—
807C22—21no—
808C22—21no—
809C22—62no—
810C22—92no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—181no—
820C22—181no—
821C22—244no—
822C22—724no—
823C22#6379612yes—
824C22C2×#380211yescharacteristic
825C4—21no—
826C4—92no—
827C4—121no—
828C4—121no—
829C4—121no—
830C4—121no—
831C4—121no—
832C4—181no—
833C4—181no—
834C4D3×#23711yescharacteristic
835C4#6431411yescharacteristic
836C3—21no—
837C3#8015811yescharacteristic, complemented
838C3#8134211yescharacteristic, complemented
839C2—22no—
840C2—122no—
841C2—182no—
842C2—241no—
843C2—241no—
844C2#1059429411yescharacteristic
845C2C2×#6379611yescharacteristic
846C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595069C2
hypercenterC22⋊C8D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594991C2semidirect
3. #10592424C2semidirect
4. C3×#4735C2semidirect
5. C3×#4731C2semidirect
6. #10591179C2semidirect
7. C2×#63562C2semidirect
8. #10590943C2semidirect
9. #10590940C2semidirect
10. #10590885C2semidirect
11. #10590876C2semidirect
12. #10590843C2semidirect
13. #10590776C2semidirect
14. #10590775C2semidirect
15. #10590649C2semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
23. C2×C8×C3⋊D3C22semidirect
25. C2×C3×C4⋊Dic3C22semidirect
26. C3×#924C22semidirect
28. C2×C3×#204C22semidirect
33. #63919C22semidirect
36. #63900C22semidirect
40. #63871C22semidirect
42. #63843C22semidirect
43. C2×#3715C22semidirect
44. C32×C22⋊C8C22semidirect
45. #63647C22semidirect
46. #63641C22semidirect
47. C8×C3⋊Dic3C22semidirect
49. C3×#821C22semidirect
50. C3×#821C22semidirect
51. C3×#821C22semidirect
52. C3×#817C22semidirect
53. C3×#817C22semidirect
54. #63574C22semidirect
55. #63565C22semidirect
58. #63562C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
87. #4735D3semidirect
88. #4731D3semidirect
174. C2×C4⋊Dic3C2×D3semidirect
176. #924C2×D3semidirect
181. C2×#204C2×D3semidirect
208. C3×C22⋊C8C2×D3semidirect
209. C3×C22⋊C8C2×D3semidirect
217. #821C2×D3semidirect
218. #821C2×D3semidirect
219. #821C2×D3semidirect
223. #817C2×D3semidirect
224. #817C2×D3semidirect
254. #638SD16semidirect
491. C22⋊C8D32semidirect
737. C32#3295semidirect
837. C3#80158semidirect
838. C3#81342semidirect

Maximal subgroups

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

subgroupindex
#105950692
#105949912
#105924242
C3×#47352
C3×#47312
#105911792
C2×#635622
#105909432
#105909402
#105908852
#105908762
#105908432
#105907762
#105907752
#105906492
#813423
#801583