Finite Group Databasebeta

← #11864604

Subgroups — #11864604

Order 1152.

1607 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2#10594923C211yesmaximal, characteristic, complemented
3C2×#63809C211yesmaximal, characteristic, complemented
4C2×#63798C211yesmaximal, characteristic, complemented
5#10592426C211yesmaximal, characteristic, complemented
6C3×#4734C211yesmaximal, characteristic, complemented
7C3×#4731C211yesmaximal, characteristic, complemented
8#10591170C211yesmaximal, characteristic, complemented
9#10591160C211yesmaximal, characteristic, complemented
10#10590964C211yesmaximal, characteristic, complemented
11#10590961C211yesmaximal, characteristic, complemented
12#10590957C211yesmaximal, characteristic, complemented
13#10590945C211yesmaximal, characteristic, complemented
14#10590943C211yesmaximal, characteristic, complemented
15#10590940C211yesmaximal, characteristic, complemented
16#80149—31nomaximal
17#80087—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C2×D3×#67—21no—
22C2×D3×#67—21no—
23#64307—24no—
24#64307—24no—
25C2×#3802C2211yescharacteristic
26C2×#3802C2211yescharacteristic
27C2×D3×D12—21no—
28C2×#3796C2211yescharacteristic
29C2×#3796C2211yescharacteristic
30C2×#3796C2211yescharacteristic, complemented
31C2×#3795—21no—
32C2×#3743C2211yescharacteristic, complemented
33C2×C8×C3⋊D3C2211yescharacteristic, complemented
34C3×#930C2211yescharacteristic, complemented
35C3×#924C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×#204C2211yescharacteristic, complemented
39C2×C3×#204C2211yescharacteristic, complemented
40#63971—21no—
41#63958—21no—
42#63916C2211yescharacteristic, complemented
43#63910—21no—
44#63900C2211yescharacteristic, complemented
45#63896—21no—
46#63871C2211yescharacteristic, complemented
47C2×#3718C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51#63809—24no—
52#63798—24no—
53C32×C22⋊C8C2211yescharacteristic, complemented
54#63657C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56#63647C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×#821C2211yescharacteristic, complemented
59C3×#821C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63562C2211yescharacteristic, complemented
64#63562C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1004—31no—
67C2×#916—31no—
68C2×#916—31no—
69C2×#914—31no—
70C2×#911—31no—
71#5629—31no—
72#5608—31no—
73C3×#450—31no—
74C3×#449—31no—
75#5239—31no—
76#5217—31no—
77#5173—31no—
78#5172—31no—
79#5169—31no—
80#5156—31no—
81#5047—31no—
82#5036—31no—
83#4808—31no—
84#4803—31no—
85#4781—31no—
86#4776—31no—
87#4773—31no—
88#4771—31no—
89D3×#102—31no—
90D3×#102—31no—
91#4734D311yescharacteristic, complemented
92#4731D311yescharacteristic, complemented
93#4727—31no—
94#4727—31no—
95#4727—61no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C22×D32—21no—
99C22×C32×C4C2311yescharacteristic
100C2×#638D411yescharacteristic
101C2×#638D411yescharacteristic
102#3828—22no—
103#3828—22no—
104C2×C4⋊(C3⋊D3)D411yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634D411yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C3×#235—22no—
111C3×#235—22no—
112C2×C3×D12—21no—
113C2×C3×D12—22no—
114C2×C3×D12—22no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122D3×#67—28no—
123D3×#67—28no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#625—21no—
129C2×#625—21no—
130C2×#624—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3—21no—
133C2×D3×Dic3—21no—
134#3802—22no—
135#3802—22no—
136#3802—22no—
137#3802D414yescomplemented
138D3×D12—28no—
139#3796—22no—
140#3796—22no—
141#3796—22no—
142#3796—22no—
143#3796—22no—
144#3796D414yescomplemented
145#3795—28no—
146C2×C32×C8C2311yescharacteristic
147C2×C32×C8C2311yescharacteristic
148C2×C3⋊(C3⋊C8)C2311yescharacteristic
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150#3743—22no—
151C8×C3⋊D3—22no—
152C3×#217—21no—
153C3×(C2×D3)⋊C4—21no—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×C4⋊Dic3C2311yescharacteristic
156C3×Dic3⋊C4—21no—
157C3×D24—22no—
158C3×#204—22no—
159C3×#204—22no—
160C3×#204—22no—
161#3724—21no—
162Dic3⋊Dic3—21no—
163#3722—21no—
164(C2×D3)⋊Dic3—21no—
165#3718—22no—
166#3715—22no—
167#3713—22no—
168#3713—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C22×C3×D4—31no—
172C22×#67—61no—
173C22×#67—61no—
174#1009—64no—
175#1009—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179#1004—64no—
180#1004—64no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—61no—
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—31no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4—61no—
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—61no—
195C2×#235—61no—
196C2×#235C2×D311yescharacteristic
197C22×D12—61no—
198C22×D12C2×D311yescharacteristic
199C2×C3×SD16—31no—
200C2×C3×SD16—31no—
201C2×C3×SD16—31no—
202C2×C3×D8—31no—
203C3×C22⋊Q8—31no—
204C3×#121—31no—
205#946—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#215—31no—
209#939—61no—
210#938—31no—
211#938—61no—
212C2×#214—31no—
213C2×#213—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—31no—
217#930C2×D311yescharacteristic, complemented
218#924C2×D311yescharacteristic, complemented
219#916—64no—
220#916—64no—
221#914—64no—
222#911—64no—
223C2×D24C2×D311yescharacteristic, complemented
224C2×#204C2×D311yescharacteristic, complemented
225C2×#204C2×D311yescharacteristic, complemented
226C2×#204C2×D311yescharacteristic, complemented
227C2×ΓL(1,𝔽25)—31no—
228C2×ΓL(1,𝔽25)—31no—
229C2×ΓL(1,𝔽25)—61no—
230C2×D3×C8—31no—
231C2×D3×C8—31no—
232C2×D3×C8—61no—
233#897—31no—
234#896—61no—
235#895—31no—
236#895—61no—
237D3×C4⋊C4—31no—
238D3×C4⋊C4—31no—
239#884—61no—
240#884—61no—
241#884—61no—
242#878—61no—
243C3×#103—31no—
244C3×#102—31no—
245C3×#102—31no—
246C3×#102—31no—
247C3×C22⋊C8—21no—
248C3×C22⋊C8C2×D311yescharacteristic, complemented
249C3×C22⋊C8C2×D311yescharacteristic, complemented
250#835—31no—
251#832—31no—
252#832—31no—
253#832—31no—
254#830—31no—
255#830—31no—
256#830—61no—
257#821C2×D311yescharacteristic, complemented
258#821C2×D311yescharacteristic, complemented
259#821C2×D311yescharacteristic, complemented
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—61no—
265(C2×D3)⋊C8—61no—
266#816C2×D311yescharacteristic, complemented
267#810—31no—
268#809—31no—
269#809—31no—
270#809—31no—
271C23×C32C2×D411yescharacteristic
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3—24no—
278C22×C3×D3—21no—
279C22×C3×D3—81no—
280C22×C3×D3—81no—
281C2×D32—24no—
282C2×D32—24no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×D32—81no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4C2×D411yescharacteristic
290C2×C32×C4C2411yescharacteristic
291#638—22no—
292#638—22no—
293C2×C3⋊Dic3C2×D411yescharacteristic
294C2×C3⋊Dic3C2×D411yescharacteristic
295C4⋊(C3⋊D3)—22no—
296C4×C3⋊D3—21no—
297C4×C3⋊D3—21no—
298C4×C3⋊D3C2×D412yes—
299C4×C3⋊D3C2×D412yes—
300#634—22no—
301C3×#67—24no—
302C3×#67—81no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C3×D12—24no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12C2×D412yes—
314C3×D12C2×D412yes—
315C3×D12C2×D412yes—
316C3×C4×D3—24no—
317C3×Dic6—21no—
318C3×Dic6—21no—
319C3×Dic6—21no—
320C3×Dic6C2×D412yes—
321#626—24no—
322#626—24no—
323#626—42no—
324#626—81no—
325#625—24no—
326#625—24no—
327#624—81no—
328D3×Dic3—24no—
329D3×Dic3—24no—
330D3×Dic3—42no—
331C32×C8—21no—
332C32×C8—21no—
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)—21no—
335C2×H(5,𝔽2)—91no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
338#537—91no—
339#452—91no—
340#452—91no—
341#450—31no—
342#450—91no—
343#449—31no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—91no—
350C24×C3—61no—
351C23×D3—21no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C3×#41—62no—
357C3×#41—62no—
358C2×C3×Q8—31no—
359C2×C3×Q8—31no—
360C2×C3×D4—31no—
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—31no—
364C2×C3×D4—62no—
365C2×C3×D4—62no—
366C2×C3×D4—61no—
367C2×C3×D4—61no—
368C2×C3×D4—61no—
369C22×C3×C4—21no—
370C22×C3×C4—61no—
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C2×#67—21no—
374C2×#67—21no—
375C2×#67—31no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—68no—
390C2×#67—68no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394#239—34no—
395#239—62no—
396#239—62no—
397#239—62no—
398#239—62no—
399#239—62no—
400#237—34no—
401#237—62no—
402#237—62no—
403#237—62no—
404#237—62no—
405#237—68no—
406#237—62no—
407D3×D4—34no—
408D3×D4—34no—
409D3×D4—68no—
410D3×D4—62no—
411D3×D4—62no—
412D3×D4—62no—
413D3×D4—62no—
414D3×D4—68no—
415D3×D4—68no—
416D3×D4—62no—
417D3×D4—62no—
418#235—22no—
419#235—22no—
420#235—62no—
421#235—62no—
422#235—62no—
423#235—62no—
424#235—68no—
425#235—122no—
426#235—122no—
427C2×D12—21no—
428C2×D12—22no—
429C2×D12—22no—
430C2×D12—31no—
431C2×D12—31no—
432C2×D12—61no—
433C2×D12—68no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12C22×D311yescharacteristic
439C2×D12C22×D311yescharacteristic
440C2×D12C22×D311yescharacteristic
441C2×D12C22×D311yescharacteristic
442C2×C4×D3—21no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—61no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×Dic6—31no—
455C2×Dic6—31no—
456C2×Dic6—61no—
457C2×Dic6C22×D311yescharacteristic
458C2×Dic6C22×D311yescharacteristic
459C3×SD16—62no—
460C3×SD16—62no—
461C3×SD16—62no—
462C3×D8—62no—
463C2×C3×C8—21no—
464C2×C3×C8—21no—
465C2×C3×C8C22×D311yescharacteristic
466C2×C3×C8C22×D311yescharacteristic
467C2×C3×C8C22×D311yescharacteristic
468C2×C3×C8C22×D311yescharacteristic
469C3×C4⋊C4—31no—
470C3×C4⋊C4—31no—
471C3×C4⋊C4—61no—
472C3×C22⋊C4—61no—
473C3×C22⋊C4—61no—
474#217—21no—
475#217—61no—
476#216—62no—
477#216—62no—
478#215—62no—
479#214—62no—
480#213—62no—
481#213—62no—
482#213—62no—
483#213—62no—
484(C2×D3)⋊C4—21no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—61no—
488C4⋊Dic3—61no—
489C4⋊Dic3C22×D311yescharacteristic
490C4⋊Dic3C22×D311yescharacteristic
491Dic3⋊C4—21no—
492Dic3⋊C4—61no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—31no—
497C2×C3⋊C8—31no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—61no—
500C2×C3⋊C8—61no—
501D24—22no—
502#204—22no—
503#204—22no—
504#204—22no—
505ΓL(1,𝔽25)—62no—
506ΓL(1,𝔽25)—62no—
507ΓL(1,𝔽25)—122no—
508D3×C8—62no—
509D3×C8—62no—
510D3×C8—122no—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—21no—
514C22×C32C22×D411yescharacteristic
515C2×C3⋊D3—21no—
516C2×C3⋊D3—21no—
517C2×C3⋊D3—21no—
518C2×C3⋊D3—21no—
519C2×C3⋊D3—21no—
520C2×C3⋊D3#12012yes—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—84no—
534D32—84no—
535D32—84no—
536C32×C4—21no—
537C32×C4C22×D411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3—21no—
540C3⋊Dic3#12012yes—
541C3×Dic3—22no—
542C3×Dic3—41no—
543C3×Dic3—41no—
544C3×Dic3—41no—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—31no—
548C2×#41—91no—
549C2×#41—91no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—181no—
553C22×D4—31no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—181no—
557C22×D4—181no—
558C22×D4—181no—
559AGL(1,ℤ/8)—184no—
560#135—184no—
561C2×Q16—91no—
562C2×SD16—31no—
563C2×SD16—31no—
564C2×SD16—31no—
565C2×SD16—91no—
566C2×D8—31no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—91no—
570C22×C8—91no—
571C22⋊Q8—31no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—31no—
575#121—91no—
576#121—181no—
577#121—181no—
578#121—181no—
579C2×C4⋊C4—91no—
580#103—31no—
581#103—91no—
582#102—31no—
583#102—31no—
584#102—31no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—91no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8D3211yescharacteristic, complemented
592C23×C3—21no—
593C23×C3—64no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—241no—
599C23×C3—241no—
600C23×C3D3×D411yescharacteristic
601C23×C3D3×D411yescharacteristic
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—24no—
606C22×D3—21no—
607C22×D3—31no—
608C22×D3—31no—
609C22×D3—31no—
610C22×D3—31no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—64no—
614C22×D3—64no—
615C22×D3—64no—
616C22×D3—64no—
617C22×D3—81no—
618C22×D3—81no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3—241no—
626C22×D3—241no—
627C3×Q8—32no—
628C3×Q8—61no—
629C3×Q8—61no—
630C3×Q8—61no—
631C3×D4—32no—
632C3×D4—32no—
633C3×D4—32no—
634C3×D4—64no—
635C3×D4—64no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—61no—
640C3×D4—61no—
641C3×D4—241no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—64no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4D3×D411yescharacteristic
656C2×C3×C4D3×D411yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659#67—24no—
660#67—64no—
661#67—64no—
662#67—64no—
663#67—64no—
664#67—62no—
665#67—62no—
666#67—64no—
667#67—64no—
668#67—62no—
669#67—62no—
670#67—81no—
671#67—122no—
672#67—122no—
673#67—122no—
674#67—241no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—31no—
682C2×Dic3—31no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—64no—
686C2×Dic3—64no—
687C2×Dic3—122no—
688D12—24no—
689D12—21no—
690D12—21no—
691D12—21no—
692D12—21no—
693D12—21no—
694D12—62no—
695D12—62no—
696D12—64no—
697D12—64no—
698D12—122no—
699D12—122no—
700D12—241no—
701D12D3×D412yes—
702D12D3×D412yes—
703D12D3×D412yes—
704C4×D3—24no—
705C4×D3—32no—
706C4×D3—32no—
707C4×D3—32no—
708C4×D3—32no—
709C4×D3—62no—
710C4×D3—62no—
711C4×D3—64no—
712C4×D3—64no—
713C4×D3—61no—
714C4×D3—61no—
715C4×D3—61no—
716C4×D3—61no—
717C4×D3—121no—
718C4×D3—121no—
719C4×D3—122no—
720C4×D3—241no—
721C4×D3—241no—
722Dic6—21no—
723Dic6—21no—
724Dic6—21no—
725Dic6—62no—
726Dic6—62no—
727Dic6—122no—
728Dic6D3×D412yes—
729C3×C8—21no—
730C3×C8—21no—
731C3×C8—21no—
732C3×C8—21no—
733C3×C8—41no—
734C3×C8—41no—
735C3⋊C8—61no—
736C3⋊C8—61no—
737C3⋊C8—61no—
738C3⋊C8—61no—
739C3⋊C8—121no—
740C3⋊C8—121no—
741C2×C32—41no—
742C2×C32C2×#12011yescharacteristic
743C2×C32#57611yescharacteristic
744C2×C32#57711yescharacteristic
745C3⋊D3—22no—
746C3⋊D3—41no—
747C3×D3—42no—
748C3×D3—42no—
749C3×D3—42no—
750C3×D3—81no—
751C24—61no—
752C24—181no—
753C24—181no—
754#41—62no—
755#41—62no—
756#41—94no—
757#41—182no—
758#41—182no—
759#41—188no—
760#41—182no—
761#41—182no—
762#41—182no—
763#41—182no—
764#41—182no—
765C2×Q8—31no—
766C2×Q8—31no—
767C2×Q8—91no—
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—31no—
771C2×D4—31no—
772C2×D4—62no—
773C2×D4—62no—
774C2×D4—61no—
775C2×D4—61no—
776C2×D4—61no—
777C2×D4—94no—
778C2×D4—91no—
779C2×D4—91no—
780C2×D4—91no—
781C2×D4—188no—
782C2×D4—181no—
783C2×D4—181no—
784C2×D4—181no—
785C2×D4—181no—
786C2×D4—182no—
787C2×D4—181no—
788C2×D4—181no—
789C2×D4—182no—
790C2×D4—182no—
791C2×D4—188no—
792C2×D4—188no—
793C22×C4—61no—
794C22×C4—91no—
795C22×C4—91no—
796C22×C4—181no—
797C22×C4—181no—
798C22×C4—181no—
799C22×C4—181no—
800C22×C4C2×D3211yescharacteristic
801Q16—182no—
802SD16—62no—
803SD16—62no—
804SD16—62no—
805SD16—182no—
806D8—62no—
807D8—182no—
808D8—182no—
809M16—182no—
810C2×C8—91no—
811C2×C8—91no—
812C2×C8—182no—
813C2×C8C2×D3211yescharacteristic
814C2×C8C2×D3211yescharacteristic
815C4⋊C4—31no—
816C4⋊C4—31no—
817C4⋊C4—61no—
818C4⋊C4—181no—
819C4⋊C4—181no—
820C22⋊C4—61no—
821C22⋊C4—61no—
822C22⋊C4—181no—
823C22⋊C4—181no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—121no—
838C22×C3—121no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—244no—
847C22×C3C2×D3×D411yescharacteristic
848C22×C3C2×D3×D411yescharacteristic
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—32no—
853C2×D3—32no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—62no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—61no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—61no—
873C2×D3—61no—
874C2×D3—84no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3—244no—
883C2×D3—244no—
884C3×C4—21no—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—41no—
889C3×C4—62no—
890C3×C4—121no—
891C3×C4—121no—
892C3×C4—121no—
893C3×C4C2×D3×D411yescharacteristic
894C3×C4C2×D3×D411yescharacteristic
895C3×C4C2×D3×D411yescharacteristic
896C3×C4C2×D3×D411yescharacteristic
897Dic3—22no—
898Dic3—32no—
899Dic3—32no—
900Dic3—41no—
901Dic3—41no—
902Dic3—41no—
903Dic3—62no—
904Dic3—61no—
905Dic3—61no—
906Dic3—121no—
907C32#301211yescharacteristic, complemented, Sylow
908C23—64no—
909C23—61no—
910C23—61no—
911C23—61no—
912C23—61no—
913C23—91no—
914C23—91no—
915C23—184no—
916C23—184no—
917C23—241no—
918C23—241no—
919C23—721no—
920C23—721no—
921C23—721no—
922C23—721no—
923C23#380211yescharacteristic
924Q8—32no—
925Q8—61no—
926Q8—61no—
927Q8—61no—
928Q8—182no—
929D4—32no—
930D4—32no—
931D4—32no—
932D4—64no—
933D4—64no—
934D4—61no—
935D4—61no—
936D4—61no—
937D4—61no—
938D4—61no—
939D4—182no—
940D4—184no—
941D4—184no—
942D4—182no—
943D4—184no—
944D4—182no—
945D4—184no—
946D4—241no—
947D4—362no—
948D4—721no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—64no—
952C2×C4—61no—
953C2×C4—61no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—91no—
957C2×C4—92no—
958C2×C4—92no—
959C2×C4—91no—
960C2×C4—184no—
961C2×C4—184no—
962C2×C4—181no—
963C2×C4—181no—
964C2×C4—362no—
965C2×C4—721no—
966C2×C4#380211yescharacteristic
967C2×C4C22×D3211yescharacteristic
968C8—21no—
969C8—21no—
970C8—181no—
971C8—181no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—41no—
976C2×C3—41no—
977C2×C3—81no—
978C2×C3—122no—
979C2×C3—122no—
980C2×C3—122no—
981C2×C3—241no—
982C2×C3D3×#12011yescharacteristic
983C2×C3D3×#12011yescharacteristic
984C2×C3#576211yescharacteristic
985C2×C3#577011yescharacteristic
986C2×C3#577411yescharacteristic
987C2×C3#577411yescharacteristic
988D3—42no—
989D3—42no—
990D3—42no—
991D3—62no—
992D3—62no—
993D3—81no—
994D3—122no—
995D3—121no—
996D3—121no—
997D3—241no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—62no—
1002C22—62no—
1003C22—62no—
1004C22—92no—
1005C22—121no—
1006C22—121no—
1007C22—121no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—181no—
1015C22—181no—
1016C22—181no—
1017C22—181no—
1018C22—181no—
1019C22—244no—
1020C22—724no—
1021C22—724no—
1022C22C2×#380211yescharacteristic
1023C4—21no—
1024C4—62no—
1025C4—92no—
1026C4—121no—
1027C4—121no—
1028C4—121no—
1029C4—181no—
1030C4D32×D411yescharacteristic
1031C4D32×D411yescharacteristic
1032C3—21no—
1033C3#8008711yescharacteristic, complemented
1034C3#8014911yescharacteristic, complemented
1035C2—41no—
1036C2—122no—
1037C2—122no—
1038C2—122no—
1039C2—182no—
1040C2—241no—
1041C2—361no—
1042C2#1059425811yescharacteristic
1043C2#1059468611yescharacteristic
1044C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3012
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
1. C2×#64307C2semidirect
2. #10594923C2semidirect
3. C2×#63809C2semidirect
4. C2×#63798C2semidirect
5. #10592426C2semidirect
6. C3×#4734C2semidirect
7. C3×#4731C2semidirect
8. #10591170C2semidirect
9. #10591160C2semidirect
10. #10590964C2semidirect
11. #10590961C2semidirect
12. #10590957C2semidirect
13. #10590945C2semidirect
14. #10590943C2semidirect
15. #10590940C2semidirect
30. C2×#3796C22semidirect
32. C2×#3743C22semidirect
33. C2×C8×C3⋊D3C22semidirect
34. C3×#930C22semidirect
35. C3×#924C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×#204C22semidirect
38. C2×C3×#204C22semidirect
39. C2×C3×#204C22semidirect
42. #63916C22semidirect
44. #63900C22semidirect
46. #63871C22semidirect
47. C2×#3718C22semidirect
48. C2×#3715C22semidirect
49. C2×#3713C22semidirect
50. C2×#3713C22semidirect
53. C32×C22⋊C8C22semidirect
54. #63657C22semidirect
55. #63647C22semidirect
56. #63647C22semidirect
57. C3×#821C22semidirect
58. C3×#821C22semidirect
59. C3×#821C22semidirect
60. C3×#816C22semidirect
61. #63565C22semidirect
62. #63562C22semidirect
63. #63562C22semidirect
64. #63562C22semidirect
91. #4734D3semidirect
92. #4731D3semidirect
137. #3802D4semidirect
144. #3796D4semidirect
217. #930C2×D3semidirect
218. #924C2×D3semidirect
223. C2×D24C2×D3semidirect
224. C2×#204C2×D3semidirect
225. C2×#204C2×D3semidirect
226. C2×#204C2×D3semidirect
248. C3×C22⋊C8C2×D3semidirect
249. C3×C22⋊C8C2×D3semidirect
257. #821C2×D3semidirect
258. #821C2×D3semidirect
259. #821C2×D3semidirect
266. #816C2×D3semidirect
591. C22⋊C8D32semidirect
907. C32#3012semidirect
1033. C3#80087semidirect
1034. C3#80149semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
#105949232
C2×#638092
C2×#637982
#105924262
C3×#47342
C3×#47312
#105911702
#105911602
#105909642
#105909612
#105909572
#105909452
#105909432
#105909402
#801493
#800873