Finite Group Databasebeta

← #11884410

Subgroups — #11884410

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5577C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63939C211yesmaximal, characteristic, complemented
4#10594007C211yesmaximal, characteristic, complemented
5#10592725C211yesmaximal, characteristic, complemented
6C3×#5028C211yesmaximal, characteristic, complemented
7#10591597C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10590615C211yesmaximal, characteristic, complemented
10#10590595C211yesmaximal, characteristic, complemented
11#10590515C211yesmaximal, characteristic, complemented
12#10590499C211yesmaximal, characteristic, complemented
13#10590355C211yesmaximal, characteristic, complemented
14#10590354C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83577—31nomaximal
17#80628—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C3×#895—21no—
28C3×#895—21no—
29C3×#895C2211yescharacteristic
30C3×#895C2211yescharacteristic, complemented
31C3×#875C2211yescharacteristic
32C3×#874—21no—
33C3×#874C2211yescharacteristic, complemented
34C3×C4×D12—21no—
35C3×C4×D12C2211yescharacteristic
36#63949—24no—
37#63939—24no—
38#63922—21no—
39#63921—21no—
40#63912—21no—
41#63908C2211yescharacteristic
42#63856C2211yescharacteristic
43#63854—21no—
44C2×#3715C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54#63634C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#550—31no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#919—31no—
67C2×#914—31no—
68#5676—31no—
69#5577D311yescharacteristic, complemented
70#5550—31no—
71C3×#464—31no—
72#5239—31no—
73#5238—31no—
74#5187—31no—
75#5172—31no—
76#5074—31no—
77#5072—31no—
78#5058—31no—
79#5042—31no—
80#5038—31no—
81#5037—31no—
82#5036—31no—
83#5028D311yescharacteristic, complemented
84#5026—31no—
85#5026—31no—
86#5026—61no—
87#5011—31no—
88#4843—31no—
89#4836—31no—
90#4812—31no—
91#4810—31no—
92#4775—31no—
93#4773—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C3×#239—22no—
99C3×#239—22no—
100C3×#239—41no—
101C3×#239—41no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119C2×#625—21no—
120C2×#624—21no—
121D3×D12—22no—
122D3×D12—41no—
123#3799—22no—
124#3799—41no—
125C32×C4⋊C4—21no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C42—21no—
128C32×C42C2311yescharacteristic
129#3755D414yescomplemented
130#3752—21no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C3×#216—22no—
135C3×#215—22no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3D411yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3724—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3715—22no—
149#3715—41no—
150#3714—22no—
151#3714—22no—
152#3713—22no—
153#3713—41no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#239C2×D311yescharacteristic
161C2×#239C2×D311yescharacteristic, complemented
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C3×#127—31no—
168C3×#127—61no—
169C3×#124—31no—
170C3×#121—31no—
171C3×#121—31no—
172C3×#121—61no—
173C3×#121—61no—
174C3×C4×Q8—21no—
175C3×C4×Q8C2×D311yescharacteristic, complemented
176C3×C4×Q8C2×D311yescharacteristic, complemented
177C3×C4×D4—31no—
178C3×C4×D4—61no—
179#950—64no—
180#949—64no—
181#946—31no—
182C2×#216C2×D311yescharacteristic, complemented
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—61no—
188C2×#215C2×D311yescharacteristic
189#938—31no—
190#937—61no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199#930—31no—
200#924—31no—
201C2×#208—31no—
202C22×C3⋊C8—31no—
203#919—64no—
204#914—64no—
205C2×D24—31no—
206C2×D24—31no—
207C2×ΓL(1,𝔽25)—31no—
208C2×D3×C8—31no—
209#895—21no—
210#895—21no—
211#895C2×D311yescharacteristic
212#895C2×D311yescharacteristic, complemented
213#894—61no—
214#884—61no—
215#884—61no—
216#883—61no—
217#882—61no—
218D3×C22⋊C4—61no—
219D3×C22⋊C4—61no—
220#875C2×D311yescharacteristic
221#874—21no—
222#874C2×D311yescharacteristic, complemented
223C4×D12—21no—
224C4×D12—31no—
225C4×D12—31no—
226C4×D12—61no—
227C4×D12C2×D311yescharacteristic
228C3×C4⋊C8—31no—
229C3×#103—31no—
230C3×#102—31no—
231#835—31no—
232#835—31no—
233#835—61no—
234#832—31no—
235#832—31no—
236#830—31no—
237#830—31no—
238#821—31no—
239#821—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242#810C2×D311yescharacteristic, complemented
243#809—31no—
244#809—31no—
245#809—61no—
246#809C2×D311yescharacteristic
247#807—31no—
248#807—31no—
249#807—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251#803—31no—
252#803—31no—
253#803—61no—
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×Q8—21no—
264C32×Q8C2×D412yes—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)C2×D412yes—
273C4×C3⋊D3—81no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—41no—
284C3×D12—42no—
285C3×D12—42no—
286C3×D12—42no—
287C3×D12—81no—
288C3×D12—81no—
289C3×D12—81no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×C4×D3—42no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298#626—42no—
299#626—42no—
300#625—81no—
301#624—42no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—31no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—31no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—121no—
326C3×#41—121no—
327C2×C3×Q8—21no—
328C2×C3×Q8—31no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349#239—22no—
350#239—22no—
351#239—41no—
352#239—41no—
353#239—62no—
354#239—121no—
355D3×D4—62no—
356D3×D4—121no—
357#235—62no—
358#235—121no—
359C2×D12—21no—
360C2×D12—21no—
361C2×D12—21no—
362C2×D12—21no—
363C2×D12—21no—
364C2×D12—21no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—61no—
368C2×D12—62no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—121no—
372C2×D12#6711yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×C4×D3—21no—
377C2×C4×D3—21no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—121no—
383C2×C4×D3C22×D311yescharacteristic
384C2×C4×D3C22×D311yescharacteristic
385C2×Dic6C22×D311yescharacteristic
386C3×Q16—62no—
387C3×SD16—62no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—41no—
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C4⋊C4C22×D311yescharacteristic
397C3×C22⋊C4—31no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C42—21no—
404C3×C42—21no—
405C3×C42—21no—
406C3×C42—41no—
407C3×C42C22×D311yescharacteristic
408C3×C42C22×D311yescharacteristic
409#217—61no—
410#217—61no—
411#216—22no—
412#215—22no—
413#215—34no—
414#215—34no—
415#215—64no—
416#215—62no—
417#215—121no—
418#214—62no—
419#214—121no—
420#213—62no—
421#213—62no—
422#213—62no—
423#213—62no—
424#213—121no—
425#213—121no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—121no—
435(C2×D3)⋊C4#6711yescharacteristic
436(C2×D3)⋊C4#6711yescharacteristic
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—61no—
440C4⋊Dic3#6711yescharacteristic
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443#208—62no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8—62no—
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453D24—62no—
454D24—62no—
455ΓL(1,𝔽25)—62no—
456D3×C8—62no—
457C22×C32C22×D411yescharacteristic
458C2×C3⋊D3—22no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476D32—84no—
477C32×C4—22no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—41no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—41no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—41no—
487C2×#41—31no—
488C2×#41—31no—
489C2×#41—91no—
490C22×D4—91no—
491AGL(1,ℤ/8)—184no—
492#135—184no—
493C2×Q16—31no—
494C2×SD16—31no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—91no—
499C2×D8—91no—
500C2×D8—91no—
501C2×D8—91no—
502C2×M16—91no—
503C22×C8—91no—
504#127—31no—
505#127—61no—
506#124—31no—
507#123—181no—
508C22⋊Q8—91no—
509#121—31no—
510#121—31no—
511#121—61no—
512#121—61no—
513#121—91no—
514#121—181no—
515#120—181no—
516C4×Q8D3211yescharacteristic, complemented
517C4×D4—31no—
518C4×D4—61no—
519C4×D4—91no—
520C2×C22⋊C4—181no—
521#107—91no—
522C4⋊C8—31no—
523#103—31no—
524#103—91no—
525#102—31no—
526#102—91no—
527#102—91no—
528#102—91no—
529C22⋊C8—91no—
530C22⋊C8—91no—
531#97—91no—
532C23×C3—31no—
533C23×C3—31no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—121no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3C2×#6711yescharacteristic
550C22×D3C2×#6711yescharacteristic
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—22no—
554C3×Q8—41no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8D3×D412yes—
558C3×Q8D3×D412yes—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—121no—
566C3×D4—122no—
567C3×D4—122no—
568C3×D4—122no—
569C3×D4—241no—
570C3×D4—241no—
571C3×D4—241no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—122no—
589C2×C3×C4—122no—
590C2×C3×C4D3×D411yescharacteristic
591C2×C3×C4D3×D411yescharacteristic
592C2×C3×C4C2×#6711yescharacteristic
593C2×C3×C4C2×#6711yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—122no—
597#67—122no—
598#67—241no—
599#67—241no—
600C2×Dic3—21no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—121no—
604C2×Dic3C2×#6711yescharacteristic
605C2×Dic3C2×#6711yescharacteristic
606D12—21no—
607D12—21no—
608D12—21no—
609D12—21no—
610D12—21no—
611D12—21no—
612D12—32no—
613D12—32no—
614D12—41no—
615D12—42no—
616D12—42no—
617D12—42no—
618D12—62no—
619D12—61no—
620D12—61no—
621D12—81no—
622D12—81no—
623D12—81no—
624D12—121no—
625D12—122no—
626D12—122no—
627C4×D3—21no—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—21no—
631C4×D3—42no—
632C4×D3—42no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3—241no—
636C4×D3—241no—
637C4×D3—242no—
638Dic6—21no—
639Dic6—21no—
640C3×C8—61no—
641C3×C8—61no—
642C3⋊C8—21no—
643C3⋊C8—21no—
644C3⋊C8—32no—
645C3⋊C8—32no—
646C3⋊C8—62no—
647C3⋊C8—61no—
648C3⋊C8—61no—
649C3⋊C8—121no—
650C2×C32D4211yescharacteristic
651C2×C32#57511yescharacteristic
652C2×C32#57611yescharacteristic
653C3⋊D3—42no—
654C3×D3—41no—
655C3×D3—41no—
656C3×D3—81no—
657C3×D3—81no—
658C3×D3—81no—
659C24—181no—
660#41—62no—
661#41—62no—
662#41—121no—
663#41—121no—
664#41—182no—
665#41—361no—
666C2×Q8—31no—
667C2×Q8C2×D3211yescharacteristic
668C2×D4—31no—
669C2×D4—31no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—91no—
679C2×D4—181no—
680C2×D4—182no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—361no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—181no—
689C22×C4—181no—
690Q16—62no—
691SD16—62no—
692SD16—94no—
693SD16—182no—
694SD16—361no—
695D8—182no—
696D8—182no—
697D8—182no—
698D8—361no—
699M16—182no—
700C2×C8—31no—
701C2×C8—31no—
702C2×C8—91no—
703C2×C8—91no—
704C2×C8—182no—
705C4⋊C4—21no—
706C4⋊C4—31no—
707C4⋊C4—91no—
708C4⋊C4—181no—
709C4⋊C4C2×D3211yescharacteristic
710C22⋊C4—31no—
711C22⋊C4—31no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C42—21no—
720C42C2×D3211yescharacteristic
721C22×C3—21no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3C2×D3×D411yescharacteristic
738C22×C3C22×#6711yescharacteristic
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—122no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—241no—
762C2×D3—241no—
763C2×D3—244no—
764C2×D3—244no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—22no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—22no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—42no—
776C3×C4—41no—
777C3×C4—41no—
778C3×C4—61no—
779C3×C4—61no—
780C3×C4—81no—
781C3×C4—121no—
782C3×C4C2×D3×D411yescharacteristic
783C3×C4C2×D3×D411yescharacteristic
784C3×C4#100411yescharacteristic
785C3×C4#100911yescharacteristic
786Dic3—21no—
787Dic3—21no—
788Dic3—41no—
789Dic3—121no—
790Dic3—121no—
791Dic3—241no—
792C32#326811yescharacteristic, complemented, Sylow
793C23—31no—
794C23—31no—
795C23—61no—
796C23—61no—
797C23—61no—
798C23—181no—
799C23—362no—
800C23—362no—
801C23—721no—
802Q8—21no—
803Q8—61no—
804Q8—61no—
805Q8#380212yes—
806D4—61no—
807D4—61no—
808D4—61no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—92no—
813D4—121no—
814D4—122no—
815D4—122no—
816D4—122no—
817D4—181no—
818D4—241no—
819D4—241no—
820D4—241no—
821D4—362no—
822D4—362no—
823D4—721no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—31no—
827C2×C4—31no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—122no—
834C2×C4—122no—
835C2×C4—181no—
836C2×C4—362no—
837C2×C4—721no—
838C2×C4D3×#6711yescharacteristic
839C2×C4D3×#6711yescharacteristic
840C2×C4C22×D3211yescharacteristic
841C8—61no—
842C8—61no—
843C8—92no—
844C8—181no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—121no—
849C2×C3—121no—
850C2×C3—241no—
851C2×C3—241no—
852C2×C3—241no—
853C2×C3#560911yescharacteristic
854C2×C3#576911yescharacteristic
855C2×C3#577711yescharacteristic
856C2×C3D4×#6711yescharacteristic
857C2×C3#582211yescharacteristic
858C2×C3#583511yescharacteristic
859D3—41no—
860D3—41no—
861D3—81no—
862D3—81no—
863D3—81no—
864D3—122no—
865D3—122no—
866D3—242no—
867C22—61no—
868C22—61no—
869C22—61no—
870C22—61no—
871C22—61no—
872C22—61no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—182no—
883C22—361no—
884C22—361no—
885C22—724no—
886C22C2×D3×#6711yescharacteristic
887C4—21no—
888C4—21no—
889C4—22no—
890C4—41no—
891C4—61no—
892C4—61no—
893C4—121no—
894C4—361no—
895C4C2×#380211yescharacteristic
896C4#6430711yescharacteristic
897C3—21no—
898C3#8062811yescharacteristic, complemented
899C3#8357711yescharacteristic, complemented
900C2—121no—
901C2—121no—
902C2—241no—
903C2—241no—
904C2—241no—
905C2—362no—
906C2#1059506911yescharacteristic
907C2#1059531711yescharacteristic
908C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5577C2semidirect
2. C2×#63949C2semidirect
3. C2×#63939C2semidirect
4. #10594007C2semidirect
5. #10592725C2semidirect
6. C3×#5028C2semidirect
7. #10591597C2semidirect
8. #10591586C2semidirect
9. #10590615C2semidirect
10. #10590595C2semidirect
11. #10590515C2semidirect
12. #10590499C2semidirect
13. #10590355C2semidirect
14. #10590354C2semidirect
15. #10590330C2semidirect
19. C2×C3×#239C22semidirect
22. C32×C4×Q8C22semidirect
25. C2×C3×#216C22semidirect
30. C3×#895C22semidirect
33. C3×#874C22semidirect
44. C2×#3715C22semidirect
45. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63662C22semidirect
54. #63634C22semidirect
55. #63630C22semidirect
56. C3×#810C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
69. #5577D3semidirect
83. #5028D3semidirect
129. #3755D4semidirect
161. C2×#239C2×D3semidirect
175. C3×C4×Q8C2×D3semidirect
176. C3×C4×Q8C2×D3semidirect
182. C2×#216C2×D3semidirect
212. #895C2×D3semidirect
222. #874C2×D3semidirect
242. #810C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
516. C4×Q8D32semidirect
792. C32#3268semidirect
898. C3#80628semidirect
899. C3#83577semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
C2×#639492
C2×#639392
#105940072
#105927252
C3×#50282
#105915972
#105915862
#105906152
#105905952
#105905152
#105904992
#105903552
#105903542
#105903302
#835773
#806283