Finite Group Databasebeta

← #11884282

Subgroups — #11884282

Order 1152.

1133 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
1C2×#64159C211yesmaximal, characteristic, complemented
2C3×#5829C211yesmaximal, characteristic, complemented
3C2×#63934C211yesmaximal, characteristic, complemented
4#10594834C211yesmaximal, characteristic, complemented
5C3×#5239C211yesmaximal, characteristic, complemented
6#10591657C211yesmaximal, characteristic, complemented
7#10591627C211yesmaximal, characteristic, complemented
8#10591598C211yesmaximal, characteristic, complemented
9#10591568C211yesmaximal, characteristic, complemented
10#10591489C211yesmaximal, characteristic, complemented
11#10591459C211yesmaximal, characteristic, complemented
12#10591404C211yesmaximal, characteristic, complemented
13#10591182C211yesmaximal, characteristic, complemented
14#10591179C211yesmaximal, characteristic, complemented
15#10591158C211yesmaximal, characteristic, complemented
16#83503—31nomaximal
17#80264—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22#64159—24no—
23C2×#3756C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25C2×#3754C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C3×#947C2211yescharacteristic
29C3×#946C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic, complemented
31C3×#939—21no—
32C3×#937—21no—
33C3×D4×Dic3C2211yescharacteristic
34C2×C3×#214C2211yescharacteristic
35C3×#930C2211yescharacteristic
36C3×#929—21no—
37C3×C4×#67C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4—21no—
39C3×#924C2211yescharacteristic, complemented
40#63975—21no—
41#63958—21no—
42#63934—24no—
43#63894C2211yescharacteristic, complemented
44#63883—21no—
45#63866C2211yescharacteristic, complemented
46#63857C2211yescharacteristic
47#63853—21no—
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic
54C3×#830C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64#5829D311yescharacteristic, complemented
65C2×#950—31no—
66C2×#950—31no—
67C2×#950—61no—
68C2×#932—31no—
69C2×#914—31no—
70#5631—31no—
71#5551—31no—
72C3×#452—31no—
73#5239D311yescharacteristic, complemented
74#5218—31no—
75#5190—31no—
76#5187—31no—
77#5162—31no—
78#5060—31no—
79#5057—31no—
80#5052—31no—
81#5048—31no—
82#5047—31no—
83#5041—31no—
84#5037—31no—
85#5019—31no—
86#5014—31no—
87#5011—31no—
88#4819—31no—
89#4816—31no—
90#4785—31no—
91#4776—31no—
92#4734—31no—
93#4730—31no—
94C23×C3×D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C2×#638—21no—
103#3828—22no—
104#3828—41no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C22×C3×Dic3—21no—
112C3×D3×D4—22no—
113C3×D3×D4—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#624—21no—
119C2×#624—21no—
120#3799—22no—
121#3799—41no—
122#3756—22no—
123#3755—22no—
124#3754—22no—
125#3753D414yescomplemented
126C2×C3⋊(C3⋊C8)—22no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#217—21no—
130C3×#217—21no—
131C3×#217D411yescharacteristic
132C3×#216—41no—
133C3×#214—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4D411yescharacteristic
144C3×C4×Dic3C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3—21no—
148Dic3⋊Dic3—21no—
149Dic3⋊Dic3—21no—
150#3722—21no—
151(C2×D3)⋊Dic3—21no—
152#3716—41no—
153#3715—22no—
154#3714—22no—
155#3711—22no—
156#3267—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41C2×D311yescharacteristic
159C2×C3×#41C2×D311yescharacteristic
160C22×C3×D4—31no—
161C2×#239—31no—
162C2×D3×D4C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C2×#235—31no—
166C2×#235—61no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C3×#124—31no—
170C3×#123—61no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×#121—31no—
174C3×#121—61no—
175C3×#120—61no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C2×C3×C22⋊C4—61no—
179#950—64no—
180#950—64no—
181#950—68no—
182#947C2×D311yescharacteristic
183#946C2×D311yescharacteristic
184#944—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—61no—
188C2×#216C2×D311yescharacteristic, complemented
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—61no—
193#939—21no—
194#938—61no—
195#937—21no—
196D4×Dic3C2×D311yescharacteristic
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—61no—
202C2×#214C2×D311yescharacteristic
203#932—64no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—61no—
208#930C2×D311yescharacteristic
209#929—21no—
210C4×#67C2×D311yescharacteristic
211C2×(C2×D3)⋊C4—21no—
212#924—31no—
213#924C2×D311yescharacteristic, complemented
214C2×#208—31no—
215C22×C3⋊C8—31no—
216C22×C3⋊C8—31no—
217C22×C3⋊C8—61no—
218#914—64no—
219C2×D24—31no—
220C2×#204—31no—
221C2×ΓL(1,𝔽25)—31no—
222#897—31no—
223#894—61no—
224#893—31no—
225D3×C4⋊C4—61no—
226D3×C4⋊C4—61no—
227#884—61no—
228#883—61no—
229#883—61no—
230#883—61no—
231C4×D12—31no—
232#869—31no—
233C3×#103—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#835C2×D311yescharacteristic, complemented
238#832—31no—
239#832C2×D311yescharacteristic
240#830—31no—
241#830C2×D311yescharacteristic, complemented
242#821—31no—
243(C2×D3)⋊C8—31no—
244#816—31no—
245#815—31no—
246Dic3⋊C8—31no—
247#810—31no—
248#810—31no—
249#809—31no—
250#809—31no—
251#808—31no—
252#808—31no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—42no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—42no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274#638—42no—
275C2×C3⋊Dic3—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)C2×D412yes—
278C4×C3⋊D3—42no—
279#634—21no—
280#634—21no—
281C3×#67—41no—
282C3×#67—42no—
283C3×#67—81no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—81no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×D12—21no—
292C3×D12—21no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#626—42no—
298#624—42no—
299#624—42no—
300C3⋊(C3⋊C8)—21no—
301C3⋊(C3⋊C8)C2×D412yes—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C2×AGL(1,ℤ/8)—91no—
305C2×#135—91no—
306#547—91no—
307#546—31no—
308#497—91no—
309#470—91no—
310#465—91no—
311#463—91no—
312#461—91no—
313#452—31no—
314#452—91no—
315#450—91no—
316#449—91no—
317#442—91no—
318#435—91no—
319C24×C3—61no—
320C23×D3—21no—
321C3×#41—24no—
322C3×#41—22no—
323C3×#41—22no—
324C3×#41—41no—
325C3×#41—41no—
326C3×#41—42no—
327C2×C3×Q8—21no—
328C2×C3×Q8—31no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—41no—
337C2×C3×D4—61no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4—121no—
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C22×D311yescharacteristic
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—31no—
347C22×C3×C4—41no—
348C22×C3×C4—61no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C2×#67—21no—
352C2×#67—21no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—121no—
357C2×#67#6711yescharacteristic
358C22×Dic3—21no—
359#239—62no—
360#239—121no—
361D3×D4—22no—
362D3×D4—41no—
363#235—62no—
364#235—62no—
365#235—62no—
366#235—64no—
367#235—121no—
368#235—121no—
369#235—121no—
370#235—122no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12C22×D311yescharacteristic
376C2×C4×D3—61no—
377C2×C4×D3—61no—
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×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6C22×D311yescharacteristic
388C3×Q16—121no—
389C3×SD16—62no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—31no—
395C3×C4⋊C4—61no—
396C3×C4⋊C4—61no—
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×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C42—31no—
406#217—21no—
407#217—21no—
408#217—61no—
409#217#6711yescharacteristic
410#216—41no—
411#216—62no—
412#216—62no—
413#216—64no—
414#215—62no—
415#215—62no—
416#215—62no—
417#215—64no—
418#214—22no—
419#214—62no—
420#214—64no—
421#214—62no—
422#214—62no—
423#214—121no—
424#213—34no—
425#213—34no—
426#213—64no—
427#213—62no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4#6711yescharacteristic
436C4⋊Dic3—61no—
437C4⋊Dic3—61no—
438C4⋊Dic3—61no—
439C4⋊Dic3C22×D311yescharacteristic
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—21no—
442Dic3⋊C4—21no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4#6711yescharacteristic
447C4×Dic3C22×D311yescharacteristic
448#208—62no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—62no—
456C2×C3⋊C8—62no—
457C2×C3⋊C8—64no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460D24—62no—
461#204—121no—
462ΓL(1,𝔽25)—62no—
463C22×C32—21no—
464C22×C32—22no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C2×C3⋊D3—22no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—84no—
480C32×C4—21no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—91no—
492C2×#41—91no—
493C2×#41D3211yescharacteristic
494C22×D4—31no—
495AGL(1,ℤ/8)—184no—
496#135—184no—
497C2×Q16—31no—
498C2×Q16—91no—
499C2×SD16—31no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×D8—91no—
505C2×D8—91no—
506C2×M16—91no—
507C22×C8—91no—
508C4⋊Q8—91no—
509#124—31no—
510#123—61no—
511#123—181no—
512#123—181no—
513C22⋊Q8—31no—
514C22⋊Q8—31no—
515C22⋊Q8—91no—
516#121—31no—
517#121—61no—
518#121—181no—
519#120—61no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—91no—
523C2×C4⋊C4—181no—
524C2×C22⋊C4—61no—
525#106—91no—
526C4⋊C8—91no—
527#103—31no—
528#103—91no—
529#103—91no—
530#102—31no—
531#102—91no—
532#102—91no—
533C22⋊C8—31no—
534C22⋊C8—91no—
535#97—91no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—31no—
540C23×C3—41no—
541C23×C3—61no—
542C23×C3—122no—
543C23×C3—122no—
544C23×C3—241no—
545C23×C3D3×D411yescharacteristic
546C23×C3C2×#6711yescharacteristic
547C22×D3—21no—
548C22×D3—42no—
549C22×D3—42no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—81no—
553C22×D3—121no—
554C22×D3C2×#6711yescharacteristic
555C3×Q8—22no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—41no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—22no—
566C3×D4—41no—
567C3×D4—42no—
568C3×D4—42no—
569C3×D4—44no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—121no—
573C3×D4—122no—
574C3×D4—241no—
575C3×D4D3×D412yes—
576C3×D4D3×D412yes—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—41no—
591C2×C3×C4—42no—
592C2×C3×C4—42no—
593C2×C3×C4—44no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—241no—
600C2×C3×C4D3×D411yescharacteristic
601C2×C3×C4C2×#6711yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603C2×C3×C4C23×D311yescharacteristic
604#67—41no—
605#67—42no—
606#67—81no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—124no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—81no—
617C2×Dic3—121no—
618C2×Dic3C2×#6711yescharacteristic
619C2×Dic3C2×#6711yescharacteristic
620C2×Dic3C2×#6711yescharacteristic
621D12—21no—
622D12—21no—
623D12—32no—
624D12—32no—
625D12—62no—
626D12—61no—
627D12—61no—
628D12—121no—
629D12—122no—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—122no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3—122no—
636C4×D3—122no—
637C4×D3—122no—
638C4×D3—124no—
639Dic6—21no—
640Dic6—21no—
641Dic6—62no—
642Dic6—61no—
643Dic6—61no—
644Dic6—61no—
645Dic6—61no—
646Dic6—121no—
647C3×C8—61no—
648C3×C8—61no—
649C3⋊C8—21no—
650C3⋊C8—21no—
651C3⋊C8—32no—
652C3⋊C8—32no—
653C3⋊C8—62no—
654C3⋊C8—62no—
655C3⋊C8—61no—
656C3⋊C8—61no—
657C2×C32—41no—
658C2×C32—42no—
659C2×C32D4211yescharacteristic
660C2×C32#57511yescharacteristic
661C2×C32#57711yescharacteristic
662C3⋊D3—42no—
663C3×D3—41no—
664C3×D3—81no—
665C24—61no—
666#41—22no—
667#41—41no—
668#41—182no—
669#41—182no—
670#41—361no—
671#41—361no—
672C2×Q8—31no—
673C2×Q8—91no—
674C2×Q8C2×D3211yescharacteristic
675C2×D4—21no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—61no—
679C2×D4—62no—
680C2×D4—61no—
681C2×D4—91no—
682C2×D4—121no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4C2×D3211yescharacteristic
686C22×C4—21no—
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—181no—
690C22×C4—181no—
691C22×C4—181no—
692C22×C4C2×D3211yescharacteristic
693Q16—121no—
694Q16—182no—
695SD16—62no—
696SD16—182no—
697SD16—182no—
698SD16—182no—
699SD16—361no—
700D8—94no—
701D8—182no—
702M16—182no—
703C2×C8—31no—
704C2×C8—31no—
705C2×C8—91no—
706C2×C8—91no—
707C2×C8—182no—
708C4⋊C4—31no—
709C4⋊C4—31no—
710C4⋊C4—31no—
711C4⋊C4—61no—
712C4⋊C4—61no—
713C4⋊C4—181no—
714C4⋊C4—181no—
715C4⋊C4—181no—
716C22⋊C4—31no—
717C22⋊C4—31no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C42—31no—
727C22×C3—22no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—22no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—22no—
736C22×C3—21no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—42no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—244no—
753C22×C3C2×D3×D411yescharacteristic
754C22×C3C22×#6711yescharacteristic
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—62no—
762C2×D3—62no—
763C2×D3—84no—
764C2×D3—122no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—241no—
770C2×D3—241no—
771C3×C4—22no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—42no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—61no—
780C3×C4—61no—
781C3×C4—61no—
782C3×C4—121no—
783C3×C4—121no—
784C3×C4—121no—
785C3×C4C2×D3×D411yescharacteristic
786C3×C4C2×D3×D411yescharacteristic
787C3×C4#100411yescharacteristic
788C3×C4#100411yescharacteristic
789Dic3—21no—
790Dic3—21no—
791Dic3—21no—
792Dic3—41no—
793Dic3—41no—
794Dic3—41no—
795Dic3—122no—
796Dic3—121no—
797Dic3—121no—
798C32#326711yescharacteristic, complemented, Sylow
799C23—21no—
800C23—31no—
801C23—61no—
802C23—122no—
803C23—122no—
804C23—181no—
805C23—241no—
806C23D3×#6711yescharacteristic
807Q8—21no—
808Q8—21no—
809Q8—61no—
810Q8—61no—
811Q8—181no—
812Q8—181no—
813D4—21no—
814D4—42no—
815D4—61no—
816D4—61no—
817D4—92no—
818D4—121no—
819D4—122no—
820D4—181no—
821D4—241no—
822D4—362no—
823D4—362no—
824D4#381112yes—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—42no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—181no—
838C2×C4—241no—
839C2×C4—362no—
840C2×C4—362no—
841C2×C4—362no—
842C2×C4D3×#6711yescharacteristic
843C2×C4C22×D3211yescharacteristic
844C8—61no—
845C8—61no—
846C8—92no—
847C8—181no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—42no—
852C2×C3—42no—
853C2×C3—41no—
854C2×C3—41no—
855C2×C3—42no—
856C2×C3—82no—
857C2×C3—121no—
858C2×C3—241no—
859C2×C3#559011yescharacteristic
860C2×C3#576811yescharacteristic
861C2×C3#577811yescharacteristic
862C2×C3D4×#6711yescharacteristic
863C2×C3#582211yescharacteristic
864C2×C3#583611yescharacteristic
865D3—41no—
866D3—81no—
867D3—122no—
868D3—122no—
869D3—242no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—61no—
877C22—61no—
878C22—61no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—182no—
883C22—244no—
884C22—361no—
885C22—361no—
886C22C2×D3×#6711yescharacteristic
887C4—21no—
888C4—41no—
889C4—61no—
890C4—61no—
891C4—61no—
892C4—121no—
893C4—121no—
894C4—121no—
895C4—361no—
896C4C2×#381111yescharacteristic
897C4#6433011yescharacteristic
898C3—21no—
899C3#8026411yescharacteristic, complemented
900C3#8350311yescharacteristic, complemented
901C2—41no—
902C2—42no—
903C2—121no—
904C2—241no—
905C2—362no—
906C2#1059545311yescharacteristic
907C2#1059546411yescharacteristic
908C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64159C2semidirect
2. C3×#5829C2semidirect
3. C2×#63934C2semidirect
4. #10594834C2semidirect
5. C3×#5239C2semidirect
6. #10591657C2semidirect
7. #10591627C2semidirect
8. #10591598C2semidirect
9. #10591568C2semidirect
10. #10591489C2semidirect
11. #10591459C2semidirect
12. #10591404C2semidirect
13. #10591182C2semidirect
14. #10591179C2semidirect
15. #10591158C2semidirect
19. C2×#3828C22semidirect
23. C2×#3756C22semidirect
24. C2×#3755C22semidirect
27. C22×C3⋊(C3⋊C8)C22semidirect
30. C2×C3×#216C22semidirect
39. C3×#924C22semidirect
43. #63894C22semidirect
45. #63866C22semidirect
52. C3×#835C22semidirect
54. C3×#830C22semidirect
55. #63574C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
59. #63564C22semidirect
62. #63554C22semidirect
64. #5829D3semidirect
73. #5239D3semidirect
125. #3753D4semidirect
188. C2×#216C2×D3semidirect
213. #924C2×D3semidirect
237. #835C2×D3semidirect
241. #830C2×D3semidirect
798. C32#3267semidirect
899. C3#80264semidirect
900. C3#83503semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C3×#58292
C2×#639342
#105948342
C3×#52392
#105916572
#105916272
#105915982
#105915682
#105914892
#105914592
#105914042
#105911822
#105911792
#105911582
#835033
#802643