Finite Group Databasebeta

← #11884252

Subgroups — #11884252

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64158C211yesmaximal, characteristic, complemented
2C3×#5824C211yesmaximal, characteristic, complemented
3C2×#63935C211yesmaximal, characteristic, complemented
4#10595018C211yesmaximal, characteristic, complemented
5C3×#5239C211yesmaximal, characteristic, complemented
6#10591657C211yesmaximal, characteristic, complemented
7#10591608C211yesmaximal, characteristic, complemented
8#10591585C211yesmaximal, characteristic, complemented
9#10591565C211yesmaximal, characteristic, complemented
10#10591471C211yesmaximal, characteristic, complemented
11#10591452C211yesmaximal, characteristic, complemented
12#10591404C211yesmaximal, characteristic, complemented
13#10591189C211yesmaximal, characteristic, complemented
14#10591183C211yesmaximal, characteristic, complemented
15#10591151C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#80265—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic, complemented
21C2×#3799C2211yescharacteristic
22#64158—24no—
23C2×#3755C2211yescharacteristic
24C2×#3755C2211yescharacteristic
25C2×#3753C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C2×#3748C2211yescharacteristic
28C3×#946C2211yescharacteristic, complemented
29C3×#944C2211yescharacteristic, complemented
30C2×C3×#216C2211yescharacteristic, complemented
31C3×#939—21no—
32C3×#935—21no—
33C3×D4×Dic3C2211yescharacteristic, complemented
34C2×C3×#214C2211yescharacteristic, complemented
35C3×#929—21no—
36C3×C4×#67C2211yescharacteristic
37C3×#924C2211yescharacteristic
38C3×#924C2211yescharacteristic
39C2×C3×Dic3⋊C4—21no—
40#63981—21no—
41#63974—21no—
42#63935—24no—
43#63910—21no—
44#63909C2211yescharacteristic
45#63897—21no—
46#63894C2211yescharacteristic
47#63864C2211yescharacteristic
48C2×#3718C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic
50C2×#3717C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic
55#63574C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#547—31no—
64#5824D311yescharacteristic, complemented
65C2×#950—31no—
66C2×#949—31no—
67C2×#949—31no—
68C2×#949—61no—
69C2×#916—31no—
70#5630—31no—
71#5550—31no—
72C3×#452—31no—
73#5239D311yescharacteristic, complemented
74#5238—31no—
75#5190—31no—
76#5187—31no—
77#5165—31no—
78#5086—31no—
79#5083—31no—
80#5052—31no—
81#5052—31no—
82#5048—31no—
83#5047—31no—
84#5046—31no—
85#5016—31no—
86#5014—31no—
87#5011—31no—
88#4818—31no—
89#4807—31no—
90#4785—31no—
91#4781—31no—
92#4731—31no—
93#4728—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×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)—41no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67D411yescharacteristic
109C22×C3×Dic3—21no—
110C22×C3×Dic3—21no—
111C3×#237—22no—
112C3×#237—41no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#626—21no—
117C2×#626—21no—
118C2×#624—21no—
119C2×#624—21no—
120#3799—22no—
121#3799—41no—
122#3755—22no—
123#3755—22no—
124#3753—22no—
125#3753D414yescomplemented
126#3748—22no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#217—21no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#217D411yescharacteristic
133C3×#216—41no—
134C3×#214—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4D411yescharacteristic
145C3×C4×Dic3C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148#3722—21no—
149#3722—21no—
150#3722—21no—
151#3722—21no—
152#3718—22no—
153#3717—22no—
154#3717—41no—
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41C2×D311yescharacteristic
160C2×C3×#41C2×D311yescharacteristic
161C2×#239—31no—
162C2×#237C2×D311yescharacteristic, complemented
163C2×#235—31no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—61no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C3×C4⋊Q8—31no—
170C3×#123—61no—
171C3×#123—61no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—31no—
174C3×C22⋊Q8—31no—
175C3×#121—61no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C2×C3×C4⋊C4—61no—
179#950—64no—
180#949—64no—
181#949—64no—
182#949—68no—
183#947—31no—
184#946C2×D311yescharacteristic, complemented
185#944C2×D311yescharacteristic, complemented
186C2×#216—31no—
187C2×#216—31no—
188C2×#216C2×D311yescharacteristic, complemented
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—61no—
196C2×#215—61no—
197#939—21no—
198#937—61no—
199#935—21no—
200D4×Dic3C2×D311yescharacteristic, complemented
201C2×#214C2×D311yescharacteristic, complemented
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—61no—
207C2×#213—61no—
208#930—31no—
209#929—21no—
210C4×#67C2×D311yescharacteristic
211#924C2×D311yescharacteristic
212#924C2×D311yescharacteristic
213C2×Dic3⋊C4—21no—
214C2×#208—31no—
215C2×#208—31no—
216C2×#208—61no—
217C22×C3⋊C8—31no—
218#916—64no—
219C2×#204—31no—
220C2×#204—31no—
221C2×D3×C8—31no—
222#895—31no—
223#895—61no—
224#894—61no—
225#894—61no—
226#893—31no—
227#884—61no—
228#882—61no—
229D3×C22⋊C4—61no—
230D3×C22⋊C4—61no—
231#875—31no—
232C4×D12—31no—
233C3×#103—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#835—31no—
238#835C2×D311yescharacteristic, complemented
239#832C2×D311yescharacteristic, complemented
240#830—31no—
241#830C2×D311yescharacteristic
242#821—31no—
243#821—31no—
244(C2×D3)⋊C8—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
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—42no—
278C4⋊(C3⋊D3)C2×D412yes—
279C3×#67—41no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—42no—
286C2×C3×Dic3—42no—
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#626—42no—
297#626—81no—
298#624—42no—
299#624—81no—
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—31no—
307#546—91no—
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—
319C23×D3—61no—
320C23×D3—61no—
321C23×D3—121no—
322C3×#41—24no—
323C3×#41—22no—
324C3×#41—22no—
325C3×#41—41no—
326C3×#41—41no—
327C3×#41—42no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—31no—
332C2×C3×Q8—31no—
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—31no—
339C2×C3×D4—41no—
340C2×C3×D4—61no—
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×C4—61no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—21no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67#6711yescharacteristic
356C22×Dic3—21no—
357C22×Dic3—21no—
358#239—62no—
359#239—121no—
360#237—22no—
361#237—41no—
362#235—62no—
363#235—121no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—62no—
371C2×D12—62no—
372C2×D12—64no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—121no—
378C2×D12—121no—
379C2×D12—121no—
380C2×D12—122no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3C22×D311yescharacteristic
386C2×Dic6C22×D311yescharacteristic
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×C4⋊C4—61no—
398C3×C4⋊C4—61no—
399C3×C4⋊C4—61no—
400C3×C22⋊C4—31no—
401C3×C22⋊C4—31no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C42—31no—
407#217—21no—
408#217—21no—
409#217—21no—
410#217#6711yescharacteristic
411#216—41no—
412#216—62no—
413#216—62no—
414#215—62no—
415#215—62no—
416#215—62no—
417#215—62no—
418#215—62no—
419#215—64no—
420#215—64no—
421#215—121no—
422#214—22no—
423#213—34no—
424#213—34no—
425#213—64no—
426#213—64no—
427#213—62no—
428#213—62no—
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—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4#6711yescharacteristic
439C4⋊Dic3C22×D311yescharacteristic
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—21no—
442Dic3⋊C4—21no—
443Dic3⋊C4—21no—
444Dic3⋊C4—21no—
445Dic3⋊C4—21no—
446Dic3⋊C4#6711yescharacteristic
447C4×Dic3C22×D311yescharacteristic
448#208—62no—
449#208—62no—
450#208—64no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8—62no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460#204—62no—
461#204—121no—
462D3×C8—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—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3⋊D3—84no—
477C2×C3×D3—21no—
478C2×C3×D3—21no—
479C2×C3×D3—21no—
480C32×C4—21no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—31no—
492C2×#41—91no—
493C2×#41D3211yescharacteristic
494C22×D4—91no—
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—31no—
509#124—91no—
510#123—61no—
511#123—61no—
512#123—181no—
513C22⋊Q8—31no—
514C22⋊Q8—31no—
515C22⋊Q8—31no—
516#121—61no—
517#121—91no—
518#121—181no—
519#120—181no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—91no—
523C2×C4⋊C4—61no—
524C2×C22⋊C4—181no—
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×C3D3×D411yescharacteristic
542C23×C3C2×#6711yescharacteristic
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—124no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—242no—
555C22×D3—241no—
556C22×D3—241no—
557C22×D3—242no—
558C22×D3C2×#6711yescharacteristic
559C3×Q8—22no—
560C3×Q8—21no—
561C3×Q8—21no—
562C3×Q8—21no—
563C3×Q8—21no—
564C3×Q8—41no—
565C3×Q8—61no—
566C3×Q8—61no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—22no—
572C3×D4—41no—
573C3×D4—42no—
574C3×D4—42no—
575C3×D4—44no—
576C3×D4—121no—
577C3×D4—122no—
578C3×D4D3×D412yes—
579C3×D4D3×D412yes—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—31no—
591C2×C3×C4—31no—
592C2×C3×C4—31no—
593C2×C3×C4—41no—
594C2×C3×C4—42no—
595C2×C3×C4—42no—
596C2×C3×C4—44no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—122no—
604C2×C3×C4—122no—
605C2×C3×C4D3×D411yescharacteristic
606C2×C3×C4C2×#6711yescharacteristic
607C2×C3×C4C23×D311yescharacteristic
608C2×C3×C4C23×D311yescharacteristic
609#67—41no—
610#67—42no—
611#67—122no—
612#67—241no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—42no—
618C2×Dic3—42no—
619C2×Dic3C2×#6711yescharacteristic
620C2×Dic3C2×#6711yescharacteristic
621C2×Dic3C2×#6711yescharacteristic
622D12—32no—
623D12—32no—
624D12—62no—
625D12—62no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—121no—
633D12—121no—
634D12—122no—
635D12—122no—
636D12—124no—
637D12—122no—
638D12—241no—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—122no—
642C4×D3—122no—
643C4×D3—241no—
644C4×D3—241no—
645Dic6—21no—
646Dic6—21no—
647Dic6—21no—
648Dic6—21no—
649C3×C8—61no—
650C3×C8—61no—
651C3⋊C8—21no—
652C3⋊C8—21no—
653C3⋊C8—32no—
654C3⋊C8—32no—
655C3⋊C8—62no—
656C3⋊C8—62no—
657C3⋊C8—61no—
658C3⋊C8—61no—
659C2×C32—41no—
660C2×C32—42no—
661C2×C32D4211yescharacteristic
662C2×C32#57511yescharacteristic
663C2×C32#57711yescharacteristic
664C3⋊D3—42no—
665C3⋊D3—81no—
666C3×D3—41no—
667C24—181no—
668#41—22no—
669#41—41no—
670#41—62no—
671#41—121no—
672#41—182no—
673#41—361no—
674C2×Q8—31no—
675C2×Q8—31no—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—21no—
678C2×D4—31no—
679C2×D4—61no—
680C2×D4—91no—
681C2×D4—91no—
682C2×D4—182no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—361no—
687C2×D4C2×D3211yescharacteristic
688C22×C4—21no—
689C22×C4—31no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—181no—
693C22×C4—181no—
694C22×C4C2×D3211yescharacteristic
695Q16—121no—
696Q16—182no—
697SD16—62no—
698SD16—182no—
699SD16—182no—
700SD16—182no—
701SD16—361no—
702D8—94no—
703D8—182no—
704M16—182no—
705C2×C8—31no—
706C2×C8—31no—
707C2×C8—91no—
708C2×C8—91no—
709C2×C8—182no—
710C4⋊C4—31no—
711C4⋊C4—31no—
712C4⋊C4—31no—
713C4⋊C4—61no—
714C4⋊C4—61no—
715C4⋊C4—61no—
716C4⋊C4—61no—
717C4⋊C4—61no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C42—31no—
729C22×C3—22no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—22no—
738C22×C3—21no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—42no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—61no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C22×#6711yescharacteristic
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—122no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—122no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—241no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—241no—
774C2×D3—244no—
775C2×D3—244no—
776C2×D3—248no—
777C3×C4—22no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—42no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—61no—
786C3×C4—61no—
787C3×C4—61no—
788C3×C4—121no—
789C3×C4—121no—
790C3×C4—121no—
791C3×C4—121no—
792C3×C4C2×D3×D411yescharacteristic
793C3×C4C2×D3×D411yescharacteristic
794C3×C4#100411yescharacteristic
795C3×C4#100411yescharacteristic
796Dic3—21no—
797Dic3—21no—
798Dic3—21no—
799Dic3—41no—
800Dic3—41no—
801Dic3—41no—
802Dic3—41no—
803C32#326711yescharacteristic, complemented, Sylow
804C23—21no—
805C23—31no—
806C23—181no—
807C23—181no—
808C23—362no—
809C23—362no—
810C23—721no—
811C23D3×#6711yescharacteristic
812Q8—21no—
813Q8—21no—
814Q8—61no—
815Q8—61no—
816Q8—61no—
817Q8—61no—
818D4—21no—
819D4—42no—
820D4—92no—
821D4—121no—
822D4—122no—
823D4—181no—
824D4—181no—
825D4—181no—
826D4—362no—
827D4—362no—
828D4—721no—
829D4#381112yes—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—42no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—122no—
844C2×C4—122no—
845C2×C4—362no—
846C2×C4—721no—
847C2×C4D3×#6711yescharacteristic
848C2×C4C22×D3211yescharacteristic
849C8—61no—
850C8—61no—
851C8—92no—
852C8—181no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—42no—
857C2×C3—41no—
858C2×C3—42no—
859C2×C3—41no—
860C2×C3—42no—
861C2×C3—82no—
862C2×C3—121no—
863C2×C3#559011yescharacteristic
864C2×C3#577011yescharacteristic
865C2×C3#577711yescharacteristic
866C2×C3D4×#6711yescharacteristic
867C2×C3#582211yescharacteristic
868C2×C3#583711yescharacteristic
869D3—41no—
870D3—122no—
871D3—122no—
872D3—242no—
873D3—242no—
874D3—241no—
875D3—241no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—22no—
880C22—41no—
881C22—41no—
882C22—61no—
883C22—61no—
884C22—61no—
885C22—182no—
886C22—361no—
887C22—361no—
888C22—361no—
889C22—361no—
890C22—361no—
891C22—724no—
892C22C2×D3×#6711yescharacteristic
893C4—21no—
894C4—41no—
895C4—61no—
896C4—61no—
897C4—61no—
898C4—121no—
899C4—121no—
900C4—121no—
901C4—121no—
902C4C2×#381111yescharacteristic
903C4#6433011yescharacteristic
904C3—21no—
905C3#8026511yescharacteristic, complemented
906C3#8352211yescharacteristic, complemented
907C2—41no—
908C2—42no—
909C2—121no—
910C2—362no—
911C2—721no—
912C2#1059545711yescharacteristic
913C2#1059547011yescharacteristic
914C2#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×#64158C2semidirect
2. C3×#5824C2semidirect
3. C2×#63935C2semidirect
4. #10595018C2semidirect
5. C3×#5239C2semidirect
6. #10591657C2semidirect
7. #10591608C2semidirect
8. #10591585C2semidirect
9. #10591565C2semidirect
10. #10591471C2semidirect
11. #10591452C2semidirect
12. #10591404C2semidirect
13. #10591189C2semidirect
14. #10591183C2semidirect
15. #10591151C2semidirect
20. C2×C3×#237C22semidirect
28. C3×#946C22semidirect
29. C3×#944C22semidirect
30. C2×C3×#216C22semidirect
33. C3×D4×Dic3C22semidirect
34. C2×C3×#214C22semidirect
48. C2×#3718C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
55. #63574C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
64. #5824D3semidirect
73. #5239D3semidirect
125. #3753D4semidirect
162. C2×#237C2×D3semidirect
184. #946C2×D3semidirect
185. #944C2×D3semidirect
188. C2×#216C2×D3semidirect
200. D4×Dic3C2×D3semidirect
201. C2×#214C2×D3semidirect
238. #835C2×D3semidirect
239. #832C2×D3semidirect
803. C32#3267semidirect
905. C3#80265semidirect
906. C3#83522semidirect

Maximal subgroups

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

subgroupindex
C2×#641582
C3×#58242
C2×#639352
#105950182
C3×#52392
#105916572
#105916082
#105915852
#105915652
#105914712
#105914522
#105914042
#105911892
#105911832
#105911512
#835223
#802653