Finite Group Databasebeta

← #11884313

Subgroups — #11884313

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63807C211yesmaximal, characteristic, complemented
2C2×#63798C211yesmaximal, characteristic, complemented
3#10594630C211yesmaximal, characteristic, complemented
4#10594381C211yesmaximal, characteristic, complemented
5#10592566C211yesmaximal, characteristic, complemented
6C3×#4869C211yesmaximal, characteristic, complemented
7C3×#4864C211yesmaximal, characteristic, complemented
8#10590897C211yesmaximal, characteristic, complemented
9#10590726C211yesmaximal, characteristic, complemented
10#10590618C211yesmaximal, characteristic, complemented
11#10590614C211yesmaximal, characteristic, complemented
12#10590613C211yesmaximal, characteristic, complemented
13#10590597C211yesmaximal, characteristic, complemented
14#10590559C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16#80675—31nomaximal
17#79879—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×#3746C2211yescharacteristic, complemented
23C2×#3743C2211yescharacteristic
24#64106C2211yescharacteristic
25#64106C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#893C2211yescharacteristic, complemented
33#63922—21no—
34D3×(C2×D3)⋊C4—21no—
35#63908—21no—
36#63906—21no—
37C4×#626C2211yescharacteristic
38#63891—21no—
39#63891—21no—
40#63890—21no—
41D3×C4⋊Dic3—21no—
42#63866C2211yescharacteristic, complemented
43#63860C2211yescharacteristic
44C2×#3719C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50#63807—24no—
51#63798—24no—
52C32×#106C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#809C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#912—31no—
65C2×#911—31no—
66C2×#904—31no—
67#5631—31no—
68#5612—31no—
69#5555—31no—
70#5554—31no—
71C3×#465—31no—
72C3×#442—31no—
73#5167—31no—
74#5111—31no—
75#5047—31no—
76#5037—31no—
77#5019—31no—
78#5016—31no—
79#4869D311yescharacteristic, complemented
80#4867—31no—
81#4867—31no—
82#4867—61no—
83#4864D311yescharacteristic, complemented
84#4818—31no—
85#4808—31no—
86#4787—31no—
87#4783—31no—
88#4783—31no—
89#4781—31no—
90#4776—31no—
91#4776—31no—
92#4715—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626D411yescharacteristic
108C2×#625—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114#3802—22no—
115#3802—41no—
116#3796—22no—
117#3796—41no—
118#3795—22no—
119#3795—22no—
120#3795—41no—
121#3795—41no—
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3752—21no—
126#3752—21no—
127C4⋊(C3⋊Dic3)—21no—
128C4⋊(C3⋊Dic3)—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3746—22no—
131#3743—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D24D414yescomplemented
141C3×#204—22no—
142C3×D3×C8—22no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3D411yescharacteristic
146#3722D411yescharacteristic
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150#3719—41no—
151#3716—22no—
152#3716—22no—
153#3716—41no—
154#3715—22no—
155#3713—22no—
156#3267—91noSylow
157C2×#239—31no—
158C2×#237—31no—
159C2×#237—31no—
160C2×#237—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×#235—31no—
164C2×#235—31no—
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C22×C3×C8—31no—
168C3×C22⋊Q8—31no—
169C3×#121—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172#944—31no—
173C2×#216—31no—
174C2×#215—31no—
175#938—61no—
176#937—61no—
177#936—31no—
178C2×#214—31no—
179C2×#214—31no—
180C2×#214—31no—
181C2×#214—31no—
182C2×#213—31no—
183C2×#213—31no—
184#930—61no—
185#930—61no—
186C4×#67—31no—
187C2×(C2×D3)⋊C4—61no—
188C2×C4⋊Dic3—61no—
189#914—64no—
190#912—64no—
191#911—64no—
192C2×Dic12—31no—
193C2×Dic12—31no—
194C2×Dic12—31no—
195C2×Dic12—61no—
196#904—64no—
197C2×D24C2×D311yescharacteristic
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204C2×D311yescharacteristic
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—61no—
205C2×D3×C8C2×D311yescharacteristic, complemented
206#897—31no—
207#897—31no—
208#897—31no—
209#897—31no—
210#897—61no—
211#897—61no—
212#897C2×D311yescharacteristic, complemented
213#895C2×D311yescharacteristic
214#894—61no—
215#893C2×D311yescharacteristic
216#893C2×D311yescharacteristic, complemented
217D3×C4⋊C4—61no—
218#886—61no—
219#886—61no—
220#886—61no—
221#884—61no—
222#883—61no—
223#883—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226#875—31no—
227C4×D12—31no—
228#869—31no—
229C3×#106—21no—
230C3×#106C2×D311yescharacteristic, complemented
231C3×#106C2×D311yescharacteristic, complemented
232C3×#103—31no—
233C3×#102—31no—
234C3×#102—31no—
235C3×#102—31no—
236C3×#97—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241#815C2×D311yescharacteristic, complemented
242Dic3⋊C8—31no—
243#810—31no—
244#810—31no—
245#810—31no—
246#810—31no—
247#810—61no—
248#810—61no—
249#810C2×D311yescharacteristic, complemented
250#809C2×D311yescharacteristic
251#809C2×D311yescharacteristic
252#809C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254C22×C3⋊D3C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270#634—21no—
271#634—21no—
272#634—21no—
273#634—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—81no—
283C3×D12C2×D412yes—
284C3×D12C2×D412yes—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—42no—
288C3×C4×D3—81no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—41no—
292#626—42no—
293#625—42no—
294#625—42no—
295#625—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8C2×D412yes—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—31no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—31no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C2×C3×Q8—31no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—61no—
325C22×C3×C4—31no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C2×#67—31no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339#239—62no—
340#239—121no—
341#237—62no—
342#237—62no—
343#237—62no—
344#237—121no—
345#237—121no—
346#237—121no—
347D3×D4—62no—
348D3×D4—62no—
349D3×D4—121no—
350D3×D4—121no—
351#235—62no—
352#235—62no—
353#235—121no—
354#235—121no—
355C2×D12—21no—
356C2×D12—31no—
357C2×D12—61no—
358C2×D12C22×D311yescharacteristic
359C2×D12C22×D311yescharacteristic
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—21no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3C22×D311yescharacteristic
370C2×Dic6—31no—
371C2×Dic6—31no—
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6C22×D311yescharacteristic
377C3×SD16—62no—
378C3×D8—34no—
379C2×C3×C8—21no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—62no—
383C2×C3×C8C22×D311yescharacteristic
384C2×C3×C8C22×D311yescharacteristic
385C3×C4⋊C4—21no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C4⋊C4C22×D311yescharacteristic
390C3×C4⋊C4C22×D311yescharacteristic
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C42—31no—
397#217—31no—
398#217—61no—
399#217—61no—
400#216—121no—
401#215—62no—
402#214—62no—
403#214—62no—
404#214—62no—
405#214—121no—
406#213—62no—
407#213—62no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—121no—
422(C2×D3)⋊C4—121no—
423C4⋊Dic3—21no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3—121no—
432C4⋊Dic3—121no—
433Dic3⋊C4—31no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436C4×Dic3C22×D311yescharacteristic
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442Dic12—62no—
443Dic12—62no—
444Dic12—122no—
445Dic12—121no—
446D24D1214yescomplemented
447#204—22no—
448#204—62no—
449#204—62no—
450#204—121no—
451ΓL(1,𝔽25)—62no—
452ΓL(1,𝔽25)—62no—
453ΓL(1,𝔽25)—122no—
454D3×C8—22no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—41no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3⋊Dic3—21no—
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C2×#41—91no—
484C2×#41—91no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—91no—
490C2×Q16—91no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—31no—
500C4⋊Q8—91no—
501#124—91no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—31no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—31no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106D3211yescharacteristic, complemented
518C4⋊C8—91no—
519#103—31no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—31no—
524#102—31no—
525C22⋊C8—91no—
526C22⋊C8—91no—
527#97—31no—
528C23×C3—31no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—61no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3D3×D411yescharacteristic
545C3×Q8—61no—
546C3×Q8—61no—
547C3×D4—32no—
548C3×D4—32no—
549C3×D4—61no—
550C3×D4—61no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—241no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—122no—
568C2×C3×C4—241no—
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571#67—121no—
572#67—122no—
573#67—122no—
574#67—122no—
575#67—122no—
576#67—122no—
577#67—122no—
578#67—122no—
579C2×Dic3—21no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—122no—
590C2×Dic3—122no—
591C2×Dic3—122no—
592C2×Dic3D3×D411yescharacteristic
593C2×Dic3D3×D411yescharacteristic
594C2×Dic3D3×D411yescharacteristic
595D12—21no—
596D12—21no—
597D12—21no—
598D12—21no—
599D12—81no—
600D12—121no—
601D12—122no—
602D12C2×D1212yes—
603D12C2×D1212yes—
604C4×D3—21no—
605C4×D3—21no—
606C4×D3—42no—
607C4×D3—61no—
608C4×D3—61no—
609C4×D3—61no—
610C4×D3—61no—
611C4×D3—81no—
612C4×D3—121no—
613C4×D3—121no—
614C4×D3—122no—
615C4×D3—122no—
616C4×D3—122no—
617Dic6—21no—
618Dic6—21no—
619Dic6—61no—
620Dic6—61no—
621Dic6—61no—
622Dic6—61no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—61no—
627Dic6—121no—
628Dic6—121no—
629Dic6—121no—
630Dic6—121no—
631C3×C8—22no—
632C3×C8—61no—
633C3×C8—61no—
634C3×C8C2×D1212yes—
635C3×C8D3×D412yes—
636C3⋊C8—21no—
637C3⋊C8—21no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C2×C32D4211yescharacteristic
642C2×C32#57511yescharacteristic
643C2×C32#57711yescharacteristic
644C3⋊D3—41no—
645C3×D3—42no—
646C3×D3—41no—
647C3×D3—42no—
648C3×D3—81no—
649C24—181no—
650#41—182no—
651#41—182no—
652#41—182no—
653#41—361no—
654#41—361no—
655#41—361no—
656C2×Q8—31no—
657C2×Q8—91no—
658C2×Q8—91no—
659C2×D4—31no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—61no—
663C2×D4—91no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—361no—
670C22×C4—31no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—91no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677Q16—182no—
678Q16—361no—
679SD16—62no—
680SD16—182no—
681SD16—182no—
682SD16—182no—
683SD16—361no—
684D8—34no—
685D8—182no—
686M16—182no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—62no—
690C2×C8—91no—
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—61no—
693C4⋊C4—91no—
694C4⋊C4—181no—
695C4⋊C4—181no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4C2×D3211yescharacteristic
699C4⋊C4C2×D3211yescharacteristic
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—91no—
705C22⋊C4—91no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C42—31no—
711C22×C3—21no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3C2×D3×D411yescharacteristic
725C22×C3C2×D3×D411yescharacteristic
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—22no—
729C2×D3—22no—
730C2×D3—21no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—244no—
748C2×D3—244no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—81no—
759C3×C4—81no—
760C3×C4—121no—
761C3×C4C22×D1211yescharacteristic
762C3×C4C2×D3×D411yescharacteristic
763C3×C4#100911yescharacteristic
764C3×C4#100911yescharacteristic
765Dic3—21no—
766Dic3—21no—
767Dic3—21no—
768Dic3—41no—
769Dic3—61no—
770Dic3—61no—
771Dic3—121no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—241no—
777Dic3—241no—
778C32#326711yescharacteristic, complemented, Sylow
779C23—31no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—91no—
784C23—362no—
785C23—362no—
786C23—721no—
787Q8—61no—
788Q8—61no—
789Q8—181no—
790Q8—181no—
791Q8—181no—
792Q8—181no—
793D4—32no—
794D4—32no—
795D4—61no—
796D4—61no—
797D4—61no—
798D4—61no—
799D4—241no—
800D4—361no—
801D4—362no—
802D4—362no—
803D4—362no—
804D4—362no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—91no—
814C2×C4—122no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—241no—
820C2×C4—362no—
821C2×C4—362no—
822C2×C4—362no—
823C2×C4C22×D3211yescharacteristic
824C8—61no—
825C8—61no—
826C8—181no—
827C8D3×D1212yes—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—121no—
832C2×C3—122no—
833C2×C3—122no—
834C2×C3—241no—
835C2×C3D4×D1211yescharacteristic
836C2×C3#560911yescharacteristic
837C2×C3#576211yescharacteristic
838C2×C3#576811yescharacteristic
839C2×C3#577311yescharacteristic
840C2×C3#577511yescharacteristic
841D3—42no—
842D3—42no—
843D3—41no—
844D3—81no—
845D3—121no—
846D3—121no—
847D3—241no—
848C22—61no—
849C22—62no—
850C22—62no—
851C22—61no—
852C22—61no—
853C22—121no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—724no—
864C22D32×D411yescharacteristic
865C4—41no—
866C4—41no—
867C4—61no—
868C4—61no—
869C4—61no—
870C4—121no—
871C4—181no—
872C4—361no—
873C4—361no—
874C4C2×D3×D1211yescharacteristic
875C4#6432011yescharacteristic
876C3—21no—
877C3#7987911yescharacteristic, complemented
878C3#8067511yescharacteristic, complemented
879C2—121no—
880C2—122no—
881C2—122no—
882C2—241no—
883C2—361no—
884C2#1059462111yescharacteristic
885C2#1059474511yescharacteristic
886C2#1059474911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C2×#63807C2semidirect
2. C2×#63798C2semidirect
3. #10594630C2semidirect
4. #10594381C2semidirect
5. #10592566C2semidirect
6. C3×#4869C2semidirect
7. C3×#4864C2semidirect
8. #10590897C2semidirect
9. #10590726C2semidirect
10. #10590618C2semidirect
11. #10590614C2semidirect
12. #10590613C2semidirect
13. #10590597C2semidirect
14. #10590559C2semidirect
15. #10590530C2semidirect
21. C2×#3795C22semidirect
22. C2×#3746C22semidirect
28. C2×C3×D3×C8C22semidirect
29. C3×#897C22semidirect
32. C3×#893C22semidirect
42. #63866C22semidirect
44. C2×#3719C22semidirect
47. C2×#3716C22semidirect
52. C32×#106C22semidirect
53. #63637C22semidirect
54. #63637C22semidirect
55. C3×#815C22semidirect
56. C3×#810C22semidirect
59. C3×#809C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
79. #4869D3semidirect
83. #4864D3semidirect
140. C3×D24D4semidirect
205. C2×D3×C8C2×D3semidirect
212. #897C2×D3semidirect
216. #893C2×D3semidirect
230. C3×#106C2×D3semidirect
231. C3×#106C2×D3semidirect
241. #815C2×D3semidirect
249. #810C2×D3semidirect
252. #809C2×D3semidirect
446. D24D12semidirect
517. #106D32semidirect
778. C32#3267semidirect
877. C3#79879semidirect
878. C3#80675semidirect

Maximal subgroups

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

subgroupindex
C2×#638072
C2×#637982
#105946302
#105943812
#105925662
C3×#48692
C3×#48642
#105908972
#105907262
#105906182
#105906142
#105906132
#105905972
#105905592
#105905302
#806753
#798793