Finite Group Databasebeta

← #11884134

Subgroups — #11884134

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5554C211yesmaximal, characteristic
2C2×#63929C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4Dic6×D12C211yesmaximal, characteristic, complemented
5#10592718C211yesmaximal, characteristic, complemented
6C3×#5018C211yesmaximal, characteristic, complemented
7#10591463C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10590604C211yesmaximal, characteristic, complemented
10#10590603C211yesmaximal, characteristic, complemented
11#10590588C211yesmaximal, characteristic, complemented
12#10590579C211yesmaximal, characteristic, complemented
13#10590372C211yesmaximal, characteristic, complemented
14#10590326C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83506—31nomaximal
17#79795—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25#64078C2211yescharacteristic, complemented
26C2×C3×#214C2211yescharacteristic
27C3×#930—21no—
28C2×C3×(C2×D3)⋊C4—21no—
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic
31C3×#886—21no—
32C3×#882—21no—
33C3×#875C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic, complemented
36#63929—24no—
37D3×#214—24no—
38#63918—21no—
39#63893—21no—
40#63893—21no—
41Dic3×D12—21no—
42#63857C2211yescharacteristic
43#63857C2211yescharacteristic, complemented
44C2×#3719C2211yescharacteristic, complemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3718C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52#63637C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×#810C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58C3×#803C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#951—31no—
65C22×#214—31no—
66C2×#915—31no—
67C2×D3×SD16—31no—
68Q8×D12—31no—
69#5554D311yescharacteristic
70D4×Dic6—31no—
71C3×#440—31no—
72#5239—31no—
73#5218—31no—
74#5060—31no—
75#5054—31no—
76#5051—31no—
77#5050—31no—
78#5042—31no—
79#5040—31no—
80#5028—31no—
81#5019—31no—
82#5019—31no—
83#5019—61no—
84#5018D311yescharacteristic, complemented
85#5011—31no—
86#4887—31no—
87#4886—31no—
88#4809—31no—
89#4806—31no—
90#4783—31no—
91#4776—31no—
92#4715—31no—
93#4706—31no—
94C23×C3×D3—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×#634C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×#237—22no—
103C3×#237—41no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C2×C3×D12—21no—
107C2×C3×D12D411yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#627—21no—
114C2×#627—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117D3×Dic6—22no—
118D3×Dic6—22no—
119D3×Dic6—41no—
120D3×Dic6—41no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3754—22no—
125#3754—22no—
126C4⋊(C3⋊Dic3)—21no—
127C4⋊(C3⋊Dic3)—21no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#214D414yescomplemented
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3D411yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×C4×Dic3—21no—
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3719—22no—
149#3719—41no—
150#3718—22no—
151#3716—22no—
152#3716—41no—
153#3715—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×#237C2×D311yescharacteristic
162C2×D3×D4C2×D311yescharacteristic
163C22×Dic6—31no—
164C22×Dic6—31no—
165C2×C3×SD16—31no—
166C3×#124—31no—
167C3×#123—61no—
168C3×C22⋊Q8—31no—
169C3×#121—31no—
170C3×#121—61no—
171C3×#120—61no—
172C3×C4×Q8—31no—
173C3×C4×D4—21no—
174C3×C4×D4—31no—
175C3×C4×D4C2×D311yescharacteristic
176C3×C4×D4C2×D311yescharacteristic
177C2×C3×C22⋊C4—61no—
178#951—64no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—31no—
182C2×#216—31no—
183C2×#215—31no—
184D4×Dic3—61no—
185C2×#214—31no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—31no—
192C2×#214—61no—
193C2×#214—61no—
194C2×#214—64no—
195C2×#214C2×D311yescharacteristic
196#930—21no—
197C2×(C2×D3)⋊C4—21no—
198#924—31no—
199#924—31no—
200C2×#208—31no—
201C22×C3⋊C8—31no—
202#915—64no—
203D3×SD16—64no—
204C2×Dic12—31no—
205C2×Dic12—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×ΓL(1,𝔽25)—31no—
209C2×D3×C8—31no—
210#897—31no—
211#897—31no—
212#897—61no—
213#897—61no—
214#897C2×D311yescharacteristic
215#895C2×D311yescharacteristic
216#888—61no—
217#886—21no—
218#882—21no—
219#878—61no—
220#878—61no—
221#875C2×D311yescharacteristic
222C4×D12—61no—
223C4×D12C2×D311yescharacteristic
224#869—31no—
225#869—31no—
226#869—61no—
227#869—61no—
228C4×Dic6C2×D311yescharacteristic, complemented
229C3×#107—31no—
230C3×#103—31no—
231C3×#102—31no—
232C3×#97—31no—
233#835—31no—
234#832—31no—
235#832C2×D311yescharacteristic
236#830—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240#810—31no—
241#810—31no—
242#810—31no—
243#810—31no—
244#810—31no—
245#810—61no—
246#810—61no—
247#810C2×D311yescharacteristic, complemented
248#809—31no—
249#807C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—61no—
253#803C2×D311yescharacteristic, complemented
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—42no—
258C22×C3×D3—81no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C32×D4—21no—
262C32×D4C2×D412yes—
263C2×C32×C4—21no—
264C2×C32×C4—81no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270#634—21no—
271#634—21no—
272#634—21no—
273#634—21no—
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—22no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—81no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6C2×D412yes—
294#627—42no—
295#627—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—31no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—31no—
316#435—91no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C2×C3×D4—62no—
329C2×C3×D4—61no—
330C2×C3×D4—121no—
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—41no—
338C22×C3×C4—61no—
339C2×#67—21no—
340C2×#67—21no—
341C22×Dic3—21no—
342C22×Dic3—61no—
343C22×Dic3—61no—
344D3×Q8—62no—
345D3×Q8—62no—
346D3×Q8—121no—
347D3×Q8—121no—
348#237—22no—
349#237—41no—
350D3×D4—22no—
351D3×D4—41no—
352C2×D12—21no—
353C2×D12#6711yescharacteristic
354C2×D12C22×D311yescharacteristic
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3C22×D311yescharacteristic
358C2×C4×D3C22×D311yescharacteristic
359C2×Dic6—31no—
360C2×Dic6—31no—
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—61no—
364C2×Dic6—61no—
365C2×Dic6—62no—
366C2×Dic6—62no—
367C2×Dic6—61no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6—121no—
372C2×Dic6—121no—
373C2×Dic6C22×D311yescharacteristic
374C2×Dic6C22×D311yescharacteristic
375C3×SD16—34no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4C22×D311yescharacteristic
384C3×C4⋊C4C22×D311yescharacteristic
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—31no—
389C3×C22⋊C4—41no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C42—21no—
395C3×C42—61no—
396C3×C42C22×D311yescharacteristic
397C3×C42C22×D311yescharacteristic
398#217—61no—
399#217—61no—
400#216—62no—
401#216—62no—
402#216—62no—
403#216—121no—
404#215—62no—
405#214—62no—
406#214—62no—
407#214—62no—
408#214—62no—
409#214—62no—
410#214—62no—
411#214—122no—
412#214—122no—
413#214—121no—
414#214D1214yescomplemented
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4#6711yescharacteristic
422(C2×D3)⋊C4#6711yescharacteristic
423C4⋊Dic3—21no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—121no—
431C4⋊Dic3—121no—
432C4⋊Dic3#6711yescharacteristic
433C4⋊Dic3C22×D311yescharacteristic
434Dic3⋊C4—21no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437C4×Dic3—21no—
438#208—62no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—62no—
446C2×C3⋊C8C22×D311yescharacteristic
447C2×C3⋊C8C22×D311yescharacteristic
448Dic12—62no—
449Dic12—121no—
450#204—62no—
451#204—121no—
452ΓL(1,𝔽25)—62no—
453D3×C8—62no—
454C22×C32—22no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—84no—
467C2×C3×D3#13712yescomplemented
468C32×C4—21no—
469C32×C4—21no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—22no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—31no—
481C22×Q8—91no—
482C22×Q8—91no—
483C22×D4—31no—
484#137—184no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×SD16—31no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—184no—
495C2×M16—91no—
496C22×C8—91no—
497C4⋊Q8—91no—
498C4⋊Q8—181no—
499#124—31no—
500#123—61no—
501C22⋊Q8—31no—
502C22⋊Q8—91no—
503C22⋊Q8—91no—
504C22⋊Q8—181no—
505C22⋊Q8—181no—
506#121—31no—
507#121—61no—
508#120—61no—
509C4×Q8—31no—
510C4×D4—31no—
511C4×D4—181no—
512C4×D4D3211yescharacteristic
513C2×C22⋊C4—61no—
514#107—31no—
515C4⋊C8—91no—
516#103—31no—
517#103—91no—
518#103—91no—
519#103—91no—
520#102—31no—
521#102—91no—
522C22⋊C8—91no—
523C22⋊C8—91no—
524#97—31no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—31no—
528C23×C3—31no—
529C23×C3—41no—
530C23×C3—61no—
531C23×C3—122no—
532C23×C3—122no—
533C23×C3—241no—
534C22×D3—21no—
535C22×D3—42no—
536C22×D3—42no—
537C22×D3—81no—
538C22×D3C2×#6711yescharacteristic
539C22×D3C2×#6711yescharacteristic
540C3×Q8—32no—
541C3×Q8—61no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×D4—21no—
545C3×D4—21no—
546C3×D4—22no—
547C3×D4—41no—
548C3×D4—62no—
549C3×D4—61no—
550C3×D4—61no—
551C3×D4—122no—
552C3×D4—122no—
553C3×D4—241no—
554C3×D4C2×D1212yes—
555C3×D4D3×D412yes—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—41no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—81no—
572C2×C3×C4—81no—
573C2×C3×C4—82no—
574C2×C3×C4—122no—
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4C2×#6711yescharacteristic
578C2×C3×C4C2×#6711yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581#67—42no—
582#67—42no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—42no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3—122no—
594C2×Dic3—122no—
595C2×Dic3C2×#6711yescharacteristic
596C2×Dic3C2×#6711yescharacteristic
597D12—22no—
598D12—21no—
599D12—21no—
600D12—81no—
601C4×D3—21no—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—21no—
605C4×D3—122no—
606C4×D3—122no—
607Dic6—21no—
608Dic6—21no—
609Dic6—21no—
610Dic6—61no—
611Dic6—61no—
612Dic6—61no—
613Dic6—61no—
614Dic6—61no—
615Dic6—61no—
616Dic6—61no—
617Dic6—61no—
618Dic6—121no—
619Dic6—121no—
620Dic6—121no—
621Dic6—121no—
622Dic6—122no—
623Dic6—122no—
624Dic6—122no—
625Dic6—122no—
626Dic6C2×D1212yes—
627C3×C8—32no—
628C3×C8—61no—
629C3⋊C8—21no—
630C3⋊C8—61no—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C3⋊C8—61no—
634C3⋊C8—121no—
635C3⋊C8—121no—
636C3⋊C8C2×D1212yes—
637C2×C32—42no—
638C2×C32D4211yescharacteristic
639C2×C32C2×#13711yescharacteristic
640C2×C32#57711yescharacteristic
641C3×D3—22no—
642C3×D3—41no—
643C3×D3—81no—
644C24—61no—
645#41—62no—
646#41—121no—
647C2×Q8—31no—
648C2×Q8—31no—
649C2×Q8—91no—
650C2×Q8—91no—
651C2×Q8—181no—
652C2×Q8—181no—
653C2×Q8—182no—
654C2×Q8—182no—
655C2×Q8—361no—
656C2×Q8—361no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4—62no—
662C2×D4—61no—
663C2×D4—121no—
664C2×D4C2×D3211yescharacteristic
665C22×C4—21no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—61no—
669C22×C4—181no—
670C22×C4—181no—
671Q16—182no—
672Q16—182no—
673Q16—361no—
674SD16—34no—
675SD16—182no—
676SD16—182no—
677SD16—182no—
678SD16—182no—
679SD16—361no—
680M16—182no—
681C2×C8—31no—
682C2×C8—31no—
683C2×C8—91no—
684C2×C8—91no—
685C2×C8—182no—
686C4⋊C4—31no—
687C4⋊C4—31no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C4⋊C4C2×D3211yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—31no—
697C22⋊C4—31no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C42—61no—
705C42C2×D3211yescharacteristic
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—21no—
709C22×C3—32no—
710C22×C3—42no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—244no—
726C22×C3C2×D3×D411yescharacteristic
727C22×C3C22×#6711yescharacteristic
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—84no—
737C2×D3#95112yescomplemented
738C3×C4—22no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—62no—
749C3×C4—61no—
750C3×C4—61no—
751C3×C4—81no—
752C3×C4—121no—
753C3×C4—121no—
754C3×C4C22×D1211yescharacteristic
755C3×C4C2×D3×D411yescharacteristic
756C3×C4#100411yescharacteristic
757C3×C4#100911yescharacteristic
758Dic3—21no—
759Dic3—21no—
760Dic3—22no—
761Dic3—41no—
762Dic3—41no—
763Dic3—121no—
764Dic3—121no—
765Dic3—121no—
766Dic3—121no—
767Dic3—241no—
768Dic3—241no—
769C32#326611yescharacteristic, complemented, Sylow
770C23—21no—
771C23—31no—
772C23—31no—
773C23—61no—
774C23—122no—
775C23—122no—
776C23—241no—
777Q8—32no—
778Q8—61no—
779Q8—61no—
780Q8—61no—
781Q8—181no—
782Q8—181no—
783Q8—181no—
784Q8—181no—
785Q8—362no—
786Q8—362no—
787D4—21no—
788D4—62no—
789D4—61no—
790D4—61no—
791D4—122no—
792D4—122no—
793D4—241no—
794D4D3×D1212yes—
795C2×C4—21no—
796C2×C4—31no—
797C2×C4—31no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—81no—
806C2×C4—122no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—362no—
810C2×C4—362no—
811C2×C4D3×#6711yescharacteristic
812C2×C4D3×#6711yescharacteristic
813C2×C4C22×D3211yescharacteristic
814C8—32no—
815C8—61no—
816C8—181no—
817C8—181no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—42no—
822C2×C3—42no—
823C2×C3—62no—
824C2×C3—82no—
825C2×C3—121no—
826C2×C3—241no—
827C2×C3D4×D1211yescharacteristic
828C2×C3#577511yescharacteristic
829C2×C3D3×#13711yescharacteristic
830C2×C3D4×#6711yescharacteristic
831C2×C3C2×#95111yescharacteristic
832C2×C3#583611yescharacteristic
833D3—22no—
834D3—41no—
835D3—81no—
836C22—22no—
837C22—32no—
838C22—41no—
839C22—41no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—244no—
849C22C2×D3×#6711yescharacteristic
850C4—21no—
851C4—21no—
852C4—41no—
853C4—61no—
854C4—61no—
855C4—62no—
856C4—121no—
857C4—121no—
858C4—361no—
859C4—361no—
860C4C2×D3×D1211yescharacteristic
861C4#6430711yescharacteristic
862C3—21no—
863C3#7979511yescharacteristic, complemented
864C3#8350611yescharacteristic, complemented
865C2—42no—
866C2—62no—
867C2—121no—
868C2—241no—
869C2D12×#6711yescharacteristic
870C2#1059510611yescharacteristic
871C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5554C2
hypercenterC4×D4D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63929C2semidirect
3. C2×D3×#214C2semidirect
4. Dic6×D12C2semidirect
5. #10592718C2semidirect
6. C3×#5018C2semidirect
7. #10591463C2semidirect
8. #10591459C2semidirect
9. #10590604C2semidirect
10. #10590603C2semidirect
11. #10590588C2semidirect
12. #10590579C2semidirect
13. #10590372C2semidirect
14. #10590326C2semidirect
15. #10590267C2semidirect
21. C2×D3×Dic6C22semidirect
25. #64078C22semidirect
35. C3×C4×Dic6C22semidirect
43. #63857C22semidirect
44. C2×#3719C22semidirect
45. C2×#3719C22semidirect
46. C2×#3718C22semidirect
50. C2×#3711C22semidirect
52. #63637C22semidirect
53. #63637C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
56. C3×#810C22semidirect
57. C3×#807C22semidirect
58. C3×#803C22semidirect
59. #63565C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #5018D3semidirect
130. C3×#214D4semidirect
228. C4×Dic6C2×D3semidirect
247. #810C2×D3semidirect
249. #807C2×D3semidirect
253. #803C2×D3semidirect
414. #214D12semidirect
467. C2×C3×D3#137semidirect
737. C2×D3#951semidirect
769. C32#3266semidirect
863. C3#79795semidirect
864. C3#83506semidirect

Maximal subgroups

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

subgroupindex
C3×#55542
C2×#639292
C2×D3×#2142
Dic6×D122
#105927182
C3×#50182
#105914632
#105914592
#105906042
#105906032
#105905882
#105905792
#105903722
#105903262
#105902672
#835063
#797953