Finite Group Databasebeta

← #11884094

Subgroups — #11884094

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#625C211yesmaximal, characteristic, complemented
2C2×#63948C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10594633C211yesmaximal, characteristic
5#10592516C211yesmaximal, characteristic, complemented
6C3×#4809C211yesmaximal, characteristic, complemented
7C3×#4806C211yesmaximal, characteristic, complemented
8#10591612C211yesmaximal, characteristic, complemented
9#10590966C211yesmaximal, characteristic, complemented
10#10590942C211yesmaximal, characteristic, complemented
11#10590870C211yesmaximal, characteristic, complemented
12#10590725C211yesmaximal, characteristic, complemented
13#10590565C211yesmaximal, characteristic, complemented
14#10590518C211yesmaximal, characteristic, complemented
15#10590515C211yesmaximal, characteristic, complemented
16#80204—31nomaximal
17#80061—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24#64102C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic
31#63948—24no—
32D3×#215—24no—
33#63922—21no—
34#63921—21no—
35#63916—21no—
36C4×#625—21no—
37C4×#625C2211yescharacteristic
38#63873—21no—
39#63873C2211yescharacteristic, complemented
40#63863C2211yescharacteristic
41#63856—21no—
42#63856—21no—
43#63856C2211yescharacteristic
44#63856C2211yescharacteristic, complemented
45#63854—21no—
46C2×#3718C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52C32×#103C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63642C2211yescharacteristic, complemented
55#63634C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60#63572C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic
63Q8×#67—31no—
64Q8×#67—31no—
65C2×#942—31no—
66C22×#215—31no—
67C2×#918—31no—
68C2×D3×SD16—31no—
69#5630—31no—
70#5612—31no—
71C3×#451—31no—
72C3×#448—31no—
73#5190—31no—
74#5187—31no—
75#5185—31no—
76#5169—31no—
77#5167—31no—
78#5166—31no—
79#5051—31no—
80#5042—31no—
81#4818—31no—
82#4818—31no—
83#4817—31no—
84#4817—31no—
85#4817—61no—
86#4813—31no—
87#4812—31no—
88#4809D311yescharacteristic, complemented
89#4806D311yescharacteristic, complemented
90#4733—31no—
91#4731—31no—
92#4730—31no—
93#4728—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C3×D3×Q8—22no—
99C3×D3×Q8—22no—
100C3×D3×Q8—41no—
101C3×D3×Q8—41no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#625D411yescharacteristic
116C2×#624—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3799—22no—
120#3799—41no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3755D414yescomplemented
124#3752—21no—
125C4⋊(C3⋊Dic3)—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127C4×C3⋊Dic3—21no—
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#216—22no—
131C3×#215—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3—21no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×Dic12—41no—
138C3×#204—41no—
139#3724—21no—
140#3724—21no—
141#3724—21no—
142#3724—21no—
143#3724D411yescharacteristic
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3D411yescharacteristic
149(C2×D3)⋊Dic3D411yescharacteristic
150#3718—22no—
151#3717—22no—
152#3717—22no—
153#3715—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C22×C3×Q8—31no—
159C2×#239—31no—
160C2×D3×Q8C2×D311yescharacteristic
161C2×D3×Q8C2×D311yescharacteristic, complemented
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C3×C22⋊Q8—31no—
170C3×#121—31no—
171#947—31no—
172#946—31no—
173#946—31no—
174#946—61no—
175#946—61no—
176Q8×Dic3—31no—
177Q8×Dic3—31no—
178Q8×Dic3—61no—
179#944—31no—
180#944—31no—
181#944—61no—
182#944—61no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216C2×D311yescharacteristic, complemented
186#942—64no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—61no—
193C2×#215—64no—
194C2×#215C2×D311yescharacteristic
195#938—61no—
196#937—61no—
197#936—31no—
198C2×#214—31no—
199C4×#67—31no—
200C4×#67—31no—
201C4×#67—61no—
202C4×#67—61no—
203#924—31no—
204#924—31no—
205#924—61no—
206#924—61no—
207C2×#208—31no—
208C22×C3⋊C8—31no—
209#918—64no—
210D3×SD16—64no—
211C2×Dic12C2×D311yescharacteristic, complemented
212C2×#204—31no—
213C2×#204—31no—
214C2×#204C2×D311yescharacteristic
215C2×ΓL(1,𝔽25)—31no—
216C2×D3×C8—31no—
217#897C2×D311yescharacteristic
218#895—61no—
219#895C2×D311yescharacteristic
220#894—61no—
221#893—31no—
222#893—31no—
223#893—61no—
224#883—61no—
225#882—61no—
226D3×C22⋊C4—61no—
227D3×C22⋊C4—61no—
228C3×#103—21no—
229C3×#103—31no—
230C3×#103—31no—
231C3×#103C2×D311yescharacteristic, complemented
232C3×#103C2×D311yescharacteristic, complemented
233C3×C22⋊C8—31no—
234C3×C22⋊C8—31no—
235#835—31no—
236#832—31no—
237#821—31no—
238#821—31no—
239#821—31no—
240#821—61no—
241(C2×D3)⋊C8C2×D311yescharacteristic
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#816—31no—
244#815—31no—
245#815—31no—
246#815—61no—
247Dic3⋊C8—31no—
248Dic3⋊C8—31no—
249#810C2×D311yescharacteristic, complemented
250#810C2×D311yescharacteristic, complemented
251#807—31no—
252#807—31no—
253#807—61no—
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C32×Q8—21no—
262C32×Q8C2×D412yes—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)C2×D412yes—
271C4×C3⋊D3—81no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—81no—
280C3×C4×D3—21no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—42no—
285C3×C4×D3—42no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—42no—
293C3×Dic6—42no—
294#626—42no—
295#626—42no—
296#625—22no—
297#624—42no—
298C32×C8—21no—
299C3⋊(C3⋊C8)C2×D412yes—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—31no—
313#450—91no—
314#448—31no—
315#440—91no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—21no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—61no—
324C2×C3×Q8—61no—
325C2×C3×Q8—62no—
326C2×C3×Q8—62no—
327C2×C3×Q8—121no—
328C2×C3×Q8—121no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C2×#67—31no—
338C2×#67—31no—
339C2×#67—61no—
340C2×#67—61no—
341#239—62no—
342#239—121no—
343D3×Q8—22no—
344D3×Q8—22no—
345D3×Q8—41no—
346D3×Q8—41no—
347D3×D4—62no—
348D3×D4—121no—
349#235—62no—
350#235—121no—
351C2×D12—21no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—61no—
355C2×D12—62no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—121no—
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—21no—
361C2×C4×D3—21no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—121no—
367C2×C4×D3C22×D311yescharacteristic
368C2×C4×D3C22×D311yescharacteristic
369C2×Dic6—21no—
370C2×Dic6—21no—
371C2×Dic6C22×D311yescharacteristic
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×Q16—62no—
375C3×Q16—121no—
376C3×SD16—62no—
377C3×SD16—121no—
378C2×C3×C8—21no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C2×C3×C8C22×D311yescharacteristic
382C2×C3×C8C22×D311yescharacteristic
383C3×C4⋊C4—21no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4C22×D311yescharacteristic
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389#217—31no—
390#217—31no—
391#217—61no—
392#217—61no—
393#217—61no—
394#217—61no—
395#216—22no—
396#216—62no—
397#216—62no—
398#215—22no—
399#215—34no—
400#215—34no—
401#215—64no—
402#215—62no—
403#215—62no—
404#215—62no—
405#214—62no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—31no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—121no—
417C4⋊Dic3—21no—
418C4⋊Dic3—31no—
419C4⋊Dic3—31no—
420C4⋊Dic3—61no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3—121no—
424Dic3⋊C4—31no—
425Dic3⋊C4—31no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434C4×Dic3—31no—
435C4×Dic3—31no—
436C4×Dic3—61no—
437C4×Dic3—61no—
438C4×Dic3—61no—
439C4×Dic3—121no—
440#208—62no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8—62no—
445C2×C3⋊C8C22×D311yescharacteristic
446C2×C3⋊C8C22×D311yescharacteristic
447Dic12—41no—
448#204—41no—
449#204—62no—
450#204—62no—
451ΓL(1,𝔽25)—62no—
452D3×C8—62no—
453C22×C32C22×D411yescharacteristic
454C2×C3⋊D3—22no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3#13712yescomplemented
466D32—84no—
467C32×C4—22no—
468C32×C4—41no—
469C32×C4C22×D411yescharacteristic
470C32×C4H(5,𝔽2)11yescharacteristic
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C2×#41—91no—
480C22×Q8—31no—
481C22×Q8—31no—
482C22×D4—91no—
483#137—184no—
484C2×Q16—31no—
485C2×Q16—31no—
486C2×Q16—91no—
487C2×SD16—31no—
488C2×SD16—31no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—184no—
494C2×M16—91no—
495C22×C8—91no—
496C4⋊Q8—91no—
497C4⋊Q8—181no—
498#124—91no—
499#123—181no—
500C22⋊Q8—31no—
501C22⋊Q8—91no—
502C22⋊Q8—91no—
503C22⋊Q8—181no—
504C22⋊Q8—181no—
505#121—31no—
506#121—181no—
507#120—181no—
508C4×Q8—91no—
509C4×D4—91no—
510C4×D4—91no—
511C4×D4—181no—
512C2×C22⋊C4—181no—
513#107—91no—
514C4⋊C8—91no—
515#103—31no—
516#103—31no—
517#103—91no—
518#103D3211yescharacteristic, complemented
519#102—91no—
520#102—91no—
521C22⋊C8—31no—
522C22⋊C8—31no—
523#97—91no—
524C23×C3—31no—
525C23×C3—31no—
526C23×C3—61no—
527C22×D3—21no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—121no—
531C22×D3—122no—
532C22×D3—122no—
533C22×D3—122no—
534C22×D3—122no—
535C22×D3—241no—
536C22×D3—241no—
537C22×D3D3×D411yescharacteristic
538C22×D3D3×D411yescharacteristic
539C3×Q8—21no—
540C3×Q8—21no—
541C3×Q8—22no—
542C3×Q8—41no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—122no—
550C3×Q8—122no—
551C3×Q8D3×D412yes—
552C3×Q8D3×D412yes—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—241no—
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—41no—
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—61no—
572C2×C3×C4—122no—
573C2×C3×C4—122no—
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576#67—62no—
577#67—62no—
578#67—122no—
579#67—122no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—121no—
592C2×Dic3D3×D411yescharacteristic
593C2×Dic3D3×D411yescharacteristic
594D12—21no—
595D12—21no—
596D12—32no—
597D12—32no—
598D12—62no—
599D12—61no—
600D12—61no—
601D12—81no—
602D12—121no—
603D12—122no—
604D12—122no—
605C4×D3—21no—
606C4×D3—21no—
607C4×D3—21no—
608C4×D3—21no—
609C4×D3—42no—
610C4×D3—42no—
611C4×D3—122no—
612C4×D3—122no—
613C4×D3—241no—
614C4×D3—241no—
615C4×D3—242no—
616Dic6—21no—
617Dic6—21no—
618Dic6—21no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—42no—
623Dic6—42no—
624C3×C8—21no—
625C3×C8—21no—
626C3×C8—41no—
627C3×C8—61no—
628C3×C8—61no—
629C3⋊C8—21no—
630C3⋊C8—21no—
631C3⋊C8—32no—
632C3⋊C8—32no—
633C3⋊C8—62no—
634C2×C32D4211yescharacteristic
635C2×C32C2×#13711yescharacteristic
636C2×C32#57711yescharacteristic
637C3⋊D3—42no—
638C3×D3—22no—
639C3×D3—41no—
640C3×D3—81no—
641C24—181no—
642#41—182no—
643#41—361no—
644C2×Q8—31no—
645C2×Q8—31no—
646C2×Q8—31no—
647C2×Q8—61no—
648C2×Q8—61no—
649C2×Q8—62no—
650C2×Q8—62no—
651C2×Q8—121no—
652C2×Q8—121no—
653C2×Q8C2×D3211yescharacteristic
654C2×D4—31no—
655C2×D4—61no—
656C2×D4—91no—
657C2×D4—91no—
658C2×D4—181no—
659C2×D4—182no—
660C2×D4—181no—
661C2×D4—361no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—181no—
667C22×C4—181no—
668Q16—62no—
669Q16—121no—
670Q16—182no—
671SD16—62no—
672SD16—94no—
673SD16—121no—
674SD16—182no—
675SD16—182no—
676SD16—182no—
677M16—182no—
678C2×C8—31no—
679C2×C8—31no—
680C2×C8—91no—
681C2×C8—182no—
682C2×C8C2×D3211yescharacteristic
683C4⋊C4—61no—
684C4⋊C4—91no—
685C4⋊C4—91no—
686C4⋊C4—181no—
687C4⋊C4—181no—
688C4⋊C4—181no—
689C4⋊C4—181no—
690C4⋊C4—181no—
691C4⋊C4C2×D3211yescharacteristic
692C22⋊C4—61no—
693C22⋊C4—61no—
694C22⋊C4—91no—
695C22⋊C4—91no—
696C22⋊C4—181no—
697C22⋊C4—181no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C42—91no—
702C42—181no—
703C22×C3—21no—
704C22×C3—32no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—121no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3C2×D3×D411yescharacteristic
714C22×C3C2×D3×D411yescharacteristic
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—62no—
724C2×D3—62no—
725C2×D3—122no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—241no—
731C2×D3—241no—
732C2×D3—244no—
733C2×D3—244no—
734C2×D3#91812yescomplemented
735C3×C4—22no—
736C3×C4—22no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—42no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—81no—
745C3×C4—121no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4C2×D3×D411yescharacteristic
749C3×C4C2×D3×D411yescharacteristic
750C3×C4#100411yescharacteristic
751C3×C4#100411yescharacteristic
752Dic3—21no—
753Dic3—21no—
754Dic3—41no—
755Dic3—41no—
756Dic3—41no—
757Dic3—61no—
758Dic3—61no—
759Dic3—61no—
760Dic3—61no—
761Dic3—121no—
762Dic3—121no—
763Dic3—121no—
764Dic3—121no—
765Dic3—241no—
766C32#326611yescharacteristic, complemented, Sylow
767C23—31no—
768C23—31no—
769C23—61no—
770C23—181no—
771C23—362no—
772C23—362no—
773C23—721no—
774Q8—21no—
775Q8—61no—
776Q8—61no—
777Q8—61no—
778Q8—61no—
779Q8—61no—
780Q8—61no—
781Q8—122no—
782Q8—122no—
783Q8#380212yes—
784D4—61no—
785D4—61no—
786D4—92no—
787D4—182no—
788D4—181no—
789D4—241no—
790D4—362no—
791D4—362no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—91no—
804C2×C4—91no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—181no—
808C2×C4—362no—
809C2×C4—721no—
810C2×C4C22×D3211yescharacteristic
811C8—21no—
812C8—61no—
813C8—61no—
814C8—92no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—62no—
819C2×C3—121no—
820C2×C3—241no—
821C2×C3#559011yescharacteristic
822C2×C3#559011yescharacteristic
823C2×C3#576211yescharacteristic
824C2×C3C2×#91811yescharacteristic
825C2×C3D3×#13711yescharacteristic
826C2×C3#577811yescharacteristic
827D3—22no—
828D3—41no—
829D3—81no—
830D3—122no—
831D3—122no—
832D3—242no—
833C22—32no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—182no—
843C22—361no—
844C22—361no—
845C22—724no—
846C22D32×D411yescharacteristic
847C4—22no—
848C4—41no—
849C4—61no—
850C4—61no—
851C4—121no—
852C4—121no—
853C4—121no—
854C4—181no—
855C4—181no—
856C4—361no—
857C4C2×#380211yescharacteristic
858C4#6431311yescharacteristic
859C3—21no—
860C3#8006111yescharacteristic, complemented
861C3#8020411yescharacteristic, complemented
862C2—62no—
863C2—121no—
864C2—241no—
865C2—362no—
866C2#1059427111yescharacteristic
867C2#1059475111yescharacteristic
868C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594633C2
hypercenter#103D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. Q8×#625C2semidirect
2. C2×#63948C2semidirect
3. C2×D3×#215C2semidirect
5. #10592516C2semidirect
6. C3×#4809C2semidirect
7. C3×#4806C2semidirect
8. #10591612C2semidirect
9. #10590966C2semidirect
10. #10590942C2semidirect
11. #10590870C2semidirect
12. #10590725C2semidirect
13. #10590565C2semidirect
14. #10590518C2semidirect
15. #10590515C2semidirect
19. C2×C3×D3×Q8C22semidirect
22. Q8×C3⋊Dic3C22semidirect
25. C2×C3×#216C22semidirect
27. C2×C3×Dic12C22semidirect
39. #63873C22semidirect
44. #63856C22semidirect
46. C2×#3718C22semidirect
50. C2×#3711C22semidirect
52. C32×#103C22semidirect
54. #63642C22semidirect
55. #63634C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#810C22semidirect
59. C3×#810C22semidirect
60. #63572C22semidirect
61. #63566C22semidirect
88. #4809D3semidirect
89. #4806D3semidirect
123. #3755D4semidirect
161. C2×D3×Q8C2×D3semidirect
185. C2×#216C2×D3semidirect
211. C2×Dic12C2×D3semidirect
231. C3×#103C2×D3semidirect
232. C3×#103C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
249. #810C2×D3semidirect
250. #810C2×D3semidirect
465. C2×C3×D3#137semidirect
518. #103D32semidirect
734. C2×D3#918semidirect
766. C32#3266semidirect
860. C3#80061semidirect
861. C3#80204semidirect

Maximal subgroups

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

subgroupindex
Q8×#6252
C2×#639482
C2×D3×#2152
#105946332
#105925162
C3×#48092
C3×#48062
#105916122
#105909662
#105909422
#105908702
#105907252
#105905652
#105905182
#105905152
#802043
#800613