Finite Group Databasebeta

← #11884146

Subgroups — #11884146

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595403C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3C2×#63811C211yesmaximal, characteristic, complemented
4#10594629C211yesmaximal, characteristic
5#10592511C211yesmaximal, characteristic, complemented
6C3×#4818C211yesmaximal, characteristic, complemented
7C3×#4809C211yesmaximal, characteristic, complemented
8#10591656C211yesmaximal, characteristic, complemented
9#10591608C211yesmaximal, characteristic, complemented
10#10590942C211yesmaximal, characteristic, complemented
11#10590907C211yesmaximal, characteristic, complemented
12#10590801C211yesmaximal, characteristic, complemented
13#10590606C211yesmaximal, characteristic, complemented
14#10590518C211yesmaximal, characteristic, complemented
15#10590478C211yesmaximal, characteristic, complemented
16#80444—31nomaximal
17#80204—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3797C2211yescharacteristic, complemented
21C2×#3796C2211yescharacteristic
22#64155C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24C2×#3743C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×Dic12C2211yescharacteristic, complemented
30C2×C3×#204C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#893C2211yescharacteristic
33D3×#215—24no—
34#63923—21no—
35D3×(C2×D3)⋊C4—21no—
36#63909—21no—
37#63904—21no—
38C4×#626C2211yescharacteristic
39#63890—21no—
40#63888—21no—
41#63864C2211yescharacteristic
42#63856C2211yescharacteristic
43#63851—21no—
44Dic3×Dic6C2211yescharacteristic, complemented
45#63839—21no—
46C2×#3718C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63811—24no—
52C32×#103C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63634C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61#63557C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63Q8×#67—31no—
64C22×#215—31no—
65C2×#918—31no—
66C2×#915—31no—
67C2×D3×SD16—31no—
68#5727—31no—
69#5630—31no—
70#5554—31no—
71C3×#461—31no—
72C3×#451—31no—
73#5190—31no—
74#5187—31no—
75#5185—31no—
76#5173—31no—
77#5169—31no—
78#5086—31no—
79#5051—31no—
80#5018—31no—
81#4845—31no—
82#4836—31no—
83#4818D311yescharacteristic, complemented
84#4817—31no—
85#4813—31no—
86#4812—31no—
87#4812—31no—
88#4812—61no—
89#4809D311yescharacteristic, complemented
90#4806—31no—
91#4806—31no—
92#4731—31no—
93#4730—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C3×D3×Q8—22no—
100C3×D3×Q8—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626D411yescharacteristic
113C2×#624—21no—
114C2×D3×Dic3—21no—
115D3×D12—22no—
116D3×D12—41no—
117#3797—22no—
118#3797—41no—
119#3796—22no—
120#3796—41no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3755—22no—
124#3752—21no—
125#3752—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3743—22no—
130C3×#216—41no—
131C3×#215—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×Dic12—22no—
141C3×#204—22no—
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3D411yescharacteristic
145#3722—21no—
146#3722—21no—
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150Dic32—21no—
151#3718—22no—
152#3717—22no—
153#3717—41no—
154#3715D414yescomplemented
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C2×#239—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×Q8C2×D311yescharacteristic
162C2×#237—31no—
163C2×D3×D4—31no—
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C3×C4⋊Q8—31no—
170C3×C22⋊Q8—31no—
171C3×C4×D4—31no—
172#947—31no—
173#946—31no—
174#946—31no—
175#946—31no—
176#946—61no—
177#946—61no—
178Q8×Dic3—31no—
179#944—61no—
180#944C2×D311yescharacteristic, complemented
181C2×#216—31no—
182C2×#216—31no—
183C2×#216C2×D311yescharacteristic, complemented
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—61no—
190C2×#215—64no—
191C2×#215C2×D311yescharacteristic
192C2×#214—31no—
193#930—61no—
194C4×#67—31no—
195C4×#67—61no—
196C2×(C2×D3)⋊C4—61no—
197#924—31no—
198#924—61no—
199C22×C3⋊C8—31no—
200#918—64no—
201#915—64no—
202D3×SD16—64no—
203C2×Dic12C2×D311yescharacteristic, complemented
204C2×#204—31no—
205C2×#204—31no—
206C2×#204C2×D311yescharacteristic
207C2×ΓL(1,𝔽25)—31no—
208C2×ΓL(1,𝔽25)—31no—
209C2×ΓL(1,𝔽25)—61no—
210C2×D3×C8—31no—
211#897C2×D311yescharacteristic
212#896—61no—
213#896—61no—
214#895—31no—
215#895—31no—
216#895—61no—
217#895—61no—
218#894—61no—
219#893—61no—
220#893C2×D311yescharacteristic
221#888—61no—
222#886—61no—
223#882—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226#875—31no—
227C4×D12—31no—
228C4×Dic6—31no—
229C3×C4⋊C8—31no—
230C3×#103—21no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#103C2×D311yescharacteristic, complemented
234C3×#103C2×D311yescharacteristic, complemented
235C3×C22⋊C8—31no—
236#835—31no—
237#832—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8C2×D311yescharacteristic
245#816—31no—
246#815—31no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810C2×D311yescharacteristic, complemented
249#810C2×D311yescharacteristic, complemented
250#807—31no—
251#807—31no—
252#807—61no—
253#803—31no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C32×Q8—21no—
262C32×Q8—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—81no—
271C4×C3⋊D3—21no—
272C4×C3⋊D3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12C2×D412yes—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—42no—
284C3×C4×D3—81no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—42no—
291C3×Dic6C2×D412yes—
292#627—42no—
293#626—22no—
294#626—42no—
295#626—42no—
296#624—42no—
297D3×Dic3—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—31no—
311#452—91no—
312#451—31no—
313#450—91no—
314#448—91no—
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—62no—
325C2×C3×Q8—121no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—61no—
331C22×C3×C4—61no—
332C2×#67—31no—
333C2×#67—61no—
334C2×#67—61no—
335C22×Dic3—61no—
336#239—62no—
337#239—121no—
338D3×Q8—22no—
339D3×Q8—41no—
340D3×Q8—62no—
341D3×Q8—62no—
342D3×Q8—121no—
343D3×Q8—121no—
344#237—62no—
345#237—121no—
346D3×D4—62no—
347D3×D4—121no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—61no—
352C2×D12—62no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—121no—
358C2×D12—121no—
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—21no—
361C2×C4×D3—21no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3C22×D311yescharacteristic
369C2×Dic6—21no—
370C2×Dic6—61no—
371C2×Dic6—61no—
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C2×Dic6C22×D311yescharacteristic
375C3×Q16—62no—
376C3×Q16—121no—
377C3×SD16—62no—
378C3×SD16—62no—
379C2×C3×C8—21no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8C22×D311yescharacteristic
383C2×C3×C8C22×D311yescharacteristic
384C3×C4⋊C4—21no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C4⋊C4C22×D311yescharacteristic
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C42—31no—
393#217—31no—
394#217—61no—
395#216—41no—
396#216—62no—
397#216—62no—
398#215—22no—
399#215—34no—
400#215—62no—
401#215—62no—
402#215—62no—
403#215—122no—
404#215—121no—
405#214—34no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—31no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—31no—
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—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—121no—
421(C2×D3)⋊C4—121no—
422C4⋊Dic3—21no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428Dic3⋊C4—21no—
429Dic3⋊C4—21no—
430Dic3⋊C4—31no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—121no—
437C4×Dic3—61no—
438C4×Dic3—61no—
439C4×Dic3C22×D311yescharacteristic
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8—62no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446Dic12—22no—
447#204—22no—
448#204—62no—
449#204—121no—
450ΓL(1,𝔽25)—62no—
451ΓL(1,𝔽25)—62no—
452ΓL(1,𝔽25)—122no—
453D3×C8—62no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—21no—
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—22no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#13712yescomplemented
467D32—84no—
468C32×C4—41no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4H(5,𝔽2)11yescharacteristic
472C3⋊Dic3—21no—
473C3⋊Dic3—41no—
474C3×Dic3—22no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—91no—
481C22×Q8—31no—
482C22×Q8—91no—
483C22×D4—91no—
484#137—184no—
485C2×Q16—31no—
486C2×Q16—31no—
487C2×Q16—91no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—184no—
495C2×M16—91no—
496C22×C8—91no—
497C4⋊Q8—31no—
498C4⋊Q8—181no—
499#124—91no—
500#123—181no—
501C22⋊Q8—31no—
502C22⋊Q8—91no—
503C22⋊Q8—91no—
504C22⋊Q8—181no—
505C22⋊Q8—181no—
506#121—91no—
507#121—181no—
508#120—181no—
509C4×Q8—91no—
510C4×D4—31no—
511C4×D4—91no—
512C4×D4—181no—
513C2×C22⋊C4—181no—
514#107—91no—
515C4⋊C8—31no—
516#103—31no—
517#103—31no—
518#103—91no—
519#103D3211yescharacteristic, complemented
520#102—91no—
521#102—91no—
522C22⋊C8—31no—
523C22⋊C8—91no—
524#97—91no—
525C23×C3—31no—
526C23×C3—61no—
527C22×D3—21no—
528C22×D3—31no—
529C22×D3—31no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—121no—
534C22×D3—122no—
535C22×D3—122no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—241no—
539C22×D3—241no—
540C22×D3D3×D411yescharacteristic
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—32no—
546C3×Q8—41no—
547C3×Q8—41no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×Q8—122no—
554C3×D4—32no—
555C3×D4—61no—
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—31no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—122no—
572C2×C3×C4—241no—
573C2×C3×C4C23×D311yescharacteristic
574C2×C3×C4C23×D311yescharacteristic
575#67—62no—
576#67—122no—
577#67—122no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—121no—
587C2×Dic3—122no—
588C2×Dic3D3×D411yescharacteristic
589C2×Dic3D3×D411yescharacteristic
590C2×Dic3D3×D411yescharacteristic
591D12—21no—
592D12—62no—
593D12—61no—
594D12—61no—
595D12—61no—
596D12—61no—
597D12—121no—
598D12—121no—
599D12—122no—
600D12—122no—
601D12—241no—
602D12—241no—
603D12—242no—
604D12D3×D412yes—
605C4×D3—21no—
606C4×D3—21no—
607C4×D3—42no—
608C4×D3—61no—
609C4×D3—61no—
610C4×D3—61no—
611C4×D3—61no—
612C4×D3—81no—
613C4×D3—121no—
614C4×D3—121no—
615C4×D3—122no—
616C4×D3—122no—
617C4×D3—122no—
618Dic6—21no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—21no—
623Dic6—42no—
624Dic6—122no—
625Dic6—122no—
626Dic6D3×D412yes—
627C3×C8—21no—
628C3×C8—21no—
629C3×C8—41no—
630C3×C8—61no—
631C3×C8—61no—
632C3⋊C8—21no—
633C3⋊C8—21no—
634C3⋊C8—32no—
635C3⋊C8—32no—
636C3⋊C8—62no—
637C2×C32D4211yescharacteristic
638C2×C32C2×#13711yescharacteristic
639C2×C32#57711yescharacteristic
640C3⋊D3—41no—
641C3⋊D3—81no—
642C3×D3—22no—
643C3×D3—42no—
644C24—181no—
645#41—182no—
646#41—361no—
647C2×Q8—31no—
648C2×Q8—31no—
649C2×Q8—31no—
650C2×Q8—61no—
651C2×Q8—62no—
652C2×Q8—121no—
653C2×Q8—181no—
654C2×Q8—182no—
655C2×Q8—361no—
656C2×Q8C2×D3211yescharacteristic
657C2×D4—31no—
658C2×D4—91no—
659C2×D4—91no—
660C2×D4—181no—
661C2×D4—181no—
662C2×D4—182no—
663C2×D4—181no—
664C2×D4—361no—
665C22×C4—31no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—91no—
669C22×C4—181no—
670C22×C4—181no—
671Q16—62no—
672Q16—121no—
673Q16—182no—
674SD16—62no—
675SD16—62no—
676SD16—94no—
677SD16—182no—
678SD16—182no—
679SD16—361no—
680M16—182no—
681C2×C8—31no—
682C2×C8—31no—
683C2×C8—91no—
684C2×C8—182no—
685C2×C8C2×D3211yescharacteristic
686C4⋊C4—61no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—91no—
690C4⋊C4—91no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C4⋊C4C2×D3211yescharacteristic
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—91no—
698C22⋊C4—91no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C42—31no—
705C42—181no—
706C22×C3—21no—
707C22×C3—32no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—62no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3C2×D3×D411yescharacteristic
714C22×C3C2×D3×D411yescharacteristic
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—22no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—241no—
736C2×D3—241no—
737C2×D3—241no—
738C2×D3—244no—
739C2×D3—244no—
740C2×D3#91812yescomplemented
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—61no—
748C3×C4—61no—
749C3×C4—62no—
750C3×C4—61no—
751C3×C4—81no—
752C3×C4—81no—
753C3×C4—121no—
754C3×C4—121no—
755C3×C4C2×D3×D411yescharacteristic
756C3×C4C2×D3×D411yescharacteristic
757C3×C4#100411yescharacteristic
758C3×C4#100911yescharacteristic
759Dic3—21no—
760Dic3—21no—
761Dic3—22no—
762Dic3—21no—
763Dic3—41no—
764Dic3—41no—
765Dic3—61no—
766Dic3—61no—
767Dic3—121no—
768Dic3—121no—
769Dic3—121no—
770Dic3—241no—
771C32#326611yescharacteristic, complemented, Sylow
772C23—31no—
773C23—61no—
774C23—91no—
775C23—181no—
776C23—362no—
777C23—362no—
778C23—721no—
779Q8—21no—
780Q8—21no—
781Q8—32no—
782Q8—61no—
783Q8—61no—
784Q8—61no—
785Q8—61no—
786Q8—61no—
787Q8—122no—
788Q8—362no—
789D4—32no—
790D4—61no—
791D4—182no—
792D4—181no—
793D4—181no—
794D4—362no—
795D4—362no—
796D4—721no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—31no—
800C2×C4—31no—
801C2×C4—31no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—91no—
808C2×C4—122no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4—241no—
813C2×C4—362no—
814C2×C4—362no—
815C2×C4C22×D3211yescharacteristic
816C8—21no—
817C8—61no—
818C8—61no—
819C8—92no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—62no—
824C2×C3—122no—
825C2×C3#559011yescharacteristic
826C2×C3#560911yescharacteristic
827C2×C3#576211yescharacteristic
828C2×C3C2×#91811yescharacteristic
829C2×C3D3×#13711yescharacteristic
830C2×C3#577811yescharacteristic
831D3—22no—
832D3—42no—
833D3—121no—
834D3—121no—
835D3—241no—
836D3—241no—
837D3—241no—
838D3—481no—
839C22—32no—
840C22—61no—
841C22—61no—
842C22—62no—
843C22—121no—
844C22—121no—
845C22—181no—
846C22—181no—
847C22—181no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—724no—
852C22D32×D411yescharacteristic
853C4—41no—
854C4—41no—
855C4—61no—
856C4—61no—
857C4—61no—
858C4—62no—
859C4—121no—
860C4—121no—
861C4—181no—
862C4—361no—
863C4#6430711yescharacteristic
864C4D32×D411yescharacteristic
865C3—21no—
866C3#8020411yescharacteristic, complemented
867C3#8044411yescharacteristic, complemented
868C2—62no—
869C2—122no—
870C2—361no—
871C2—721no—
872C2#1059427511yescharacteristic
873C2#1059475111yescharacteristic
874C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594629C2
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. #10595403C2semidirect
2. C2×D3×#215C2semidirect
3. C2×#63811C2semidirect
5. #10592511C2semidirect
6. C3×#4818C2semidirect
7. C3×#4809C2semidirect
8. #10591656C2semidirect
9. #10591608C2semidirect
10. #10590942C2semidirect
11. #10590907C2semidirect
12. #10590801C2semidirect
13. #10590606C2semidirect
14. #10590518C2semidirect
15. #10590478C2semidirect
20. C2×#3797C22semidirect
22. #64155C22semidirect
24. C2×#3743C22semidirect
26. C3×#944C22semidirect
27. C2×C3×#216C22semidirect
29. C2×C3×Dic12C22semidirect
44. Dic3×Dic6C22semidirect
46. C2×#3718C22semidirect
52. C32×#103C22semidirect
54. #63634C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#810C22semidirect
59. #63566C22semidirect
61. #63557C22semidirect
62. #63554C22semidirect
83. #4818D3semidirect
89. #4809D3semidirect
154. #3715D4semidirect
180. #944C2×D3semidirect
183. C2×#216C2×D3semidirect
203. C2×Dic12C2×D3semidirect
233. C3×#103C2×D3semidirect
234. C3×#103C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
248. #810C2×D3semidirect
249. #810C2×D3semidirect
466. C2×C3×D3#137semidirect
519. #103D32semidirect
740. C2×D3#918semidirect
771. C32#3266semidirect
866. C3#80204semidirect
867. C3#80444semidirect

Maximal subgroups

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

subgroupindex
#105954032
C2×D3×#2152
C2×#638112
#105946292
#105925112
C3×#48182
C3×#48092
#105916562
#105916082
#105909422
#105909072
#105908012
#105906062
#105905182
#105904782
#804443
#802043