Finite Group Databasebeta

← #11872849

Subgroups — #11872849

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5698C211yesmaximal, characteristic, complemented
2#10593994C211yesmaximal, characteristic
3#10592765C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5#10590596C211yesmaximal, characteristic
6#10590596C211yesmaximal, characteristic
7#10590458C211yesmaximal, characteristic, complemented
8#10590457C211yesmaximal, characteristic, complemented
9#10590454C211yesmaximal, characteristic, complemented
10#10590453C211yesmaximal, characteristic, complemented
11#10590448C211yesmaximal, characteristic, complemented
12#10590447C211yesmaximal, characteristic, complemented
13#10590379C211yesmaximal, characteristic, complemented
14#10590363C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#83447—31nomaximal
17#81147—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C32×#125C2211yescharacteristic, complemented
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C3×#898—21no—
22C3×#898—21no—
23C3×#897C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#890—21no—
26C3×#890—21no—
27C3×#887C2211yescharacteristic, complemented
28C3×#887C2211yescharacteristic, complemented
29C3×C4×D12C2211yescharacteristic
30C3×#872C2211yescharacteristic
31C3×#869C2211yescharacteristic, complemented
32#63921—21no—
33D3×(C2×D3)⋊C4—21no—
34#63904—21no—
35#63894C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63881—21no—
38#63841C2211yescharacteristic
39C2×#3717C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63636C2211yescharacteristic
44#63636C2211yescharacteristic
45#63635C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#541—31no—
62#5698D311yescharacteristic, complemented
63#5545—31no—
64#5521—31no—
65C3×#478—31no—
66#5083—31no—
67#5083—31no—
68#5066—31no—
69#5066—31no—
70#5066—61no—
71#5066D311yescharacteristic, complemented
72#5046—31no—
73#5046—31no—
74#5045—31no—
75#5045—31no—
76#5026—31no—
77#5026—31no—
78C4×#215—31no—
79C4×#215—31no—
80#5019—31no—
81#5000—31no—
82#4889—31no—
83#4888—31no—
84#4868—31no—
85#4852—31no—
86#4841—31no—
87#4840—31no—
88#4776—31no—
89#4776—31no—
90#4758—31no—
91#4757—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#626—21no—
101C2×#624—21no—
102C2×D3×Dic3—21no—
103D3×D12—22no—
104D3×D12—22no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C42C2311yescharacteristic
110#3752—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4D411yescharacteristic
118C3×(C2×D3)⋊C4D411yescharacteristic
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137#3717—22no—
138#3717—22no—
139#3715—22no—
140#3715—22no—
141#3123—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C3×C4⋊Q8—31no—
145C3×#126—61no—
146C3×#126—61no—
147C3×#125—21no—
148C3×#125—61no—
149C3×#125—61no—
150C3×#125C2×D311yescharacteristic, complemented
151C3×#125C2×D311yescharacteristic, complemented
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—31no—
157C3×#117—31no—
158C2×#215—31no—
159C2×#215—31no—
160C2×#215—31no—
161C2×#215—31no—
162D4×Dic3—31no—
163C2×#214—31no—
164C2×#214—31no—
165C4×#67—61no—
166C2×(C2×D3)⋊C4—61no—
167#926—31no—
168C2×#204—31no—
169C2×#204—31no—
170#898—21no—
171#898—21no—
172#897C2×D311yescharacteristic
173#897C2×D311yescharacteristic
174#893—31no—
175#893—61no—
176#893—61no—
177#892—31no—
178#890—21no—
179#890—21no—
180#887C2×D311yescharacteristic, complemented
181#887C2×D311yescharacteristic, complemented
182#67⋊C4—61no—
183D3×C22⋊C4—61no—
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—61no—
191C4×D12C2×D311yescharacteristic
192#872C2×D311yescharacteristic
193#869C2×D311yescharacteristic, complemented
194C3×#107—31no—
195C3×#106—31no—
196C3×C4⋊C8—31no—
197C3×#102—31no—
198C3×#102—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#830—31no—
204#830—31no—
205(C2×D3)⋊C8—31no—
206(C2×D3)⋊C8—31no—
207#816—31no—
208#816—31no—
209#815—31no—
210C8×Dic3—31no—
211#810—31no—
212#810—31no—
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—61no—
218#809—61no—
219#809C2×D311yescharacteristic
220#809C2×D311yescharacteristic
221#808—31no—
222#808—31no—
223#808—61no—
224#808C2×D311yescharacteristic, complemented
225#807—31no—
226#807—31no—
227#807—61no—
228#807C2×D311yescharacteristic, complemented
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
233#803—31no—
234C4×C3⋊C8—31no—
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C2×D32—24no—
239C2×D32—81no—
240C2×D32—81no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)#4112yes—
249C4×C3⋊D3—81no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12#4112yes—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—81no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265#626—24no—
266#624—81no—
267D3×Dic3—81no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—31no—
273#518—91no—
274#485—91no—
275#485—91no—
276#478—31no—
277#478—91no—
278#461—91no—
279#461—91no—
280#450—91no—
281#450—91no—
282#440—91no—
283#440—91no—
284C4×SD16—91no—
285C4×SD16—91no—
286#433—91no—
287C23×D3—61no—
288C23×D3—61no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×D4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—61no—
294C2×#67—61no—
295C22×Dic3—61no—
296D3×D4—62no—
297D3×D4—62no—
298C2×D12—31no—
299C2×D12—31no—
300C2×D12—61no—
301C2×D12—62no—
302C2×D12—61no—
303C2×D12—62no—
304C2×D12C22×D311yescharacteristic
305C2×C4×D3—21no—
306C2×C4×D3—61no—
307C2×C4×D3—61no—
308C2×C4×D3—61no—
309C2×C4×D3—61no—
310C2×C4×D3—61no—
311C2×C4×D3—121no—
312C2×C4×D3C22×D311yescharacteristic
313C2×Dic6C22×D311yescharacteristic
314C2×Dic6C22×D311yescharacteristic
315C2×C3×C8—31no—
316C2×C3×C8—31no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—41no—
327C3×C4⋊C4—41no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C22⋊C4—31no—
339C3×C22⋊C4—31no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C42—21no—
344C3×C42—31no—
345C3×C42—61no—
346C3×C42—61no—
347C3×C42C22×D311yescharacteristic
348C3×C42C22×D311yescharacteristic
349#217—61no—
350#217—61no—
351#215—62no—
352#215—62no—
353#215—62no—
354#215—62no—
355#214—62no—
356#214—62no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—121no—
367(C2×D3)⋊C4#6711yescharacteristic
368(C2×D3)⋊C4#6711yescharacteristic
369C4⋊Dic3—21no—
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4#6711yescharacteristic
380Dic3⋊C4#6711yescharacteristic
381C4×Dic3—21no—
382C4×Dic3—21no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3C22×D311yescharacteristic
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—61no—
391C2×C3⋊C8—61no—
392C2×C3⋊C8C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394#204—62no—
395#204—62no—
396C22×C32C22×D411yescharacteristic
397C2×C3⋊D3—22no—
398C2×C3⋊D3—41no—
399C2×C3⋊D3—41no—
400C2×C3×D3—22no—
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406D32—84no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3⋊Dic3—41no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C22×D4—91no—
421C2×SD16—91no—
422C2×SD16—91no—
423C2×SD16—91no—
424C2×SD16—91no—
425C4⋊Q8—31no—
426#126—61no—
427#126—61no—
428#125—61no—
429#125—61no—
430#125D3211yescharacteristic, complemented
431C22⋊Q8—31no—
432C22⋊Q8—31no—
433C4×Q8—31no—
434C4×Q8—31no—
435C4×D4—31no—
436C4×D4—91no—
437C4×D4—91no—
438C4×D4—91no—
439C4×D4—181no—
440C4×D4—181no—
441#117—31no—
442#117—91no—
443C2×C22⋊C4—181no—
444C2×C22⋊C4—181no—
445#107—31no—
446#107—91no—
447#106—31no—
448#106—91no—
449C4⋊C8—31no—
450C4⋊C8—91no—
451#103—91no—
452#103—91no—
453#103—91no—
454#103—91no—
455#102—31no—
456#102—31no—
457#102—91no—
458#102—91no—
459C22⋊C8—91no—
460C22⋊C8—91no—
461#97—91no—
462C4×C8—91no—
463C23×C3—31no—
464C23×C3—61no—
465C22×D3—21no—
466C22×D3—64no—
467C22×D3—64no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—121no—
471C22×D3—241no—
472C22×D3—241no—
473C22×D3—241no—
474C22×D3—241no—
475C22×D3C2×#6711yescharacteristic
476C3×Q8—61no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×D4—32no—
481C3×D4—61no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—241no—
500C2×C3×C4D3×D411yescharacteristic
501C2×C3×C4D3×D411yescharacteristic
502C2×C3×C4C2×#6711yescharacteristic
503C2×C3×C4C2×#6711yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506#67—64no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—121no—
513C2×Dic3—241no—
514C2×Dic3C2×#6711yescharacteristic
515C2×Dic3C2×#6711yescharacteristic
516C2×Dic3C2×#6711yescharacteristic
517D12—21no—
518D12—32no—
519D12—32no—
520D12—62no—
521D12—64no—
522D12—61no—
523D12—61no—
524D12—121no—
525D12#23912yes—
526C4×D3—21no—
527C4×D3—21no—
528C4×D3—81no—
529C4×D3—241no—
530C4×D3—241no—
531C4×D3—241no—
532C4×D3—241no—
533C4×D3—241no—
534C4×D3—242no—
535Dic6—21no—
536Dic6—21no—
537Dic6—21no—
538Dic6—21no—
539C3×C8—61no—
540C3×C8—61no—
541C3⋊C8—21no—
542C3⋊C8—21no—
543C3⋊C8—61no—
544C3⋊C8—61no—
545C3⋊C8—61no—
546C3⋊C8—61no—
547C3⋊C8—121no—
548C3⋊C8—121no—
549C2×C32#52511yescharacteristic
550C2×C32#57711yescharacteristic
551C2×C32#57711yescharacteristic
552C3⋊D3—42no—
553C3×D3—41no—
554C3×D3—42no—
555C24—181no—
556C2×Q8—31no—
557C2×Q8—31no—
558C2×D4—31no—
559C2×D4—91no—
560C2×D4—181no—
561C2×D4—182no—
562C2×D4—182no—
563C22×C4—31no—
564C22×C4—61no—
565C22×C4—181no—
566C22×C4—181no—
567C22×C4—181no—
568SD16—182no—
569SD16—182no—
570SD16—182no—
571SD16—182no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8—91no—
575C2×C8—91no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—91no—
588C4⋊C4C2×D3211yescharacteristic
589C4⋊C4C2×D3211yescharacteristic
590C22⋊C4—31no—
591C22⋊C4—31no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C22⋊C4—181no—
599C42—31no—
600C42—61no—
601C42—61no—
602C42—181no—
603C42C2×D3211yescharacteristic
604C22×C3—21no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3—62no—
608C22×C3—61no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3C2×D3×D411yescharacteristic
612C22×C3C22×#6711yescharacteristic
613C2×D3—21no—
614C2×D3—21no—
615C2×D3—21no—
616C2×D3—22no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—122no—
622C2×D3—121no—
623C2×D3—121no—
624C2×D3—121no—
625C2×D3—121no—
626C2×D3—241no—
627C2×D3—241no—
628C2×D3—244no—
629C2×D3—244no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—81no—
646C3×C4—81no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4C2×#23911yescharacteristic
651C3×C4D3×#4111yescharacteristic
652C3×C4D3×#4111yescharacteristic
653C3×C4D3×#4111yescharacteristic
654Dic3—21no—
655Dic3—21no—
656Dic3—21no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—121no—
661Dic3—121no—
662Dic3—241no—
663C32#312311yescharacteristic, complemented, Sylow
664C23—31no—
665C23—61no—
666C23—184no—
667C23—181no—
668C23—721no—
669C23—721no—
670Q8—61no—
671Q8—61no—
672Q8—61no—
673Q8—61no—
674D4—32no—
675D4—61no—
676D4—92no—
677D4—184no—
678D4—181no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—181no—
690C2×C4—241no—
691C2×C4—721no—
692C2×C4—721no—
693C2×C4—721no—
694C2×C4D3×#6711yescharacteristic
695C2×C4D3×#6711yescharacteristic
696C2×C4C22×D3211yescharacteristic
697C8—61no—
698C8—61no—
699C8—181no—
700C8—181no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—122no—
705C2×C3—121no—
706C2×C3#562711yescharacteristic
707C2×C3#577011yescharacteristic
708C2×C3#577511yescharacteristic
709C2×C3#582811yescharacteristic
710C2×C3#583711yescharacteristic
711C2×C3#583711yescharacteristic
712D3—41no—
713D3—42no—
714D3—122no—
715D3—122no—
716D3—242no—
717C22—61no—
718C22—62no—
719C22—61no—
720C22—61no—
721C22—121no—
722C22—121no—
723C22—182no—
724C22—361no—
725C22—361no—
726C22—724no—
727C22C2×D3×#6711yescharacteristic
728C4—21no—
729C4—21no—
730C4—41no—
731C4—41no—
732C4—61no—
733C4—61no—
734C4—61no—
735C4—121no—
736C4—121no—
737C4—121no—
738C4—361no—
739C4D3×#23911yescharacteristic
740C4#6431911yescharacteristic
741C3—21no—
742C3#8114711yescharacteristic, complemented
743C3#8344711yescharacteristic, complemented
744C2—121no—
745C2—122no—
746C2—362no—
747C2#1059542411yescharacteristic
748C2#1059545511yescharacteristic
749C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenter#125D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×#5698C2semidirect
3. #10592765C2semidirect
4. C3×#5066C2semidirect
7. #10590458C2semidirect
8. #10590457C2semidirect
9. #10590454C2semidirect
10. #10590453C2semidirect
11. #10590448C2semidirect
12. #10590447C2semidirect
13. #10590379C2semidirect
14. #10590363C2semidirect
15. #10590253C2semidirect
19. C32×#125C22semidirect
27. C3×#887C22semidirect
28. C3×#887C22semidirect
31. C3×#869C22semidirect
45. #63635C22semidirect
46. #63634C22semidirect
47. C4⋊(C3⋊(C3⋊C8))C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×C4⋊(C3⋊C8)C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
55. #63565C22semidirect
56. #63565C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5698D3semidirect
71. #5066D3semidirect
150. C3×#125C2×D3semidirect
151. C3×#125C2×D3semidirect
180. #887C2×D3semidirect
181. #887C2×D3semidirect
193. #869C2×D3semidirect
224. #808C2×D3semidirect
228. #807C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
430. #125D32semidirect
663. C32#3123semidirect
742. C3#81147semidirect
743. C3#83447semidirect

Maximal subgroups

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

subgroupindex
C3×#56982
#105939942
#105927652
C3×#50662
#105905962
#105904582
#105904572
#105904542
#105904532
#105904482
#105904472
#105903792
#105903632
#105902532
#834473
#811473