Finite Group Databasebeta

← #11868953

Subgroups — #11868953

Order 1152.

847 conjugacy classes of subgroups.

The subgroup lattice has 739 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5689C211yesmaximal, characteristic, complemented
2#10593994C211yesmaximal, characteristic
3#10592765C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5#10590592C211yesmaximal, characteristic
6D3×#809C211yesmaximal, characteristic
7#10590580C211yesmaximal, characteristic, complemented
8#10590572C211yesmaximal, characteristic, complemented
9#10590470C211yesmaximal, characteristic, complemented
10#10590467C211yesmaximal, characteristic, complemented
11#10590465C211yesmaximal, characteristic, complemented
12#10590464C211yesmaximal, characteristic, complemented
13#10590324C211yesmaximal, characteristic, complemented
14#10590300C211yesmaximal, characteristic, complemented
15#10590269C211yesmaximal, characteristic, complemented
16#83474—31nomaximal
17#81168—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C32×#125C2211yescharacteristic, complemented
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C3×#897—21no—
22C3×#896—21no—
23C3×#892C2211yescharacteristic
24C3×D3×C4⋊C4C2211yescharacteristic
25C3×#890C2211yescharacteristic, complemented
26C3×#889—21no—
27C3×#888—21no—
28C3×#888C2211yescharacteristic, 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×#3711C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41#63636C2211yescharacteristic
42#63636C2211yescharacteristic
43#63635C2211yescharacteristic, complemented
44#63634C2211yescharacteristic, complemented
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#808C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63576C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61C3×#544—31no—
62#5689D311yescharacteristic, complemented
63#5545—31no—
64#5521—31no—
65C3×#478—31no—
66#5087—31no—
67#5087—31no—
68#5084—31no—
69#5084—31no—
70#5066—31no—
71#5066—31no—
72#5066—31no—
73#5066—31no—
74#5066—61no—
75#5066D311yescharacteristic, complemented
76#5007—31no—
77#5001—31no—
78#4999—31no—
79#4998—31no—
80C2×#809—31no—
81#4964—31no—
82#4890—31no—
83#4881—31no—
84#4871—31no—
85#4860—31no—
86#4842—31no—
87#4839—31no—
88#4770—31no—
89D3×#102—31no—
90#4763—31no—
91#4761—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×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6—21no—
100C2×C3×Dic6—21no—
101C2×#626—21no—
102C2×#624—21no—
103C2×D3×Dic3—21no—
104D3×D12—22no—
105D3×D12Q814yescomplemented
106C32×C4⋊C4—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C42C2311yescharacteristic
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
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⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
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#3711—22no—
138D3×C3⋊C8—22no—
139#3081—91noSylow
140C2×D3×D4—31no—
141C22×D12—31no—
142C3×C4⋊Q8—31no—
143C3×C4⋊Q8—31no—
144C3×C4⋊Q8—61no—
145C3×#125—21no—
146C3×#125—31no—
147C3×#125—61no—
148C3×#125C2×D311yescharacteristic, complemented
149C3×#125C2×D311yescharacteristic, complemented
150C3×C22⋊Q8—61no—
151C3×C22⋊Q8—61no—
152C3×C4×D4—31no—
153C3×#117—31no—
154C3×#117—31no—
155C2×C3×C4⋊C4—31no—
156D4×Dic3—31no—
157C4×#67—61no—
158C2×(C2×D3)⋊C4—61no—
159#926—31no—
160C2×#208—31no—
161C22×C3⋊C8—31no—
162C2×ΓL(1,𝔽25)—31no—
163C2×D3×C8—31no—
164#897—21no—
165#896—21no—
166#893—31no—
167#893—61no—
168#893—61no—
169#892—31no—
170#892C2×D311yescharacteristic
171D3×C4⋊C4C2×D311yescharacteristic
172#890C2×D311yescharacteristic, complemented
173#889—21no—
174#888—21no—
175#888C2×D311yescharacteristic, complemented
176#67⋊C4—61no—
177D3×C22⋊C4—61no—
178D3×C22⋊C4—61no—
179D3×C22⋊C4—61no—
180C4×D12—31no—
181C4×D12—31no—
182C4×D12—31no—
183C4×D12—31no—
184C4×D12—61no—
185C4×D12C2×D311yescharacteristic
186#872C2×D311yescharacteristic
187#869C2×D311yescharacteristic, complemented
188C3×#107—31no—
189C3×#106—31no—
190C3×C4⋊C8—31no—
191C3×#102—31no—
192C3×#102—31no—
193#832—31no—
194#832—31no—
195#821—31no—
196#821—31no—
197#817—31no—
198#817—31no—
199Dic3⋊C8—31no—
200Dic3⋊C8—31no—
201#809—31no—
202#809—31no—
203#809—31no—
204#809—31no—
205#809—31no—
206#809—31no—
207#809—31no—
208#809—31no—
209#809—61no—
210#809—61no—
211#809C2×D311yescharacteristic
212#809C2×D311yescharacteristic
213#808—31no—
214#808—31no—
215#808—31no—
216#808—31no—
217#808—61no—
218#808C2×D311yescharacteristic, complemented
219#807—31no—
220#807—31no—
221#807—31no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—61no—
226#807C2×D311yescharacteristic, complemented
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
233C22×C3⋊D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3C2×D411yescharacteristic
236C2×D32—24no—
237C2×D32—81no—
238C2×D32—81no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)C2×Q812yes—
247C4×C3⋊D3—81no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—21no—
255C3×D12C2×Q812yes—
256C3×C4×D3—81no—
257C3×C4×D3—81no—
258C3×C4×D3C2×Q812yes—
259C3×C4×D3#4112yes—
260C3×Dic6—81no—
261C3×Dic6—81no—
262#626—24no—
263#624—81no—
264D3×Dic3—81no—
265C3⋊(C3⋊C8)—21no—
266C3⋊(C3⋊C8)—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#544—31no—
270#518—91no—
271#478—31no—
272#478—91no—
273#478—91no—
274#478—91no—
275#476—91no—
276#476—91no—
277#474—91no—
278#474—91no—
279#428—91no—
280#427—91no—
281#424—91no—
282#418—91no—
283C2×#102—91no—
284C23×D3—61no—
285C23×D3—61no—
286C2×C3×Q8—61no—
287C2×C3×Q8—61no—
288C2×C3×D4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C2×#67—61no—
293C22×Dic3—61no—
294D3×D4—34no—
295D3×D4—62no—
296C2×D12—31no—
297C2×D12—31no—
298C2×D12—34no—
299C2×D12—61no—
300C2×D12—62no—
301C2×D12—61no—
302C2×D12C22×D311yescharacteristic
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—61no—
306C2×C4×D3—61no—
307C2×C4×D3—61no—
308C2×C4×D3—61no—
309C2×C4×D3—61no—
310C2×C4×D3—121no—
311C2×C4×D3C22×D311yescharacteristic
312C2×Dic6—21no—
313C2×Dic6—21no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—41no—
328C3×C4⋊C4—41no—
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×C42—21no—
343C3×C42—31no—
344C3×C42—61no—
345C3×C42C22×D311yescharacteristic
346C3×C42C22×D311yescharacteristic
347#217—61no—
348#217—61no—
349(C2×D3)⋊C4—21no—
350(C2×D3)⋊C4—21no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—121no—
358(C2×D3)⋊C4#6711yescharacteristic
359(C2×D3)⋊C4#6711yescharacteristic
360C4⋊Dic3—21no—
361C4⋊Dic3—21no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—61no—
365C4⋊Dic3C22×D311yescharacteristic
366C4⋊Dic3C22×D311yescharacteristic
367C4⋊Dic3C22×D311yescharacteristic
368Dic3⋊C4—21no—
369Dic3⋊C4—21no—
370Dic3⋊C4—21no—
371Dic3⋊C4#6711yescharacteristic
372Dic3⋊C4#6711yescharacteristic
373C4×Dic3—21no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3C22×D311yescharacteristic
377#208—62no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—31no—
381C2×C3⋊C8—31no—
382C2×C3⋊C8—61no—
383C2×C3⋊C8—61no—
384C2×C3⋊C8—62no—
385C2×C3⋊C8C22×D311yescharacteristic
386C2×C3⋊C8C22×D311yescharacteristic
387ΓL(1,𝔽25)—62no—
388D3×C8—62no—
389C22×C32C22×D411yescharacteristic
390C2×C3⋊D3—22no—
391C2×C3⋊D3—41no—
392C2×C3⋊D3—41no—
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C2×C3×D3—22no—
396C2×C3×D3—41no—
397C2×C3×D3—41no—
398C2×C3×D3C22⋊Q812yes—
399D32—84no—
400C32×C4—21no—
401C32×C4—21no—
402C32×C4—41no—
403C32×C4—41no—
404C32×C4C22×Q811yescharacteristic
405C32×C4C2×#4111yescharacteristic
406C3⋊Dic3—41no—
407C3×Dic3—21no—
408C3×Dic3—21no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C3×Dic3C22⋊Q812yes—
413C22×D4—91no—
414C2×M16—91no—
415C22×C8—91no—
416C4⋊Q8—31no—
417C4⋊Q8—31no—
418C4⋊Q8—61no—
419#125—31no—
420#125—61no—
421#125D3211yescharacteristic, complemented
422C22⋊Q8—61no—
423C22⋊Q8—61no—
424C4×D4—31no—
425C4×D4—91no—
426C4×D4—91no—
427C4×D4—91no—
428C4×D4—181no—
429C4×D4—181no—
430#117—31no—
431#117—31no—
432#117—91no—
433C2×C4⋊C4—31no—
434C2×C22⋊C4—181no—
435C2×C22⋊C4—181no—
436#107—31no—
437#107—91no—
438#107—91no—
439#107—91no—
440#106—31no—
441#106—91no—
442#106—91no—
443#106—91no—
444C4⋊C8—31no—
445C4⋊C8—91no—
446C4⋊C8—91no—
447C4⋊C8—91no—
448#102—31no—
449#102—31no—
450#102—91no—
451#102—91no—
452#102—91no—
453#102—91no—
454#102—91no—
455#102—91no—
456C23×C3—31no—
457C23×C3—61no—
458C22×D3—21no—
459C22×D3—64no—
460C22×D3—61no—
461C22×D3—61no—
462C22×D3—64no—
463C22×D3—121no—
464C22×D3—241no—
465C22×D3—241no—
466C22×D3—241no—
467C22×D3—241no—
468C22×D3C2×#6711yescharacteristic
469C3×Q8—241no—
470C3×Q8—241no—
471C3×D4—32no—
472C3×D4—61no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—31no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—241no—
491C2×C3×C4—241no—
492C2×C3×C4D3×D411yescharacteristic
493C2×C3×C4D3×D411yescharacteristic
494C2×C3×C4C2×#6711yescharacteristic
495C2×C3×C4C2×#6711yescharacteristic
496C2×C3×C4C23×D311yescharacteristic
497C2×C3×C4C23×D311yescharacteristic
498#67—64no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—121no—
505C2×Dic3—241no—
506C2×Dic3C2×#6711yescharacteristic
507C2×Dic3C2×#6711yescharacteristic
508C2×Dic3C2×#6711yescharacteristic
509D12—21no—
510D12—32no—
511D12—32no—
512D12—62no—
513D12—64no—
514D12—61no—
515D12—61no—
516D12—121no—
517D12D3×Q812yes—
518C4×D3—81no—
519C4×D3—81no—
520C4×D3—241no—
521C4×D3—241no—
522C4×D3—241no—
523C4×D3—241no—
524C4×D3—241no—
525C4×D3—242no—
526C4×D3D3×Q812yes—
527C4×D3#23912yes—
528Dic6—81no—
529Dic6—81no—
530C3×C8—61no—
531C3×C8—61no—
532C3⋊C8—21no—
533C3⋊C8—21no—
534C3⋊C8—61no—
535C3⋊C8—61no—
536C3⋊C8—61no—
537C3⋊C8—61no—
538C3⋊C8—121no—
539C3⋊C8—121no—
540C2×C32C2×C22⋊Q811yescharacteristic
541C2×C32#57611yescharacteristic
542C2×C32#57711yescharacteristic
543C3⋊D3—42no—
544C3×D3—22no—
545C3×D3—42no—
546C24—181no—
547C2×Q8—61no—
548C2×Q8—61no—
549C2×D4—31no—
550C2×D4—94no—
551C2×D4—91no—
552C2×D4—182no—
553C2×D4—181no—
554C22×C4—31no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—181no—
558C22×C4—181no—
559C22×C4—181no—
560M16—182no—
561C2×C8—31no—
562C2×C8—31no—
563C2×C8—91no—
564C2×C8—91no—
565C2×C8—182no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—91no—
579C4⋊C4C2×D3211yescharacteristic
580C4⋊C4C2×D3211yescharacteristic
581C22⋊C4—31no—
582C22⋊C4—31no—
583C22⋊C4—61no—
584C22⋊C4—61no—
585C22⋊C4—181no—
586C22⋊C4—181no—
587C22⋊C4—181no—
588C22⋊C4—181no—
589C42—31no—
590C42—61no—
591C42—181no—
592C42C2×D3211yescharacteristic
593C22×C3—21no—
594C22×C3—32no—
595C22×C3—61no—
596C22×C3—61no—
597C22×C3—62no—
598C22×C3—121no—
599C22×C3—121no—
600C22×C3C2×D3×D411yescharacteristic
601C22×C3C22×#6711yescharacteristic
602C2×D3—21no—
603C2×D3—21no—
604C2×D3—22no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—62no—
608C2×D3—62no—
609C2×D3—122no—
610C2×D3—121no—
611C2×D3—121no—
612C2×D3—121no—
613C2×D3—121no—
614C2×D3—241no—
615C2×D3—241no—
616C2×D3—244no—
617C2×D3—244no—
618C2×D3#94612yes—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—32no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—61no—
633C3×C4—61no—
634C3×C4—81no—
635C3×C4—81no—
636C3×C4—121no—
637C3×C4—121no—
638C3×C4—121no—
639C3×C4C2×D3×Q811yescharacteristic
640C3×C4C2×D3×Q811yescharacteristic
641C3×C4C2×#23911yescharacteristic
642C3×C4D3×#4111yescharacteristic
643Dic3—21no—
644Dic3—21no—
645Dic3—41no—
646Dic3—41no—
647Dic3—41no—
648Dic3—121no—
649Dic3—121no—
650Dic3—241no—
651Dic3#94612yes—
652C32#308111yescharacteristic, complemented, Sylow
653C23—31no—
654C23—61no—
655C23—184no—
656C23—181no—
657C23—721no—
658C23—721no—
659Q8—241no—
660Q8—241no—
661D4—32no—
662D4—61no—
663D4—92no—
664D4—184no—
665D4—181no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—31no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—31no—
672C2×C4—31no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—181no—
677C2×C4—241no—
678C2×C4—241no—
679C2×C4—721no—
680C2×C4—721no—
681C2×C4—721no—
682C2×C4D3×#6711yescharacteristic
683C2×C4D3×#6711yescharacteristic
684C2×C4C22×D3211yescharacteristic
685C8—61no—
686C8—61no—
687C8—181no—
688C8—181no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—62no—
693C2×C3—122no—
694C2×C3D3×C22⋊Q811yescharacteristic
695C2×C3#577011yescharacteristic
696C2×C3#577411yescharacteristic
697C2×C3C2×#94611yescharacteristic
698C2×C3#583511yescharacteristic
699C2×C3#583711yescharacteristic
700D3—22no—
701D3—42no—
702D3—122no—
703D3—122no—
704D3—242no—
705C22—32no—
706C22—61no—
707C22—61no—
708C22—62no—
709C22—121no—
710C22—121no—
711C22—182no—
712C22—361no—
713C22—361no—
714C22—724no—
715C22C2×D3×#6711yescharacteristic
716C4—21no—
717C4—21no—
718C4—32no—
719C4—41no—
720C4—41no—
721C4—61no—
722C4—61no—
723C4—121no—
724C4—121no—
725C4—121no—
726C4—361no—
727C4D32×Q811yescharacteristic
728C4D3×#23911yescharacteristic
729C3—21no—
730C3#8116811yescharacteristic, complemented
731C3#8347411yescharacteristic, complemented
732C2—62no—
733C2—122no—
734C2—362no—
735C2D3×#94611yescharacteristic
736C2#1059545411yescharacteristic
737C2#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#3081
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×#5689C2semidirect
3. #10592765C2semidirect
4. C3×#5066C2semidirect
7. #10590580C2semidirect
8. #10590572C2semidirect
9. #10590470C2semidirect
10. #10590467C2semidirect
11. #10590465C2semidirect
12. #10590464C2semidirect
13. #10590324C2semidirect
14. #10590300C2semidirect
15. #10590269C2semidirect
19. C32×#125C22semidirect
25. C3×#890C22semidirect
28. C3×#888C22semidirect
31. C3×#869C22semidirect
43. #63635C22semidirect
44. #63634C22semidirect
45. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#808C22semidirect
49. C3×#807C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63576C22semidirect
52. #63576C22semidirect
53. #63573C22semidirect
54. #63573C22semidirect
55. Dic3⋊(C3⋊C8)C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
62. #5689D3semidirect
75. #5066D3semidirect
105. D3×D12Q8semidirect
148. C3×#125C2×D3semidirect
149. C3×#125C2×D3semidirect
172. #890C2×D3semidirect
175. #888C2×D3semidirect
187. #869C2×D3semidirect
218. #808C2×D3semidirect
226. #807C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
421. #125D32semidirect
652. C32#3081semidirect
730. C3#81168semidirect
731. C3#83474semidirect

Maximal subgroups

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

subgroupindex
C3×#56892
#105939942
#105927652
C3×#50662
#105905922
D3×#8092
#105905802
#105905722
#105904702
#105904672
#105904652
#105904642
#105903242
#105903002
#105902692
#834743
#811683