Finite Group Databasebeta

← #11872844

Subgroups — #11872844

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5731C211yesmaximal, characteristic, complemented
2#10593994C211yesmaximal, characteristic
3#10592782C211yesmaximal, characteristic, complemented
4C3×#5083C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic
6#10591651C211yesmaximal, characteristic
7#10591566C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#10591559C211yesmaximal, characteristic, complemented
10#10591558C211yesmaximal, characteristic, complemented
11#10591540C211yesmaximal, characteristic, complemented
12#10591536C211yesmaximal, characteristic, complemented
13#10590308C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#83447—31nomaximal
17#80413—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic, complemented
20C2×#3755C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×#898—21no—
30C3×#898—21no—
31C3×#889—21no—
32C3×#889—21no—
33C3×C4×D12C2211yescharacteristic
34C3×#872C2211yescharacteristic
35C3×#870C2211yescharacteristic, complemented
36#63921—21no—
37D3×(C2×D3)⋊C4—21no—
38#63904—21no—
39#63894C2211yescharacteristic
40Dic3×D12C2211yescharacteristic
41#63881—21no—
42#63841C2211yescharacteristic
43#63662C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
49#63576C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#541—31no—
62#5731D311yescharacteristic, complemented
63#5545—31no—
64#5521—31no—
65C3×#461—31no—
66#5169—31no—
67#5169—31no—
68#5164—31no—
69Dic3×SD16—31no—
70#5083—31no—
71#5083—31no—
72#5083—61no—
73#5083D311yescharacteristic, complemented
74#5066—31no—
75#5066—31no—
76#5046—31no—
77#5046—31no—
78#5045—31no—
79#5045—31no—
80#5026—31no—
81#5026—31no—
82C4×#215—31no—
83C4×#215—31no—
84#5009—31no—
85#5000—31no—
86#4847—31no—
87#4840—31no—
88#4817—31no—
89#4815—31no—
90#4814—31no—
91#4788—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
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×C42C2311yescharacteristic
108#3755—22no—
109#3755—22no—
110#3752—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#215—22no—
115C3×#215—22no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3123—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C3×C4⋊Q8—21no—
147C3×C4⋊Q8C2×D311yescharacteristic, complemented
148C3×C4⋊Q8C2×D311yescharacteristic, complemented
149C3×#126—61no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#125—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160#946C2×D311yescharacteristic
161#946C2×D311yescharacteristic
162Q8×Dic3C2×D311yescharacteristic, complemented
163Q8×Dic3C2×D311yescharacteristic, complemented
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—31no—
167C2×#215—31no—
168C2×#215—61no—
169C2×#215—61no—
170C2×#215C2×D311yescharacteristic
171C2×#215C2×D311yescharacteristic
172D4×Dic3—31no—
173C4×#67—61no—
174C2×(C2×D3)⋊C4—61no—
175#926—31no—
176#898—21no—
177#898—21no—
178#893—31no—
179#893—61no—
180#893—61no—
181#892—31no—
182#889—21no—
183#889—21no—
184#67⋊C4—61no—
185D3×C22⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12C2×D311yescharacteristic
194#872C2×D311yescharacteristic
195#870C2×D311yescharacteristic, complemented
196C3×C4⋊C8—31no—
197C3×#103—31no—
198C3×#103—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—61no—
204#835—61no—
205#835C2×D311yescharacteristic, complemented
206#835C2×D311yescharacteristic, complemented
207#832—31no—
208#832—31no—
209#830—31no—
210#830—31no—
211#821—31no—
212#821—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215#818—31no—
216#817—31no—
217#815—31no—
218C8×Dic3—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#807—31no—
227#807—31no—
228#807—31no—
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—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
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—91no—
277#478—91no—
278#461—31no—
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—21no—
290C2×C3×Q8—21no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C2×#67—61no—
299C22×Dic3—61no—
300D3×D4—62no—
301D3×D4—62no—
302C2×D12—31no—
303C2×D12—31no—
304C2×D12—61no—
305C2×D12—62no—
306C2×D12—61no—
307C2×D12—62no—
308C2×D12C22×D311yescharacteristic
309C2×C4×D3—21no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—121no—
316C2×C4×D3C22×D311yescharacteristic
317C3×SD16—62no—
318C3×SD16—62no—
319C2×C3×C8—31no—
320C2×C3×C8—31no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—41no—
331C3×C4⋊C4—41no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
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—22no—
352#215—22no—
353#215—62no—
354#215—62no—
355#215—62no—
356#215—62no—
357#215—122no—
358#215—122no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—121no—
369(C2×D3)⋊C4#6711yescharacteristic
370(C2×D3)⋊C4#6711yescharacteristic
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4#6711yescharacteristic
384Dic3⋊C4#6711yescharacteristic
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3C22×D311yescharacteristic
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398C22×C32C22×D411yescharacteristic
399C2×C3⋊D3—22no—
400C2×C3⋊D3—41no—
401C2×C3⋊D3—41no—
402C2×C3×D3—22no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408D32—84no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—41no—
412C32×C4—41no—
413C32×C4C2×#4111yescharacteristic
414C32×C4C2×#4111yescharacteristic
415C3⋊Dic3—41no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C22×D4—91no—
423C2×SD16—31no—
424C2×SD16—31no—
425C2×SD16—91no—
426C2×SD16—91no—
427C4⋊Q8D3211yescharacteristic, complemented
428#126—61no—
429#126—61no—
430#125—31no—
431#125—61no—
432#125—61no—
433C22⋊Q8—31no—
434C22⋊Q8—31no—
435C4×Q8—31no—
436C4×Q8—31no—
437C4×D4—31no—
438C4×D4—91no—
439C4×D4—91no—
440C4×D4—91no—
441C4×D4—181no—
442C4×D4—181no—
443#117—31no—
444#117—91no—
445C2×C22⋊C4—181no—
446C2×C22⋊C4—181no—
447#107—91no—
448#107—91no—
449#106—91no—
450#106—91no—
451C4⋊C8—31no—
452C4⋊C8—91no—
453#103—31no—
454#103—31no—
455#103—91no—
456#103—91no—
457#102—91no—
458#102—91no—
459#102—91no—
460#102—91no—
461C22⋊C8—91no—
462C22⋊C8—91no—
463#97—91no—
464C4×C8—91no—
465C23×C3—31no—
466C23×C3—61no—
467C22×D3—21no—
468C22×D3—64no—
469C22×D3—64no—
470C22×D3—61no—
471C22×D3—61no—
472C22×D3—121no—
473C22×D3—241no—
474C22×D3—241no—
475C22×D3—241no—
476C22×D3—241no—
477C22×D3C2×#6711yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×D4—32no—
491C3×D4—61no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—241no—
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—64no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—241no—
524C2×Dic3C2×#6711yescharacteristic
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527D12—21no—
528D12—32no—
529D12—32no—
530D12—62no—
531D12—64no—
532D12—61no—
533D12—61no—
534D12—121no—
535D12#23712yes—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—81no—
539C4×D3—241no—
540C4×D3—241no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—242no—
545C3×C8—61no—
546C3×C8—61no—
547C3⋊C8—21no—
548C3⋊C8—21no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—121no—
554C3⋊C8—121no—
555C2×C32#52511yescharacteristic
556C2×C32#57711yescharacteristic
557C2×C32#57711yescharacteristic
558C3⋊D3—42no—
559C3×D3—41no—
560C3×D3—42no—
561C24—181no—
562C2×Q8C2×D3211yescharacteristic
563C2×Q8C2×D3211yescharacteristic
564C2×D4—31no—
565C2×D4—91no—
566C2×D4—181no—
567C2×D4—182no—
568C2×D4—182no—
569C22×C4—31no—
570C22×C4—61no—
571C22×C4—181no—
572C22×C4—181no—
573C22×C4—181no—
574SD16—62no—
575SD16—62no—
576SD16—182no—
577SD16—182no—
578C2×C8—31no—
579C2×C8—31no—
580C2×C8—91no—
581C2×C8—91no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—31no—
588C4⋊C4—31no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—91no—
596C22⋊C4—31no—
597C22⋊C4—31no—
598C22⋊C4—61no—
599C22⋊C4—61no—
600C22⋊C4—61no—
601C22⋊C4—181no—
602C22⋊C4—181no—
603C22⋊C4—181no—
604C22⋊C4—181no—
605C42—31no—
606C42—61no—
607C42—61no—
608C42—181no—
609C42C2×D3211yescharacteristic
610C22×C3—21no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—62no—
614C22×C3—61no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3C2×D3×D411yescharacteristic
618C22×C3C22×#6711yescharacteristic
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—22no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—62no—
626C2×D3—62no—
627C2×D3—122no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—241no—
633C2×D3—241no—
634C2×D3—244no—
635C2×D3—244no—
636C3×C4—22no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4C2×#23711yescharacteristic
657C3×C4D3×#4111yescharacteristic
658C3×C4D3×#4111yescharacteristic
659C3×C4D3×#4111yescharacteristic
660Dic3—21no—
661Dic3—21no—
662Dic3—21no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—121no—
667Dic3—121no—
668Dic3—241no—
669C32#312311yescharacteristic, complemented, Sylow
670C23—31no—
671C23—61no—
672C23—184no—
673C23—181no—
674C23—721no—
675C23—721no—
676Q8—21no—
677Q8—21no—
678Q8—21no—
679Q8—21no—
680D4—32no—
681D4—61no—
682D4—92no—
683D4—184no—
684D4—181no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—31no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—181no—
696C2×C4—241no—
697C2×C4—721no—
698C2×C4—721no—
699C2×C4—721no—
700C2×C4D3×#6711yescharacteristic
701C2×C4D3×#6711yescharacteristic
702C2×C4C22×D3211yescharacteristic
703C8—61no—
704C8—61no—
705C8—181no—
706C8—181no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—121no—
711C2×C3—122no—
712C2×C3#560611yescharacteristic
713C2×C3#576211yescharacteristic
714C2×C3#577811yescharacteristic
715C2×C3#582811yescharacteristic
716C2×C3#583711yescharacteristic
717C2×C3#583711yescharacteristic
718D3—42no—
719D3—41no—
720D3—122no—
721D3—122no—
722D3—242no—
723C22—61no—
724C22—62no—
725C22—61no—
726C22—61no—
727C22—121no—
728C22—121no—
729C22—182no—
730C22—361no—
731C22—361no—
732C22—724no—
733C22C2×D3×#6711yescharacteristic
734C4—21no—
735C4—21no—
736C4—41no—
737C4—41no—
738C4—61no—
739C4—61no—
740C4—61no—
741C4—121no—
742C4—121no—
743C4—121no—
744C4—361no—
745C4D3×#23711yescharacteristic
746C4#6431211yescharacteristic
747C3—21no—
748C3#8041311yescharacteristic, complemented
749C3#8344711yescharacteristic, complemented
750C2—121no—
751C2—122no—
752C2—362no—
753C2#1059530111yescharacteristic
754C2#1059531811yescharacteristic
755C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4⋊Q8D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5731C2semidirect
3. #10592782C2semidirect
4. C3×#5083C2semidirect
7. #10591566C2semidirect
8. Dic3×#215C2semidirect
9. #10591559C2semidirect
10. #10591558C2semidirect
11. #10591540C2semidirect
12. #10591536C2semidirect
13. #10590308C2semidirect
14. #10590270C2semidirect
15. #10590253C2semidirect
19. C32×C4⋊Q8C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C3×Q8×Dic3C22semidirect
35. C3×#870C22semidirect
43. #63662C22semidirect
44. #63662C22semidirect
45. C4⋊(C3⋊(C3⋊C8))C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
48. C3×C4⋊(C3⋊C8)C22semidirect
49. #63576C22semidirect
50. #63575C22semidirect
51. #63574C22semidirect
52. #63573C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5731D3semidirect
73. #5083D3semidirect
147. C3×C4⋊Q8C2×D3semidirect
148. C3×C4⋊Q8C2×D3semidirect
162. Q8×Dic3C2×D3semidirect
163. Q8×Dic3C2×D3semidirect
195. #870C2×D3semidirect
205. #835C2×D3semidirect
206. #835C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
427. C4⋊Q8D32semidirect
669. C32#3123semidirect
748. C3#80413semidirect
749. C3#83447semidirect

Maximal subgroups

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

subgroupindex
C3×#57312
#105939942
#105927822
C3×#50832
#105916512
#105915662
Dic3×#2152
#105915592
#105915582
#105915402
#105915362
#105903082
#105902702
#105902532
#834473
#804133