Finite Group Databasebeta

← #11872833

Subgroups — #11872833

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5583C211yesmaximal, characteristic, complemented
2#10593994C211yesmaximal, characteristic
3#10592725C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic
6#10591565C211yesmaximal, characteristic, complemented
7#10591564C211yesmaximal, characteristic, complemented
8#10591559C211yesmaximal, characteristic, complemented
9#10590596C211yesmaximal, characteristic
10#10590470C211yesmaximal, characteristic, complemented
11#10590467C211yesmaximal, characteristic, complemented
12#10590447C211yesmaximal, characteristic, complemented
13C4×#3717C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590264C211yesmaximal, characteristic, complemented
16#83447—31nomaximal
17#79659—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic, complemented
20C2×#3755C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#944C2211yescharacteristic, complemented
24C2×C3×#215C2211yescharacteristic
25C3×#898—21no—
26C3×#897C2211yescharacteristic
27C3×#890C2211yescharacteristic, complemented
28C3×#889—21no—
29C3×#876—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#872C2211yescharacteristic
32C3×#870—21no—
33C3×C4×Dic6C2211yescharacteristic, complemented
34#63921—21no—
35D3×(C2×D3)⋊C4—21no—
36#63904—21no—
37#63894C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39#63881—21no—
40#63841C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63662C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63634C2211yescharacteristic, complemented
46#63630C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#541—31no—
62#5583D311yescharacteristic, complemented
63#5545—31no—
64#5521—31no—
65C3×C4×SD16—31no—
66#5169—31no—
67#5162—31no—
68#5083—31no—
69#5083—31no—
70#5066—31no—
71#5066—31no—
72#5046—31no—
73#5046—31no—
74#5045—31no—
75#5045—31no—
76#5026—31no—
77#5026—31no—
78#5026—31no—
79#5026—61no—
80C4×#215—31no—
81C4×#215D311yescharacteristic, complemented
82#5018—31no—
83#5000—31no—
84#4871—31no—
85#4868—31no—
86#4818—31no—
87#4815—31no—
88#4776—31no—
89#4763—31no—
90C4×#204—31no—
91#4690—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
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⋊C4C2311yescharacteristic
107C32×C42—21no—
108C32×C42C2311yescharacteristic
109#3755—22no—
110#3752—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#215—22no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4D411yescharacteristic
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3717—22no—
140#3715—22no—
141#3123—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×SD16—31no—
145C3×C4⋊Q8—31no—
146C3×#126—61no—
147C3×#126—61no—
148C3×#125—31no—
149C3×#125—61no—
150C3×#125—61no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C3×C4×Q8—21no—
154C3×C4×Q8—31no—
155C3×C4×Q8C2×D311yescharacteristic, complemented
156C3×C4×Q8C2×D311yescharacteristic, complemented
157C3×C4×D4—31no—
158C3×#117—31no—
159#946C2×D311yescharacteristic
160#944C2×D311yescharacteristic, complemented
161C2×#215—31no—
162C2×#215—31no—
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—61no—
166C2×#215C2×D311yescharacteristic
167D4×Dic3—31no—
168C2×#214—31no—
169C4×#67—61no—
170C2×(C2×D3)⋊C4—61no—
171#926—31no—
172C2×#204—31no—
173#898—21no—
174#897C2×D311yescharacteristic
175#893—31no—
176#893—61no—
177#893—61no—
178#892—31no—
179#890C2×D311yescharacteristic, complemented
180#889—21no—
181#67⋊C4—61no—
182D3×C22⋊C4—61no—
183D3×C22⋊C4—61no—
184D3×C22⋊C4—61no—
185#876—21no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—61no—
191C4×D12C2×D311yescharacteristic
192#872C2×D311yescharacteristic
193#870—21no—
194C4×Dic6C2×D311yescharacteristic, complemented
195C3×#106—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—61no—
204#835C2×D311yescharacteristic, complemented
205#832—31no—
206#830—31no—
207#830—31no—
208#821—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#817—31no—
212#816—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—61no—
221#809C2×D311yescharacteristic
222#808—31no—
223#808C2×D311yescharacteristic, complemented
224#807—31no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—61no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231#803—31no—
232#803—31no—
233#803—61no—
234C4×C3⋊C8C2×D311yescharacteristic, complemented
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—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4×C3⋊D3—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12#4112yes—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—81no—
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—91no—
277#478—91no—
278#461—91no—
279#461—91no—
280#450—91no—
281#450—91no—
282#440—91no—
283#440—91no—
284C4×SD16—31no—
285C4×SD16—91no—
286#433—91no—
287C23×D3—61no—
288C23×D3—61no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×D4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—61no—
296C2×#67—61no—
297C22×Dic3—61no—
298D3×D4—62no—
299D3×D4—62no—
300C2×D12—31no—
301C2×D12—31no—
302C2×D12—61no—
303C2×D12—62no—
304C2×D12—61no—
305C2×D12—62no—
306C2×D12C22×D311yescharacteristic
307C2×C4×D3—21no—
308C2×C4×D3—61no—
309C2×C4×D3—61no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—121no—
314C2×C4×D3C22×D311yescharacteristic
315C2×Dic6C22×D311yescharacteristic
316C3×SD16—62no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
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—41no—
327C3×C4⋊C4—61no—
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×C22⋊C4—31no—
337C3×C22⋊C4—31no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C42—21no—
342C3×C42—21no—
343C3×C42—21no—
344C3×C42—31no—
345C3×C42—41no—
346C3×C42—61no—
347C3×C42C22×D311yescharacteristic
348C3×C42C22×D311yescharacteristic
349#217—61no—
350#217—61no—
351#215—22no—
352#215—62no—
353#215—62no—
354#215—62no—
355#215—64no—
356#215—62no—
357#214—62no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
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—61no—
367(C2×D3)⋊C4—121no—
368(C2×D3)⋊C4#6711yescharacteristic
369(C2×D3)⋊C4#6711yescharacteristic
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4#6711yescharacteristic
383Dic3⋊C4#6711yescharacteristic
384C4×Dic3—21no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3C22×D311yescharacteristic
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396#204—62no—
397C22×C32C22×D411yescharacteristic
398C2×C3⋊D3—22no—
399C2×C3⋊D3—41no—
400C2×C3⋊D3—41no—
401C2×C3×D3—22no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407D32—84no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3⋊Dic3—41no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C22×D4—91no—
422C2×SD16—31no—
423C2×SD16—91no—
424C2×SD16—91no—
425C2×SD16—91no—
426C4⋊Q8—31no—
427#126—61no—
428#126—61no—
429#125—31no—
430#125—61no—
431#125—61no—
432C22⋊Q8—31no—
433C22⋊Q8—31no—
434C4×Q8—31no—
435C4×Q8D3211yescharacteristic, complemented
436C4×D4—31no—
437C4×D4—91no—
438C4×D4—91no—
439C4×D4—91no—
440C4×D4—181no—
441C4×D4—181no—
442#117—31no—
443#117—91no—
444C2×C22⋊C4—181no—
445C2×C22⋊C4—181no—
446#107—91no—
447#107—91no—
448#106—31no—
449#106—91no—
450C4⋊C8—91no—
451C4⋊C8—91no—
452#103—31no—
453#103—91no—
454#103—91no—
455#103—91no—
456#102—31no—
457#102—91no—
458#102—91no—
459#102—91no—
460C22⋊C8—91no—
461C22⋊C8—91no—
462#97—91no—
463C4×C8—31no—
464C23×C3—31no—
465C23×C3—61no—
466C22×D3—21no—
467C22×D3—64no—
468C22×D3—64no—
469C22×D3—61no—
470C22×D3—61no—
471C22×D3—121no—
472C22×D3—241no—
473C22×D3—241no—
474C22×D3—241no—
475C22×D3—241no—
476C22×D3C2×#6711yescharacteristic
477C3×Q8—22no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—41no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×D4—32no—
486C3×D4—61no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—241no—
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4C2×#6711yescharacteristic
508C2×C3×C4C2×#6711yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—64no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—121no—
518C2×Dic3—241no—
519C2×Dic3C2×#6711yescharacteristic
520C2×Dic3C2×#6711yescharacteristic
521C2×Dic3C2×#6711yescharacteristic
522D12—21no—
523D12—32no—
524D12—32no—
525D12—62no—
526D12—64no—
527D12—61no—
528D12—61no—
529D12—121no—
530D12#23512yes—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—81no—
534C4×D3—241no—
535C4×D3—241no—
536C4×D3—241no—
537C4×D3—241no—
538C4×D3—241no—
539C4×D3—242no—
540Dic6—21no—
541Dic6—21no—
542C3×C8—61no—
543C3×C8—61no—
544C3⋊C8—21no—
545C3⋊C8—21no—
546C3⋊C8—62no—
547C3⋊C8—61no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—121no—
552C2×C32#52511yescharacteristic
553C2×C32#57711yescharacteristic
554C2×C32#57711yescharacteristic
555C3⋊D3—42no—
556C3×D3—41no—
557C3×D3—42no—
558C24—181no—
559C2×Q8—31no—
560C2×Q8C2×D3211yescharacteristic
561C2×D4—31no—
562C2×D4—91no—
563C2×D4—181no—
564C2×D4—182no—
565C2×D4—182no—
566C22×C4—31no—
567C22×C4—61no—
568C22×C4—181no—
569C22×C4—181no—
570C22×C4—181no—
571SD16—62no—
572SD16—182no—
573SD16—182no—
574SD16—182no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8—91no—
578C2×C8—91no—
579C4⋊C4—21no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—91no—
592C4⋊C4C2×D3211yescharacteristic
593C22⋊C4—31no—
594C22⋊C4—31no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—181no—
599C22⋊C4—181no—
600C22⋊C4—181no—
601C22⋊C4—181no—
602C42—21no—
603C42—31no—
604C42—61no—
605C42—181no—
606C42C2×D3211yescharacteristic
607C22×C3—21no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—62no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3C2×D3×D411yescharacteristic
615C22×C3C22×#6711yescharacteristic
616C2×D3—22no—
617C2×D3—21no—
618C2×D3—21no—
619C2×D3—21no—
620C2×D3—41no—
621C2×D3—41no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3—122no—
625C2×D3—121no—
626C2×D3—121no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—241no—
630C2×D3—241no—
631C2×D3—244no—
632C2×D3—244no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—42no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—81no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C2×#23511yescharacteristic
654C3×C4D3×#4111yescharacteristic
655C3×C4D3×#4111yescharacteristic
656C3×C4D3×#4111yescharacteristic
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—121no—
664Dic3—121no—
665Dic3—241no—
666C32#312311yescharacteristic, complemented, Sylow
667C23—31no—
668C23—61no—
669C23—184no—
670C23—181no—
671C23—721no—
672C23—721no—
673Q8—21no—
674Q8—21no—
675Q8—61no—
676Q8—61no—
677D4—32no—
678D4—61no—
679D4—92no—
680D4—184no—
681D4—181no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—181no—
693C2×C4—241no—
694C2×C4—721no—
695C2×C4—721no—
696C2×C4—721no—
697C2×C4D3×#6711yescharacteristic
698C2×C4D3×#6711yescharacteristic
699C2×C4C22×D3211yescharacteristic
700C8—61no—
701C8—61no—
702C8—181no—
703C8—181no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—121no—
708C2×C3—122no—
709C2×C3#554711yescharacteristic
710C2×C3#576211yescharacteristic
711C2×C3#577011yescharacteristic
712C2×C3#582811yescharacteristic
713C2×C3#583711yescharacteristic
714C2×C3#583711yescharacteristic
715D3—42no—
716D3—41no—
717D3—122no—
718D3—122no—
719D3—242no—
720C22—61no—
721C22—61no—
722C22—62no—
723C22—61no—
724C22—121no—
725C22—121no—
726C22—182no—
727C22—361no—
728C22—361no—
729C22—724no—
730C22C2×D3×#6711yescharacteristic
731C4—21no—
732C4—21no—
733C4—41no—
734C4—41no—
735C4—61no—
736C4—61no—
737C4—61no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4—361no—
742C4D3×#23511yescharacteristic
743C4#6430611yescharacteristic
744C3—21no—
745C3#7965911yescharacteristic, complemented
746C3#8344711yescharacteristic, complemented
747C2—121no—
748C2—122no—
749C2—362no—
750C2#1059506011yescharacteristic
751C2#1059531811yescharacteristic
752C2#1059545711yescharacteristic
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×#5583C2semidirect
3. #10592725C2semidirect
4. C3×C4×#215C2semidirect
6. #10591565C2semidirect
7. #10591564C2semidirect
8. #10591559C2semidirect
10. #10590470C2semidirect
11. #10590467C2semidirect
12. #10590447C2semidirect
13. C4×#3717C2semidirect
14. #10590358C2semidirect
15. #10590264C2semidirect
19. C32×C4×Q8C22semidirect
23. C3×#944C22semidirect
27. C3×#890C22semidirect
33. C3×C4×Dic6C22semidirect
43. #63662C22semidirect
45. #63634C22semidirect
46. #63630C22semidirect
47. C3×#835C22semidirect
49. C3×#808C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63576C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
62. #5583D3semidirect
81. C4×#215D3semidirect
155. C3×C4×Q8C2×D3semidirect
156. C3×C4×Q8C2×D3semidirect
160. #944C2×D3semidirect
179. #890C2×D3semidirect
194. C4×Dic6C2×D3semidirect
204. #835C2×D3semidirect
223. #808C2×D3semidirect
234. C4×C3⋊C8C2×D3semidirect
435. C4×Q8D32semidirect
666. C32#3123semidirect
745. C3#79659semidirect
746. C3#83447semidirect

Maximal subgroups

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

subgroupindex
C3×#55832
#105939942
#105927252
C3×C4×#2152
#105916512
#105915652
#105915642
#105915592
#105905962
#105904702
#105904672
#105904472
C4×#37172
#105903582
#105902642
#834473
#796593