Finite Group Databasebeta

← #11870620

Subgroups — #11870620

Order 1152.

851 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic, complemented
3#10592624C211yesmaximal, characteristic, complemented
4#10591170C211yesmaximal, characteristic, complemented
5#10591161C211yesmaximal, characteristic
6#10591102C211yesmaximal, characteristic, complemented
7#10591090C211yesmaximal, characteristic, complemented
8C4×#3718C211yesmaximal, characteristic, complemented
9C4×#3715C211yesmaximal, characteristic, complemented
10C4×#3715C211yesmaximal, characteristic, complemented
11#10590348C211yesmaximal, characteristic, complemented
12C4×#3713C211yesmaximal, characteristic, complemented
13#10590286C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83140—31nomaximal
17#82528—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C32×C42C2211yescharacteristic
20C3×#930C2211yescharacteristic
21C3×#929—21no—
22C3×C4×#67—21no—
23C3×C4×#67—21no—
24C3×C4×#67—21no—
25C3×#926C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#876—21no—
28C3×#875C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×#872—21no—
33C3×#872—21no—
34C3×C42×D3—21no—
35C3×#870C2211yescharacteristic
36C3×C4×Dic6C2211yescharacteristic
37C3×C4×Dic6C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic
39C2×#3718C2211yescharacteristic
40C2×#3715C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63657C2211yescharacteristic
44#63657C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
47C4×C3⋊(C3⋊C8)C2211yescharacteristic
48C4×C3⋊(C3⋊C8)C2211yescharacteristic
49#63576C2211yescharacteristic
50#63576C2211yescharacteristic
51#63574C2211yescharacteristic
52#63574C2211yescharacteristic
53#63565C2211yescharacteristic
54#63565C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63#5479D311yescharacteristic, complemented
64C4×#235D311yescharacteristic, complemented
65#5239—31no—
66#5238—31no—
67#5066—31no—
68#5063—31no—
69#5057—31no—
70#5054—31no—
71#5047—31no—
72#5045—31no—
73#5037—31no—
74#5035—31no—
75C4×#216—31no—
76C4×#216—31no—
77#5028—31no—
78C4×#215—31no—
79C4×#215—31no—
80#5022—31no—
81C4×#214—31no—
82C4×#214—31no—
83#5016—31no—
84C4×#213—31no—
85C4×#213—31no—
86#5009—31no—
87#5003—31no—
88#4996—31no—
89#4925—31no—
90#4925—31no—
91#4925—61no—
92C22×C32×C4D411yescharacteristic
93C22×C32×C4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C3×#235—22no—
98C3×#235—22no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C32×C42D411yescharacteristic
108C32×C42D411yescharacteristic
109C32×C42C2311yescharacteristic
110C32×C42C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×#217—21no—
116C3×#217—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137#3718—22no—
138#3715—22no—
139#3715—22no—
140#3713—22no—
141#3102—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×D311yescharacteristic
144C3×#126—61no—
145C3×#125—31no—
146C3×#124—31no—
147C3×#123—61no—
148C3×C22⋊Q8—31no—
149C3×#121—31no—
150C3×C4×Q8—31no—
151C3×C4×Q8—31no—
152C3×C4×Q8—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—61no—
157C3×C4×D4—61no—
158C3×C4×D4—61no—
159C3×#117—31no—
160C3×#117—61no—
161C3×#117—61no—
162C2×C3×C42—21no—
163C2×C3×C42—61no—
164C2×C3×C42C2×D311yescharacteristic
165C2×C3×C42C2×D311yescharacteristic
166C2×#216—31no—
167C2×#216—31no—
168C2×#215—31no—
169C2×#215—31no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#213—31no—
173C2×#213—31no—
174#930C2×D311yescharacteristic
175#929—21no—
176C4×#67—21no—
177C4×#67—21no—
178C4×#67—21no—
179#926C2×D311yescharacteristic
180#924C2×D311yescharacteristic
181#876—21no—
182#875C2×D311yescharacteristic
183C4×D12C2×D311yescharacteristic
184C4×D12C2×D311yescharacteristic
185C4×D12C2×D311yescharacteristic
186#872—21no—
187#872—21no—
188C42×D3—21no—
189#870C2×D311yescharacteristic
190C4×Dic6C2×D311yescharacteristic
191C4×Dic6C2×D311yescharacteristic
192C4×Dic6C2×D311yescharacteristic
193#835—31no—
194#835—31no—
195#835—31no—
196#835—31no—
197#832—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#830—31no—
202#830—31no—
203#830—31no—
204#830—31no—
205#830—61no—
206#830—61no—
207#810—31no—
208#810—31no—
209#810—31no—
210#810—31no—
211#809—31no—
212#809—31no—
213#809—31no—
214#809—31no—
215#808—31no—
216#808—31no—
217#808—31no—
218#808—31no—
219#807—31no—
220#807—31no—
221#807—31no—
222#807—31no—
223C4⋊(C3⋊C8)—31no—
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—61no—
228C4⋊(C3⋊C8)—61no—
229C4×C3⋊C8—31no—
230C4×C3⋊C8—31no—
231C4×C3⋊C8—31no—
232C4×C3⋊C8—31no—
233C4×C3⋊C8—61no—
234C4×C3⋊C8—61no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C2×C32×C4—22no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—41no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C3×#67—24no—
249C3×#67—42no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12#4112yes—
260C3×C4×D3—24no—
261C3×C4×D3—42no—
262C3×C4×D3—42no—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6#4112yes—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3⋊(C3⋊C8)—21no—
271C3⋊(C3⋊C8)—21no—
272#529—31no—
273C4×#41—31no—
274#485—91no—
275#482—91no—
276#479—91no—
277#478—91no—
278#464—91no—
279#463—91no—
280#452—91no—
281#449—91no—
282C4×Q16—91no—
283C4×SD16—91no—
284C4×SD16—91no—
285C4×D8—91no—
286#431—91no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×D4—31no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C2×C3×D4—61no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4#6711yescharacteristic
303C22×C3×C4#6711yescharacteristic
304C22×C3×C4#6711yescharacteristic
305C22×C3×C4#6711yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C2×#67—21no—
309C2×#67—21no—
310#235—22no—
311#235—22no—
312C2×D12C22×D311yescharacteristic
313C2×D12C22×D311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×Dic6C22×D311yescharacteristic
319C2×Dic6C22×D311yescharacteristic
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4—61no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C22⋊C4—61no—
331C3×C22⋊C4—61no—
332C3×C22⋊C4—61no—
333C3×C22⋊C4—61no—
334C3×C22⋊C4—61no—
335C3×C22⋊C4—61no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C42—21no—
339C3×C42—21no—
340C3×C42—21no—
341C3×C42—21no—
342C3×C42—61no—
343C3×C42—61no—
344C3×C42—61no—
345C3×C42—61no—
346C3×C42#6711yescharacteristic
347C3×C42#6711yescharacteristic
348C3×C42#6711yescharacteristic
349C3×C42#6711yescharacteristic
350C3×C42C22×D311yescharacteristic
351C3×C42C22×D311yescharacteristic
352C3×C42C22×D311yescharacteristic
353C3×C42C22×D311yescharacteristic
354#217—21no—
355#217—21no—
356#216—62no—
357#216—62no—
358#215—62no—
359#215—62no—
360#214—62no—
361#214—62no—
362#213—62no—
363#213—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380C4×Dic3—21no—
381C4×Dic3—21no—
382C4×Dic3—21no—
383C4×Dic3—21no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
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⋊C8—61no—
395C2×C3⋊C8—61no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32C22×D411yescharacteristic
400C2×C3×D3—22no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4#13512yes—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3×Dic3—22no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C2×#41—31no—
420C2×Q16—91no—
421C2×SD16—91no—
422C2×SD16—91no—
423C2×D8—91no—
424#126—61no—
425#125—31no—
426#124—31no—
427#123—61no—
428C22⋊Q8—31no—
429#121—31no—
430C4×Q8—31no—
431C4×Q8—31no—
432C4×Q8—31no—
433C4×D4—31no—
434C4×D4—31no—
435C4×D4—31no—
436C4×D4—61no—
437C4×D4—61no—
438C4×D4—61no—
439#117—31no—
440#117—61no—
441#117—61no—
442C2×C42—61no—
443C2×C42D3211yescharacteristic
444#107—91no—
445#107—91no—
446#106—91no—
447#106—91no—
448C4⋊C8—91no—
449C4⋊C8—91no—
450#103—91no—
451#103—91no—
452#103—91no—
453#103—91no—
454#102—91no—
455#102—91no—
456#102—91no—
457#102—91no—
458C22⋊C8—91no—
459C22⋊C8—91no—
460C4×C8—91no—
461C4×C8—91no—
462C23×C3—21no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3C2×#6711yescharacteristic
466C23×C3C2×#6711yescharacteristic
467C22×D3—21no—
468C22×D3—21no—
469C3×Q8—32no—
470C3×Q8—61no—
471C3×Q8—61no—
472C3×Q8—61no—
473C3×D4—32no—
474C3×D4—64no—
475C3×D4—61no—
476C3×D4—61no—
477C3×D4—61no—
478C3×D4—122no—
479C2×C3×C4—24no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
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—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—42no—
497C2×C3×C4—64no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—122no—
505C2×C3×C4—122no—
506C2×C3×C4—122no—
507C2×C3×C4C2×#6711yescharacteristic
508C2×C3×C4C2×#6711yescharacteristic
509C2×C3×C4C2×#6711yescharacteristic
510C2×C3×C4C2×#6711yescharacteristic
511C2×C3×C4C2×#6711yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C2×#6711yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—24no—
520#67—42no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527D12—21no—
528D12—21no—
529D12—21no—
530D12#23512yes—
531C4×D3—24no—
532C4×D3—42no—
533C4×D3—42no—
534C4×D3—42no—
535Dic6—21no—
536Dic6—21no—
537Dic6—21no—
538Dic6#23512yes—
539C3⋊C8—61no—
540C3⋊C8—61no—
541C3⋊C8—61no—
542C3⋊C8—61no—
543C3⋊C8—61no—
544C3⋊C8—61no—
545C3⋊C8—61no—
546C3⋊C8—61no—
547C3⋊C8—121no—
548C3⋊C8—121no—
549C3⋊C8—121no—
550C3⋊C8—121no—
551C2×C32—41no—
552C2×C32#52511yescharacteristic
553C2×C32C2×#13511yescharacteristic
554C2×C32#57511yescharacteristic
555C3×D3—42no—
556C3×D3—81no—
557#41—62no—
558#41—62no—
559C2×Q8—31no—
560C2×Q8—31no—
561C2×D4—31no—
562C2×D4—31no—
563C2×D4—61no—
564C2×D4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4#62511yescharacteristic
570C22×C4#62511yescharacteristic
571C22×C4C2×D3211yescharacteristic
572Q16—182no—
573SD16—182no—
574SD16—182no—
575D8—182no—
576C2×C8—91no—
577C2×C8—91no—
578C2×C8—91no—
579C2×C8—91no—
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—
590C22⋊C4—61no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C42—61no—
599C42—61no—
600C42—61no—
601C42—61no—
602C42#62511yescharacteristic
603C42#62511yescharacteristic
604C42C2×D3211yescharacteristic
605C42C2×D3211yescharacteristic
606C22×C3—22no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—62no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3C22×#6711yescharacteristic
623C22×C3C22×#6711yescharacteristic
624C2×D3—22no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—41no—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—22no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—62no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4#95012yes—
652C3×C4#95012yes—
653C3×C4C2×#23511yescharacteristic
654C3×C4C2×#23511yescharacteristic
655C3×C4D3×#4111yescharacteristic
656C3×C4D3×#4111yescharacteristic
657Dic3—22no—
658Dic3—41no—
659Dic3—41no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663C32#310211yescharacteristic, complemented, Sylow
664C23—61no—
665C23—61no—
666C23C2×#62511yescharacteristic
667Q8—32no—
668Q8—61no—
669Q8—61no—
670Q8—61no—
671D4—32no—
672D4—64no—
673D4—61no—
674D4—61no—
675D4—61no—
676D4—122no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—64no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—122no—
689C2×C4—122no—
690C2×C4—122no—
691C2×C4C2×#62511yescharacteristic
692C2×C4C2×#62511yescharacteristic
693C2×C4C2×#62511yescharacteristic
694C2×C4C2×#62511yescharacteristic
695C2×C4C2×#62511yescharacteristic
696C2×C4C22×D3211yescharacteristic
697C8—181no—
698C8—181no—
699C8—181no—
700C8—181no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—42no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—122no—
708C2×C3—241no—
709C2×C3#579111yescharacteristic
710C2×C3C2×#95011yescharacteristic
711C2×C3C2×#95011yescharacteristic
712C2×C3#582211yescharacteristic
713C2×C3#582211yescharacteristic
714C2×C3#582811yescharacteristic
715D3—42no—
716D3—81no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—62no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22—121no—
725C22—121no—
726C22C22×#62511yescharacteristic
727C4—21no—
728C4—21no—
729C4—21no—
730C4—21no—
731C4—62no—
732C4—121no—
733C4—121no—
734C4—121no—
735C4—121no—
736C4—121no—
737C4#6382212yes—
738C4D3×#23511yescharacteristic
739C4D3×#23511yescharacteristic
740C3—21no—
741C3#8252811yescharacteristic, complemented
742C3#8314011yescharacteristic, complemented
743C2—41no—
744C2—122no—
745C2—241no—
746C2C2×#6382211yescharacteristic
747C2#1059478611yescharacteristic
748C2#1059502211yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radical#10591161C2
hypercenterC2×C42D32
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C3×#5479C2semidirect
2. C3×C4×#235C2semidirect
3. #10592624C2semidirect
4. #10591170C2semidirect
6. #10591102C2semidirect
7. #10591090C2semidirect
8. C4×#3718C2semidirect
9. C4×#3715C2semidirect
10. C4×#3715C2semidirect
11. #10590348C2semidirect
12. C4×#3713C2semidirect
13. #10590286C2semidirect
14. #10590270C2semidirect
15. #10590267C2semidirect
63. #5479D3semidirect
64. C4×#235D3semidirect
663. C32#3102semidirect
741. C3#82528semidirect
742. C3#83140semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C3×C4×#2352
#105926242
#105911702
#105911612
#105911022
#105910902
C4×#37182
C4×#37152
#105903482
C4×#37132
#105902862
#105902702
#105902672
#831403
#825283