Finite Group Databasebeta

← #11872159

Subgroups — #11872159

Order 1152.

860 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5534C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3#10592699C211yesmaximal, characteristic, complemented
4#10591169C211yesmaximal, characteristic, complemented
5#10591160C211yesmaximal, characteristic
6#10591102C211yesmaximal, characteristic, complemented
7#10591090C211yesmaximal, characteristic, complemented
8#10590358C211yesmaximal, characteristic, complemented
9C4×#3715C211yesmaximal, characteristic, complemented
10#10590348C211yesmaximal, characteristic, complemented
11#10590348C211yesmaximal, characteristic, complemented
12#10590344C211yesmaximal, characteristic, complemented
13C4×#3713C211yesmaximal, characteristic, complemented
14#10590269C211yesmaximal, characteristic, complemented
15#10590266C211yesmaximal, characteristic, complemented
16#83460—31nomaximal
17#82541—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C32×#117C2211yescharacteristic
20C3×#930C2211yescharacteristic
21C3×#926C2211yescharacteristic
22C3×#924C2211yescharacteristic
23C3×#898—21no—
24C3×#896—21no—
25C3×#893—21no—
26C3×#893—21no—
27C3×#885—21no—
28C3×#883—21no—
29C3×D3×C22⋊C4—21no—
30C3×D3×C22⋊C4—21no—
31C3×#875C2211yescharacteristic, complemented
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic
36C3×C4×D12C2211yescharacteristic, complemented
37C3×#869C2211yescharacteristic, complemented
38C3×C4×Dic6C2211yescharacteristic, complemented
39C2×#3715C2211yescharacteristic
40C2×#3715C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63657C2211yescharacteristic
44#63657C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47#63630C2211yescharacteristic, complemented
48C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
49#63576C2211yescharacteristic, complemented
50#63576C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61C3×#542—31no—
62C3×#518—31no—
63#5534D311yescharacteristic, complemented
64#5521D311yescharacteristic, complemented
65#5218—31no—
66#5217—31no—
67#5087—31no—
68#5084—31no—
69#5057—31no—
70#5057—31no—
71#5046—31no—
72#5045—31no—
73#5036—31no—
74#5035—31no—
75#5026—31no—
76C4×#215—31no—
77#5018—31no—
78C4×#214—31no—
79#5016—31no—
80#5016—31no—
81#5014—31no—
82#5014—31no—
83C4×#213—31no—
84C4×#213—31no—
85#5008—31no—
86#5007—31no—
87#5003—31no—
88#5000—31no—
89#5000—31no—
90#5000—61no—
91#4996—31no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×D12—21no—
96C2×C3×D12—22no—
97C2×C3×D12—22no—
98C2×C3×D12C2311yescharacteristic
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×C4×D3—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C32×C4⋊C4D411yescharacteristic
109C32×C4⋊C4D411yescharacteristic
110C32×C22⋊C4D411yescharacteristic
111C32×C22⋊C4D411yescharacteristic
112C32×C42C2311yescharacteristic
113C32×C42C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137#3715—22no—
138#3715—22no—
139#3713—22no—
140#3713—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C3×C4⋊Q8—31no—
145C3×#126—61no—
146C3×#124—31no—
147C3×#124—61no—
148C3×#123—61no—
149C3×C22⋊Q8—31no—
150C3×C22⋊Q8—61no—
151C3×#121—31no—
152C3×C4×Q8—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—61no—
159C3×C4×D4—61no—
160C3×#117—21no—
161C3×#117—31no—
162C3×#117C2×D311yescharacteristic
163C3×#117C2×D311yescharacteristic
164C2×C3×C22⋊C4—61no—
165C2×C3×C22⋊C4—61no—
166C2×#215—31no—
167C2×#215—31no—
168C2×#214—31no—
169C2×#214—31no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174#930C2×D311yescharacteristic
175#926C2×D311yescharacteristic
176#924C2×D311yescharacteristic
177#898—21no—
178#896—21no—
179#893—21no—
180#893—21no—
181#885—21no—
182#883—21no—
183D3×C22⋊C4—21no—
184D3×C22⋊C4—21no—
185#875C2×D311yescharacteristic, complemented
186C4×D12C2×D311yescharacteristic
187C4×D12C2×D311yescharacteristic
188C4×D12C2×D311yescharacteristic
189C4×D12C2×D311yescharacteristic
190C4×D12C2×D311yescharacteristic, complemented
191#869C2×D311yescharacteristic, complemented
192C4×Dic6C2×D311yescharacteristic, complemented
193#835—31no—
194#835—31no—
195#832—31no—
196#832—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#809—31no—
210#809—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—
229#803—31no—
230#803—31no—
231#803—61no—
232C4×C3⋊C8—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—61no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C3×#67—81no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C3×D12—24no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12#4112yes—
262C3×D12#4112yes—
263C3×C4×D3—81no—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3⋊(C3⋊C8)—21no—
275#542—31no—
276#518—31no—
277#485—91no—
278#482—91no—
279#476—91no—
280#474—91no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—62no—
298C2×C3×D4—62no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C22×C3×C4—21no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—21no—
310C2×D12—21no—
311C2×D12—22no—
312C2×D12—22no—
313C2×D12C22×D311yescharacteristic
314C2×D12C22×D311yescharacteristic
315C2×D12C22×D311yescharacteristic
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×Dic6—21no—
322C2×Dic6C22×D311yescharacteristic
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—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4#6711yescharacteristic
333C3×C4⋊C4#6711yescharacteristic
334C3×C4⋊C4#6711yescharacteristic
335C3×C4⋊C4#6711yescharacteristic
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4#6711yescharacteristic
349C3×C22⋊C4#6711yescharacteristic
350C3×C22⋊C4#6711yescharacteristic
351C3×C22⋊C4#6711yescharacteristic
352C3×C42—21no—
353C3×C42—21no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42C22×D311yescharacteristic
357C3×C42C22×D311yescharacteristic
358C3×C42C22×D311yescharacteristic
359C3×C42C22×D311yescharacteristic
360#217—21no—
361#217—21no—
362#215—62no—
363#215—62no—
364#214—62no—
365#214—62no—
366#213—62no—
367#213—62no—
368#213—62no—
369#213—62no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—61no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32C22×D411yescharacteristic
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—84no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—31no—
426C2×SD16—91no—
427C2×SD16—91no—
428C2×D8—91no—
429C2×D8—91no—
430C4⋊Q8—31no—
431#126—61no—
432#124—31no—
433#124—61no—
434#123—61no—
435C22⋊Q8—31no—
436C22⋊Q8—61no—
437#121—31no—
438C4×Q8—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—31no—
444C4×D4—61no—
445C4×D4—61no—
446#117—31no—
447#117D3211yescharacteristic
448C2×C22⋊C4—61no—
449C2×C22⋊C4—61no—
450#107—91no—
451#107—91no—
452#106—91no—
453#106—91no—
454C4⋊C8—91no—
455C4⋊C8—91no—
456#103—91no—
457#103—91no—
458#102—91no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—91no—
465C22⋊C8—91no—
466#97—91no—
467C4×C8—91no—
468C23×C3—21no—
469C23×C3—64no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—241no—
474C23×C3—241no—
475C23×C3C2×#6711yescharacteristic
476C23×C3C2×#6711yescharacteristic
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—24no—
480C22×D3—21no—
481C22×D3—81no—
482C22×D3—81no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—241no—
486C3×D4—32no—
487C3×D4—32no—
488C3×D4—64no—
489C3×D4—61no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—241no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—241no—
512C2×C3×C4—241no—
513C2×C3×C4—241no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C2×#6711yescharacteristic
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C2×#6711yescharacteristic
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—81no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534D12—24no—
535D12—21no—
536D12—21no—
537D12—21no—
538D12—21no—
539D12#23512yes—
540D12#23512yes—
541C4×D3—81no—
542C4×D3—81no—
543C4×D3—81no—
544C4×D3—81no—
545C4×D3—81no—
546Dic6—21no—
547Dic6—21no—
548Dic6—81no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—121no—
558C3⋊C8—121no—
559C3⋊C8—121no—
560C3⋊C8—121no—
561C2×C32—41no—
562C2×C32#52511yescharacteristic
563C2×C32#57611yescharacteristic
564C2×C32#57711yescharacteristic
565C3×D3—42no—
566C3×D3—42no—
567C3×D3—81no—
568C24—61no—
569C2×Q8—31no—
570C2×Q8—61no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—62no—
575C2×D4—62no—
576C2×D4—61no—
577C2×D4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4C2×D3211yescharacteristic
584SD16—182no—
585SD16—182no—
586D8—182no—
587D8—182no—
588C2×C8—91no—
589C2×C8—91no—
590C2×C8—91no—
591C2×C8—91no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4#62511yescharacteristic
600C4⋊C4#62511yescharacteristic
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4#62511yescharacteristic
612C22⋊C4#62511yescharacteristic
613C42—61no—
614C42—61no—
615C42C2×D3211yescharacteristic
616C42C2×D3211yescharacteristic
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—62no—
628C22×C3—62no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—244no—
637C22×C3C22×#6711yescharacteristic
638C22×C3C22×#6711yescharacteristic
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—84no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4C2×#23511yescharacteristic
672C3×C4C2×#23511yescharacteristic
673C3×C4D3×#4111yescharacteristic
674C3×C4D3×#4111yescharacteristic
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680C32#311811yescharacteristic, complemented, Sylow
681C23—64no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—241no—
686C23—241no—
687C23C2×#62511yescharacteristic
688Q8—61no—
689Q8—61no—
690Q8—241no—
691D4—32no—
692D4—32no—
693D4—64no—
694D4—61no—
695D4—61no—
696D4—61no—
697D4—61no—
698D4—241no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—241no—
707C2×C4—241no—
708C2×C4—241no—
709C2×C4—241no—
710C2×C4—241no—
711C2×C4C2×#62511yescharacteristic
712C2×C4C2×#62511yescharacteristic
713C2×C4C2×#62511yescharacteristic
714C2×C4C2×#62511yescharacteristic
715C2×C4C2×#62511yescharacteristic
716C2×C4C22×D3211yescharacteristic
717C8—181no—
718C8—181no—
719C8—181no—
720C8—181no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—41no—
725C2×C3—41no—
726C2×C3—81no—
727C2×C3—122no—
728C2×C3—122no—
729C2×C3—241no—
730C2×C3#579111yescharacteristic
731C2×C3#582811yescharacteristic
732C2×C3#583511yescharacteristic
733C2×C3#583511yescharacteristic
734C2×C3#583611yescharacteristic
735C2×C3#583711yescharacteristic
736D3—42no—
737D3—42no—
738D3—81no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—62no—
743C22—62no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—244no—
752C22C22×#62511yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—121no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4—121no—
763C4D3×#23511yescharacteristic
764C4D3×#23511yescharacteristic
765C3—21no—
766C3#8254111yescharacteristic, complemented
767C3#8346011yescharacteristic, complemented
768C2—41no—
769C2—122no—
770C2—122no—
771C2—241no—
772C2#1059502211yescharacteristic
773C2#1059544411yescharacteristic
774C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10591160C2
hypercenter#117D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5534C2semidirect
2. C3×#5521C2semidirect
3. #10592699C2semidirect
4. #10591169C2semidirect
6. #10591102C2semidirect
7. #10591090C2semidirect
8. #10590358C2semidirect
9. C4×#3715C2semidirect
10. #10590348C2semidirect
11. #10590348C2semidirect
12. #10590344C2semidirect
13. C4×#3713C2semidirect
14. #10590269C2semidirect
15. #10590266C2semidirect
31. C3×#875C22semidirect
36. C3×C4×D12C22semidirect
37. C3×#869C22semidirect
38. C3×C4×Dic6C22semidirect
45. C4⋊(C3⋊(C3⋊C8))C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. #63630C22semidirect
48. C4×C3⋊(C3⋊C8)C22semidirect
49. #63576C22semidirect
50. #63576C22semidirect
51. #63574C22semidirect
52. #63574C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
63. #5534D3semidirect
64. #5521D3semidirect
185. #875C2×D3semidirect
190. C4×D12C2×D3semidirect
191. #869C2×D3semidirect
192. C4×Dic6C2×D3semidirect
680. C32#3118semidirect
766. C3#82541semidirect
767. C3#83460semidirect

Maximal subgroups

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

subgroupindex
C3×#55342
C3×#55212
#105926992
#105911692
#105911602
#105911022
#105910902
#105903582
C4×#37152
#105903482
#105903442
C4×#37132
#105902692
#105902662
#834603
#825413