Finite Group Databasebeta

← #11872947

Subgroups — #11872947

Order 1152.

816 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5534C211yesmaximal, characteristic, complemented
2C3×#5523C211yesmaximal, characteristic, complemented
3#10592699C211yesmaximal, characteristic, complemented
4#10591170C211yesmaximal, characteristic, complemented
5#10591161C211yesmaximal, characteristic
6#10591132C211yesmaximal, characteristic, complemented
7#10591089C211yesmaximal, characteristic, complemented
8C4×#3718C211yesmaximal, characteristic, complemented
9#10590358C211yesmaximal, characteristic, complemented
10#10590358C211yesmaximal, characteristic, complemented
11#10590348C211yesmaximal, characteristic, complemented
12C4×#3713C211yesmaximal, characteristic, complemented
13#10590310C211yesmaximal, characteristic, complemented
14#10590269C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83461—31nomaximal
17#82569—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C32×#117C2211yescharacteristic
20C3×#930C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C3×#924C2211yescharacteristic
23C3×#898—21no—
24C3×#896—21no—
25C3×#892—21no—
26C3×D3×C4⋊C4—21no—
27C3×#885—21no—
28C3×#883—21no—
29C3×#67⋊C4—21no—
30C3×#67⋊C4—21no—
31C3×#875C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×#869C2211yescharacteristic
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
47#63630C2211yescharacteristic
48C4×C3⋊(C3⋊C8)C2211yescharacteristic
49#63576C2211yescharacteristic
50#63576C2211yescharacteristic
51#63576C2211yescharacteristic
52#63576C2211yescharacteristic
53#63565C2211yescharacteristic
54#63565C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61C3×#542—31no—
62C3×#520—31no—
63#5534D311yescharacteristic, complemented
64#5523D311yescharacteristic, complemented
65#5239—31no—
66#5238—31no—
67#5091—31no—
68#5087—31no—
69#5057—31no—
70#5054—31no—
71#5047—31no—
72#5044—31no—
73#5037—31no—
74#5033—31no—
75C4×#216—31no—
76C4×#216—31no—
77#5028—31no—
78#5026—31no—
79#5026—31no—
80#5021—31no—
81#5018—31no—
82#5018—31no—
83#5016—31no—
84C4×#213—31no—
85C4×#213—31no—
86#5007—31no—
87#5000—31no—
88#5000—31no—
89#5000—61no—
90#4970—31no—
91#4967—31no—
92C22×C32×C4C2311yescharacteristic
93C2×C3×#67—21no—
94C2×C3×#67—21no—
95C22×C3×Dic3—21no—
96C3×#235—22no—
97C3×#235—22no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C32×C4⋊C4D411yescharacteristic
108C32×C4⋊C4D411yescharacteristic
109C32×C22⋊C4D411yescharacteristic
110C32×C22⋊C4D411yescharacteristic
111C32×C42C2311yescharacteristic
112C32×C42C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—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×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—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#3124—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×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×Q8—31no—
154C3×C4×Q8—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—61no—
162C3×#117C2×D311yescharacteristic
163C3×#117C2×D311yescharacteristic
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—61no—
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
175C2×C4⋊Dic3C2×D311yescharacteristic
176#924C2×D311yescharacteristic
177#898—21no—
178#896—21no—
179#892—21no—
180D3×C4⋊C4—21no—
181#885—21no—
182#883—21no—
183#67⋊C4—21no—
184#67⋊C4—21no—
185#875C2×D311yescharacteristic
186C4×D12C2×D311yescharacteristic
187C4×D12C2×D311yescharacteristic
188C4×D12C2×D311yescharacteristic
189#869C2×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#807—31no—
216#807—31no—
217#807—31no—
218#807—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—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C3×#67—24no—
247C3×#67—81no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12#4112yes—
259C3×C4×D3—24no—
260C3×C4×D3—81no—
261C3×C4×D3—81no—
262C3×C4×D3—81no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—81no—
267C3×Dic6#4112yes—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3⋊(C3⋊C8)—21no—
271C3⋊(C3⋊C8)—21no—
272#542—31no—
273#520—31no—
274#484—91no—
275#480—91no—
276#477—91no—
277#474—91no—
278#464—91no—
279#463—91no—
280#452—91no—
281#449—91no—
282#440—91no—
283#440—91no—
284C4×Q16—91no—
285C4×D8—91no—
286#433—91no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×Q8—61no—
292C2×C3×D4—31no—
293C2×C3×D4—31no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C22×C3×C4—21no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—21no—
305C2×#67—21no—
306C22×Dic3—21no—
307#235—22no—
308#235—22no—
309C2×D12C22×D311yescharacteristic
310C2×D12C22×D311yescharacteristic
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×Dic6—21no—
316C2×Dic6C22×D311yescharacteristic
317C2×Dic6C22×D311yescharacteristic
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
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×C4⋊C4#6711yescharacteristic
331C3×C4⋊C4#6711yescharacteristic
332C3×C4⋊C4#6711yescharacteristic
333C3×C4⋊C4#6711yescharacteristic
334C3×C22⋊C4—21no—
335C3×C22⋊C4—21no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4#6711yescharacteristic
344C3×C22⋊C4#6711yescharacteristic
345C3×C22⋊C4#6711yescharacteristic
346C3×C22⋊C4#6711yescharacteristic
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—61no—
350C3×C42—61no—
351C3×C42—61no—
352C3×C42C22×D311yescharacteristic
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355C3×C42C22×D311yescharacteristic
356#217—21no—
357#216—62no—
358#216—62no—
359#215—62no—
360#215—62no—
361#214—62no—
362#214—62no—
363#213—62no—
364#213—62no—
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—
370(C2×D3)⋊C4—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—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—21no—
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—
424C4⋊Q8—31no—
425#126—61no—
426#124—31no—
427#124—61no—
428#123—61no—
429C22⋊Q8—31no—
430C22⋊Q8—61no—
431#121—31no—
432C4×Q8—31no—
433C4×Q8—31no—
434C4×Q8—31no—
435C4×D4—31no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—61no—
439C4×D4—61no—
440#117—61no—
441#117D3211yescharacteristic
442C2×C4⋊C4—31no—
443C2×C4⋊C4—61no—
444#107—91no—
445#107—91no—
446#107—91no—
447#107—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—
460#97—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×Q8—241no—
474C3×D4—32no—
475C3×D4—64no—
476C3×D4—61no—
477C3×D4—61no—
478C3×D4—61no—
479C3×D4—241no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
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—41no—
491C2×C3×C4—41no—
492C2×C3×C4—64no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—241no—
500C2×C3×C4—241no—
501C2×C3×C4—241no—
502C2×C3×C4—241no—
503C2×C3×C4C2×#6711yescharacteristic
504C2×C3×C4C2×#6711yescharacteristic
505C2×C3×C4C2×#6711yescharacteristic
506C2×C3×C4C2×#6711yescharacteristic
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×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—24no—
516#67—81no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—81no—
524D12—21no—
525D12—21no—
526D12—21no—
527D12#23512yes—
528C4×D3—24no—
529C4×D3—81no—
530C4×D3—81no—
531C4×D3—81no—
532Dic6—21no—
533Dic6—21no—
534Dic6—21no—
535Dic6—81no—
536Dic6#23512yes—
537C3⋊C8—61no—
538C3⋊C8—61no—
539C3⋊C8—61no—
540C3⋊C8—61no—
541C3⋊C8—61no—
542C3⋊C8—61no—
543C3⋊C8—61no—
544C3⋊C8—61no—
545C3⋊C8—121no—
546C3⋊C8—121no—
547C3⋊C8—121no—
548C3⋊C8—121no—
549C2×C32—41no—
550C2×C32#52511yescharacteristic
551C2×C32#57611yescharacteristic
552C2×C32#57811yescharacteristic
553C3×D3—42no—
554C3×D3—81no—
555#41—62no—
556#41—62no—
557C2×Q8—31no—
558C2×Q8—31no—
559C2×Q8—61no—
560C2×D4—31no—
561C2×D4—31no—
562C2×D4—61no—
563C2×D4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4C2×D3211yescharacteristic
570Q16—182no—
571SD16—182no—
572SD16—182no—
573D8—182no—
574C2×C8—91no—
575C2×C8—91no—
576C2×C8—91no—
577C2×C8—91no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4#62511yescharacteristic
589C4⋊C4#62511yescharacteristic
590C22⋊C4—61no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4#62511yescharacteristic
598C22⋊C4#62511yescharacteristic
599C42—61no—
600C42—61no—
601C42—61no—
602C42C2×D3211yescharacteristic
603C42C2×D3211yescharacteristic
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—62no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3C22×#6711yescharacteristic
621C22×C3C22×#6711yescharacteristic
622C2×D3—22no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
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—41no—
641C3×C4—41no—
642C3×C4—41no—
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×C4C2×#23511yescharacteristic
652C3×C4C2×#23511yescharacteristic
653C3×C4D3×#4111yescharacteristic
654C3×C4D3×#4111yescharacteristic
655Dic3—22no—
656Dic3—41no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—41no—
661C32#312411yescharacteristic, complemented, Sylow
662C23—61no—
663C23—61no—
664C23C2×#62511yescharacteristic
665Q8—32no—
666Q8—61no—
667Q8—61no—
668Q8—61no—
669Q8—241no—
670D4—32no—
671D4—64no—
672D4—61no—
673D4—61no—
674D4—61no—
675D4—241no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—64no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—241no—
686C2×C4—241no—
687C2×C4—241no—
688C2×C4—241no—
689C2×C4C2×#62511yescharacteristic
690C2×C4C2×#62511yescharacteristic
691C2×C4C2×#62511yescharacteristic
692C2×C4C2×#62511yescharacteristic
693C2×C4C2×#62511yescharacteristic
694C2×C4C22×D3211yescharacteristic
695C8—181no—
696C8—181no—
697C8—181no—
698C8—181no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—41no—
703C2×C3—41no—
704C2×C3—81no—
705C2×C3—122no—
706C2×C3—241no—
707C2×C3#579111yescharacteristic
708C2×C3#582811yescharacteristic
709C2×C3#583511yescharacteristic
710C2×C3#583511yescharacteristic
711C2×C3#583811yescharacteristic
712C2×C3#583811yescharacteristic
713D3—42no—
714D3—81no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—62no—
719C22—121no—
720C22—121no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22C22×#62511yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—21no—
730C4—62no—
731C4—121no—
732C4—121no—
733C4—121no—
734C4—121no—
735C4—121no—
736C4D3×#23511yescharacteristic
737C4D3×#23511yescharacteristic
738C3—21no—
739C3#8256911yescharacteristic, complemented
740C3#8346111yescharacteristic, complemented
741C2—41no—
742C2—122no—
743C2—241no—
744C2#1059502211yescharacteristic
745C2#1059544411yescharacteristic
746C2#1059544511yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10591161C2
hypercenter#117D32
hypocenterC32#3124
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×#5523C2semidirect
3. #10592699C2semidirect
4. #10591170C2semidirect
6. #10591132C2semidirect
7. #10591089C2semidirect
8. C4×#3718C2semidirect
9. #10590358C2semidirect
10. #10590358C2semidirect
11. #10590348C2semidirect
12. C4×#3713C2semidirect
13. #10590310C2semidirect
14. #10590269C2semidirect
15. #10590267C2semidirect
63. #5534D3semidirect
64. #5523D3semidirect
661. C32#3124semidirect
739. C3#82569semidirect
740. C3#83461semidirect

Maximal subgroups

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

subgroupindex
C3×#55342
C3×#55232
#105926992
#105911702
#105911612
#105911322
#105910892
C4×#37182
#105903582
#105903482
C4×#37132
#105903102
#105902692
#105902672
#834613
#825693