Finite Group Databasebeta

← #10812219

Subgroups — #10812219

Order 768.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5129C211yesmaximal, characteristic
2C2×#4690C211yesmaximal, characteristic, complemented
3#73563C211yesmaximal, characteristic
4C3×#1753C211yesmaximal, characteristic, complemented
5#71995C211yesmaximal, characteristic, complemented
6#69956C211yesmaximal, characteristic
7#69950C211yesmaximal, characteristic, complemented
8#69835C211yesmaximal, characteristic, complemented
9#69807C211yesmaximal, characteristic, complemented
10#69785C211yesmaximal, characteristic, complemented
11#69447C211yesmaximal, characteristic, complemented
12#68665C211yesmaximal, characteristic, complemented
13#68662C211yesmaximal, characteristic, complemented
14#68658C211yesmaximal, characteristic, complemented
15#68658C211yesmaximal, characteristic, complemented
16#22561—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C23×C3⋊C8C2211yescharacteristic
20C2×#872C2211yescharacteristic
21C2×C42×D3C2211yescharacteristic
22C2×C3×C22⋊C8C2211yescharacteristic
23C2×C3×#97C2211yescharacteristic
24C2×C3×C4×C8C2211yescharacteristic
25C3×C4×C22⋊C4C2211yescharacteristic
26C4×#217C2211yescharacteristic
27C2×#830C2211yescharacteristic
28#5129—24no—
29C2×(C2×D3)⋊C8C2211yescharacteristic
30C2×(C2×D3)⋊C8C2211yescharacteristic
31C2×(C2×D3)⋊C8C2211yescharacteristic
32C2×(C2×D3)⋊C8C2211yescharacteristic
33C2×(C2×D3)⋊C8C2211yescharacteristic
34C2×(C2×D3)⋊C8C2211yescharacteristic
35C2×(C2×D3)⋊C8C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×Dic3⋊C8C2211yescharacteristic
38C2×Dic3⋊C8C2211yescharacteristic
39C2×Dic3⋊C8C2211yescharacteristic
40C2×Dic3⋊C8C2211yescharacteristic
41#4957C411yescharacteristic
42#4957C411yescharacteristic
43#4956C411yescharacteristic
44#4956C411yescharacteristic
45C4×(C2×D3)⋊C4C2211yescharacteristic
46C4×(C2×D3)⋊C4C2211yescharacteristic
47C2×#803C2211yescharacteristic
48C2×#803C2211yescharacteristic
49#4690—24no—
50#4665C411yescharacteristic
51#4665C411yescharacteristic
52#4646C411yescharacteristic
53#4646C411yescharacteristic
54C3×#336C2211yescharacteristic
55C3×#336C2211yescharacteristic
56#4550C2211yescharacteristic
57#4550C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4524C2211yescharacteristic
61#4524C2211yescharacteristic
62C2×#433—31no—
63C2×#408—31no—
64#2297—31no—
65#1924—31no—
66#1924—31no—
67#1924—31no—
68#1923—31no—
69#1851—31no—
70#1850—31no—
71#1818—31no—
72#1797—31no—
73#1780—31no—
74#1753D311yescharacteristic, complemented
75#1752—31no—
76#1749—31no—
77C23×C3×C4C2311yescharacteristic
78C22×#67C2×C411yescharacteristic
79C22×#67C2×C411yescharacteristic
80C2×#235—22no—
81C2×#235—22no—
82C2×#235—22no—
83C2×#235—22no—
84C2×#235—41no—
85C2×#235—41no—
86C22×D12C2×C411yescharacteristic
87C22×C4×D3C2×C411yescharacteristic
88C22×C4×D3C2×C411yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C22×C4×D3C2311yescharacteristic
91C22×Dic6C2×C411yescharacteristic
92C2×C3×M16—22no—
93C2×C3×M16—22no—
94C2×C3×M16—41no—
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C2×C3×C22⋊C4C2×C411yescharacteristic
100C2×C3×C22⋊C4C2×C411yescharacteristic
101C2×C3×C42C2311yescharacteristic
102C2×C3×C42C2311yescharacteristic
103C2×#217C2×C411yescharacteristic
104C2×#217C2×C411yescharacteristic
105C2×(C2×D3)⋊C4C2×C411yescharacteristic
106C2×(C2×D3)⋊C4C2×C411yescharacteristic
107C2×(C2×D3)⋊C4C2×C411yescharacteristic
108C2×(C2×D3)⋊C4C2×C411yescharacteristic
109C2×(C2×D3)⋊C4C2×C411yescharacteristic
110C2×(C2×D3)⋊C4C2×C411yescharacteristic
111C2×Dic3⋊C4C2×C411yescharacteristic
112C2×Dic3⋊C4C2×C411yescharacteristic
113C2×C4×Dic3C2×C411yescharacteristic
114C2×C4×Dic3C2×C411yescharacteristic
115C2×C4×Dic3C2311yescharacteristic
116C2×C4×Dic3C2311yescharacteristic
117C22×C3⋊C8—22no—
118C22×C3⋊C8—22no—
119C22×C3⋊C8—41no—
120C22×C3⋊C8C2311yescharacteristic
121C22×C3⋊C8C2311yescharacteristic
122C22×C3⋊C8C2311yescharacteristic
123C22×C3⋊C8C2311yescharacteristic
124#872—22no—
125#872—22no—
126C42×D3—41no—
127C42×D3—41no—
128C3×C22⋊C8—22no—
129C3×#97—41no—
130C3×C4×C8—22no—
131C3×#95C2×C411yescharacteristic
132C3×#95C2×C411yescharacteristic
133C3⋊#95C2×C411yescharacteristic
134C3⋊#95C2×C411yescharacteristic
135C3⋊#95C2×C411yescharacteristic
136C3⋊#95C2×C411yescharacteristic
137C3⋊#95C2×C411yescharacteristic
138C3⋊#95C2×C411yescharacteristic
139#830—22no—
140(C2×D3)⋊C8—22no—
141(C2×D3)⋊C8—22no—
142(C2×D3)⋊C8—22no—
143(C2×D3)⋊C8—22no—
144(C2×D3)⋊C8—22no—
145(C2×D3)⋊C8—41no—
146(C2×D3)⋊C8—41no—
147(C2×D3)⋊C8D414yes—
148Dic3⋊C8—22no—
149Dic3⋊C8—22no—
150Dic3⋊C8—41no—
151Dic3⋊C8—41no—
152#803—22no—
153#803—41no—
154C22×#41—31no—
155C22×M16C2×D311yescharacteristic
156C23×C8—31no—
157C2×#117—31no—
158C22×C42—31no—
159#433—64no—
160C2×C4⋊C8—31no—
161C2×C4⋊C8—31no—
162C2×C4⋊C8—31no—
163C2×C4⋊C8—31no—
164#408—64no—
165C2×C22⋊C8—31no—
166C2×C22⋊C8—31no—
167C2×C22⋊C8—31no—
168C2×C22⋊C8—31no—
169C2×C22⋊C8—31no—
170C2×C22⋊C8—31no—
171C2×C22⋊C8—31no—
172C2×C22⋊C8—31no—
173C2×C22⋊C8—31no—
174C2×C22⋊C8C2×D311yescharacteristic
175C2×#97—31no—
176C2×#97—31no—
177C2×#97C2×D311yescharacteristic
178C2×C4×C8C2×D311yescharacteristic
179#391—31no—
180#391—31no—
181#390—31no—
182#390—31no—
183#386—31no—
184#386—31no—
185#386—31no—
186#386—31no—
187C4×C22⋊C4—31no—
188C4×C22⋊C4—31no—
189C4×C22⋊C4—31no—
190C4×C22⋊C4C2×D311yescharacteristic
191#336—31no—
192#336—31no—
193#336—31no—
194#336—31no—
195#336—31no—
196#336—31no—
197#336C2×D311yescharacteristic
198#336C2×D311yescharacteristic
199C24×C3C22×C411yescharacteristic
200C23×D3C22×C411yescharacteristic
201C23×D3C22×C411yescharacteristic
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4C22×C411yescharacteristic
207C22×C3×C4C22×C411yescharacteristic
208C22×C3×C4C22×C411yescharacteristic
209C22×C3×C4C22×C411yescharacteristic
210C22×C3×C4C22×C411yescharacteristic
211C22×C3×C4#4112yes—
212C22×C3×C4#4112yes—
213C22×C3×C4C2411yescharacteristic
214C2×#67—22no—
215C2×#67—22no—
216C2×#67—22no—
217C2×#67—22no—
218C2×#67—41no—
219C2×#67—41no—
220C22×Dic3C22×C411yescharacteristic
221C22×Dic3C22×C411yescharacteristic
222C22×Dic3C22×C411yescharacteristic
223C22×Dic3C22×C411yescharacteristic
224C22×Dic3C22×C411yescharacteristic
225C22×Dic3C22×C411yescharacteristic
226#235—44no—
227#235—44no—
228#235—44no—
229#235—44no—
230C2×D12—22no—
231C2×D12—22no—
232C2×D12—41no—
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3—21no—
236C2×C4×D3—21no—
237C2×C4×D3—21no—
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—22no—
244C2×C4×D3—41no—
245C2×C4×D3—41no—
246C2×C4×D3—41no—
247C2×C4×D3—41no—
248C2×C4×D3—41no—
249C2×C4×D3C2×D412yes—
250C2×C4×D3#4112yes—
251C2×Dic6—22no—
252C2×Dic6—22no—
253C2×Dic6—41no—
254C3×M16—44no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8C2×D412yes—
267C3×C22⋊C4—41no—
268C3×C22⋊C4—41no—
269C3×C42—21no—
270C3×C42—21no—
271C3×C42—21no—
272C3×C42—21no—
273#217—22no—
274#217—41no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—41no—
279(C2×D3)⋊C4—41no—
280(C2×D3)⋊C4—41no—
281Dic3⋊C4—22no—
282Dic3⋊C4—22no—
283C4×Dic3—21no—
284C4×Dic3—21no—
285C4×Dic3—21no—
286C4×Dic3—21no—
287C4×Dic3—41no—
288C4×Dic3—41no—
289C2×C3⋊C8—21no—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—21no—
292C2×C3⋊C8—21no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—44no—
301C2×C3⋊C8C2×D412yes—
302C2×#41—62no—
303C2×#41—62no—
304C2×#41—62no—
305C2×#41—62no—
306C2×#41—121no—
307C2×#41—121no—
308C22×Q8—31no—
309C22×D4—31no—
310C22×D4—31no—
311C22×D4—31no—
312C23×C4—31no—
313C23×C4—31no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4C22×D311yescharacteristic
317C2×M16—22no—
318C2×M16—22no—
319C2×M16—41no—
320C22×C8—31no—
321C22×C8—31no—
322C22×C8—31no—
323C22×C8—31no—
324C22×C8—62no—
325C22×C8—62no—
326C22×C8—121no—
327C22×C8C22×D311yescharacteristic
328C22×C8C22×D311yescharacteristic
329C22×C8C22×D311yescharacteristic
330C22×C8C22×D311yescharacteristic
331#117—62no—
332#117—62no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—31no—
335C2×C22⋊C4—31no—
336C2×C22⋊C4—31no—
337C2×C22⋊C4—31no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—31no—
340C2×C22⋊C4—31no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—31no—
343C2×C22⋊C4C4×D311yescharacteristic
344C2×C22⋊C4C4×D311yescharacteristic
345C2×C42—31no—
346C2×C42—31no—
347C2×C42—31no—
348C2×C42—31no—
349C2×C42—121no—
350C2×C42—121no—
351C2×C42C22×D311yescharacteristic
352C2×C42C22×D311yescharacteristic
353C4⋊C8—62no—
354C4⋊C8—62no—
355C4⋊C8—121no—
356C4⋊C8—121no—
357C22⋊C8—22no—
358C22⋊C8—34no—
359C22⋊C8—62no—
360C22⋊C8—62no—
361C22⋊C8—62no—
362C22⋊C8—62no—
363C22⋊C8—62no—
364C22⋊C8—62no—
365C22⋊C8—121no—
366C22⋊C8—121no—
367#97—41no—
368#97—62no—
369#97—121no—
370C4×C8—22no—
371#95—31no—
372#95—31no—
373#95—31no—
374#95—31no—
375#95—31no—
376#95—31no—
377#95C4×D311yescharacteristic
378#95C4×D311yescharacteristic
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3#11712yes—
386C23×C3C23×C411yescharacteristic
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3C4×D412yes—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4#11712yes—
420C2×C3×C4C22×D411yescharacteristic
421C2×C3×C4C2×#4111yescharacteristic
422C2×C3×C4C2×#4111yescharacteristic
423C2×C3×C4C2×#4111yescharacteristic
424C2×C3×C4H(5,𝔽2)11yescharacteristic
425C2×C3×C4H(5,𝔽2)11yescharacteristic
426#67—44no—
427#67—44no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3C4×D412yes—
445C2×Dic3#13112yes—
446D12—44no—
447C4×D3—22no—
448C4×D3—22no—
449C4×D3—22no—
450C4×D3—22no—
451C4×D3—44no—
452C4×D3—44no—
453C4×D3—41no—
454C4×D3—41no—
455C4×D3—41no—
456C4×D3—41no—
457Dic6—44no—
458C3×C8—22no—
459C3×C8—41no—
460C3×C8—41no—
461C3×C8—41no—
462C3⋊C8—22no—
463C3⋊C8—41no—
464C3⋊C8—41no—
465C3⋊C8—41no—
466C24—31no—
467C24—31no—
468C24C2×C4×D311yescharacteristic
469#41—124no—
470#41—124no—
471#41—124no—
472#41—124no—
473C2×Q8—62no—
474C2×Q8—62no—
475C2×Q8—121no—
476C2×D4—62no—
477C2×D4—62no—
478C2×D4—62no—
479C2×D4—62no—
480C2×D4—62no—
481C2×D4—62no—
482C2×D4—121no—
483C2×D4—121no—
484C2×D4—121no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4—32no—
492C22×C4—32no—
493C22×C4—31no—
494C22×C4—31no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—62no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—121no—
509C22×C4—121no—
510C22×C4—121no—
511C22×C4—121no—
512C22×C4—121no—
513C22×C4C2×C4×D311yescharacteristic
514C22×C4C2×C4×D311yescharacteristic
515C22×C4C2×C4×D311yescharacteristic
516C22×C4C2×C4×D311yescharacteristic
517C22×C4C2×C4×D311yescharacteristic
518C22×C4#23512yes—
519C22×C4#23512yes—
520C22×C4C23×D311yescharacteristic
521M16—44no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—32no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8—124no—
546C2×C8D3×D412yes—
547C4⋊C4—62no—
548C4⋊C4—62no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—62no—
552C22⋊C4—62no—
553C22⋊C4—62no—
554C22⋊C4—62no—
555C22⋊C4—121no—
556C22⋊C4—121no—
557C22⋊C4—121no—
558C22⋊C4—121no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—61no—
564C42—61no—
565C42—61no—
566C42—61no—
567C42—121no—
568C42—121no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3C2×#11711yescharacteristic
577C22×C3C2×C4×D411yescharacteristic
578C22×C3#51811yescharacteristic
579C22×C3C2×#13111yescharacteristic
580C22×C3#56811yescharacteristic
581C22×C3#56811yescharacteristic
582C22×C3#56811yescharacteristic
583C2×D3—22no—
584C2×D3—22no—
585C2×D3—22no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C2×D3—41no—
595C2×D3—41no—
596C2×D3—41no—
597C3×C4—22no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4#54611yescharacteristic
603C3×C4#54611yescharacteristic
604C3×C4#55111yescharacteristic
605C3×C4#55111yescharacteristic
606Dic3—22no—
607Dic3—22no—
608Dic3—41no—
609Dic3—41no—
610Dic3—41no—
611Dic3—41no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—32no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23—61no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23#87212yes—
633C23C22×C4×D311yescharacteristic
634Q8—124no—
635D4—124no—
636D4—124no—
637D4—124no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—124no—
679C2×C4—124no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4#87212yes—
685C2×C4C2×#23511yescharacteristic
686C2×C4C2×#23511yescharacteristic
687C2×C4C2×D3×D411yescharacteristic
688C2×C4#100411yescharacteristic
689C2×C4D3×#4111yescharacteristic
690C2×C4#100911yescharacteristic
691C8—22no—
692C8—41no—
693C8—41no—
694C8—41no—
695C8—62no—
696C8—121no—
697C8—121no—
698C8—121no—
699C2×C3—42no—
700C2×C3#234211yescharacteristic
701C2×C3#292311yescharacteristic
702C2×C3#292511yescharacteristic
703C2×C3#293211yescharacteristic
704C2×C3#293511yescharacteristic
705C2×C3#297611yescharacteristic
706C2×C3#297811yescharacteristic
707D3—42no—
708D3—81no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—62no—
717C22—62no—
718C22—62no—
719C22—121no—
720C22—121no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22—121no—
725C22—121no—
726C22—121no—
727C22—121no—
728C22—121no—
729C22—121no—
730C22C2×#87211yescharacteristic
731C22C4×D3×D411yescharacteristic
732C22#554511yescharacteristic
733C22#574511yescharacteristic
734C22#574511yescharacteristic
735C22D3×#13111yescharacteristic
736C22#575011yescharacteristic
737C4—22no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—62no—
743C4—62no—
744C4—121no—
745C4—121no—
746C4—121no—
747C4—121no—
748C4#549011yescharacteristic
749C4#552711yescharacteristic
750C4#555011yescharacteristic
751C4#555611yescharacteristic
752C3#2256111yescharacteristic, complemented, Sylow
753C2—42no—
754C2—122no—
755C2—241no—
756C2#7357411yescharacteristic
757C2#7852011yescharacteristic
758C2#7855211yescharacteristic
759C2#7948011yescharacteristic
760C2#7948411yescharacteristic
761C2#7954411yescharacteristic
762C2#7954511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1753C2
prime radicalC22×#235C22
cosocleC22×C3×C4C24
hypercenter#1753D3
hypocenterC3#22561
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×#4690C2semidirect
4. C3×#1753C2semidirect
5. #71995C2semidirect
7. #69950C2semidirect
8. #69835C2semidirect
9. #69807C2semidirect
10. #69785C2semidirect
11. #69447C2semidirect
12. #68665C2semidirect
13. #68662C2semidirect
14. #68658C2semidirect
15. #68658C2semidirect
74. #1753D3semidirect
752. C3#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#51292
C2×#46902
#735632
C3×#17532
#719952
#699562
#699502
#698352
#698072
#697852
#694472
#686652
#686622
#686582
#225613