Finite Group Databasebeta

← #10812218

Subgroups — #10812218

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
1#82228C211yesmaximal, characteristic
2C2×#5000C211yesmaximal, characteristic, complemented
3C2×#4727C211yesmaximal, characteristic
4C3×#1818C211yesmaximal, characteristic, complemented
5#69956C211yesmaximal, characteristic
6#69908C211yesmaximal, characteristic, complemented
7#69906C211yesmaximal, characteristic, complemented
8#68667C211yesmaximal, characteristic, complemented
9#68666C211yesmaximal, characteristic, complemented
10#68658C211yesmaximal, characteristic, complemented
11#68657C211yesmaximal, characteristic, complemented
12#68649C211yesmaximal, characteristic, complemented
13#68648C211yesmaximal, characteristic, complemented
14#68616C211yesmaximal, characteristic, complemented
15#68616C211yesmaximal, characteristic, complemented
16#22561—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×#117C2211yescharacteristic
19C22×C4×Dic3C2211yescharacteristic
20C22×ΓL(1,𝔽25)C2211yescharacteristic
21C22×D3×C8C2211yescharacteristic
22C2×C3×C22⋊C8C2211yescharacteristic
23C2×C3×C22⋊C8C2211yescharacteristic
24C2×#830C2211yescharacteristic
25C2×#830C2211yescharacteristic
26C2×(C2×D3)⋊C8C2211yescharacteristic
27C2×(C2×D3)⋊C8C2211yescharacteristic
28C2×(C2×D3)⋊C8C2211yescharacteristic
29C2×(C2×D3)⋊C8C2211yescharacteristic
30C2×(C2×D3)⋊C8C2211yescharacteristic
31C2×(C2×D3)⋊C8C2211yescharacteristic
32C2×#815C2211yescharacteristic
33C2×#815C2211yescharacteristic
34C2×Dic3⋊C8C2211yescharacteristic
35C2×Dic3⋊C8C2211yescharacteristic
36#5000—24no—
37#4988C411yescharacteristic
38#4988C411yescharacteristic
39#4973C411yescharacteristic
40#4973C411yescharacteristic
41#4958C411yescharacteristic
42#4958C411yescharacteristic
43#4958C411yescharacteristic
44#4958C411yescharacteristic
45C4×(C2×D3)⋊C4C2211yescharacteristic
46C4×(C2×D3)⋊C4C2211yescharacteristic
47C4×(C2×D3)⋊C4C2211yescharacteristic
48C4×(C2×D3)⋊C4C2211yescharacteristic
49C2×C4⋊(C3⋊C8)C2211yescharacteristic
50C2×C4⋊(C3⋊C8)C2211yescharacteristic
51C2×#803C2211yescharacteristic
52C2×C4×C3⋊C8C2211yescharacteristic
53#4727—24no—
54C3×#336C2211yescharacteristic
55C3×#336C2211yescharacteristic
56C3×#336C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
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#1818D311yescharacteristic, complemented
72#1797—31no—
73#1780—31no—
74#1753—31no—
75#1752—31no—
76#1749—31no—
77C23×C3×C4C2311yescharacteristic
78C22×#67C2×C411yescharacteristic
79C22×#67C2×C411yescharacteristic
80C23×Dic3C2×C411yescharacteristic
81C23×Dic3C2×C411yescharacteristic
82C2×#235—22no—
83C2×#235—22no—
84C2×#235—22no—
85C2×#235—22no—
86C2×#235—41no—
87C2×#235—41no—
88C22×D12C2×C411yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C22×C4×D3C2311yescharacteristic
91C22×Dic6C2×C411yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×#117—22no—
97C3×#117—22no—
98C2×C3×C4⋊C4C2×C411yescharacteristic
99C2×C3×C4⋊C4C2×C411yescharacteristic
100C2×C3×C22⋊C4C2×C411yescharacteristic
101C2×C3×C22⋊C4C2×C411yescharacteristic
102C2×C3×C42C2311yescharacteristic
103C2×C3×C42C2311yescharacteristic
104C2×(C2×D3)⋊C4C2×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×(C2×D3)⋊C4C2×C411yescharacteristic
112C2×C4×Dic3—41no—
113C2×C4×Dic3—41no—
114C2×C4×Dic3C2×C411yescharacteristic
115C2×C4×Dic3C2×C411yescharacteristic
116C2×C4×Dic3C2311yescharacteristic
117C2×C4×Dic3C2311yescharacteristic
118C22×C3⋊C8C2311yescharacteristic
119C22×C3⋊C8C2311yescharacteristic
120C22×C3⋊C8C2311yescharacteristic
121C22×C3⋊C8C2311yescharacteristic
122C2×ΓL(1,𝔽25)—22no—
123C2×ΓL(1,𝔽25)—22no—
124C2×ΓL(1,𝔽25)—41no—
125C2×D3×C8—22no—
126C2×D3×C8—22no—
127C2×D3×C8—41no—
128C3×C22⋊C8—22no—
129C3×C22⋊C8—22no—
130C3⋊#95C2×C411yescharacteristic
131C3⋊#95C2×C411yescharacteristic
132C3⋊#95C2×C411yescharacteristic
133C3⋊#95C2×C411yescharacteristic
134C3⋊#95C2×C411yescharacteristic
135C3⋊#95C2×C411yescharacteristic
136C3⋊#95C2×C411yescharacteristic
137C3⋊#95C2×C411yescharacteristic
138#830—22no—
139#830D414yes—
140(C2×D3)⋊C8—22no—
141(C2×D3)⋊C8—22no—
142(C2×D3)⋊C8—22no—
143(C2×D3)⋊C8—22no—
144(C2×D3)⋊C8—41no—
145(C2×D3)⋊C8—41no—
146#815—41no—
147#815—41no—
148Dic3⋊C8—41no—
149Dic3⋊C8—41no—
150C4⋊(C3⋊C8)—22no—
151C4⋊(C3⋊C8)—22no—
152#803—22no—
153C4×C3⋊C8—22no—
154C22×#41—31no—
155C22×M16—31no—
156C23×C8—31no—
157C2×#117C2×D311yescharacteristic
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⋊C8C2×D311yescharacteristic
174C2×C22⋊C8C2×D311yescharacteristic
175C2×#97—31no—
176C2×#97—31no—
177C2×#97—31no—
178C2×C4×C8—31no—
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⋊C4—31no—
191#336—31no—
192#336—31no—
193#336—31no—
194#336—31no—
195#336C2×D311yescharacteristic
196#336C2×D311yescharacteristic
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×C4C2×D412yes—
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×Dic3—22no—
221C22×Dic3—41no—
222C22×Dic3—41no—
223C22×Dic3—41no—
224C22×Dic3—41no—
225C22×Dic3—41no—
226C22×Dic3C22×C411yescharacteristic
227C22×Dic3C22×C411yescharacteristic
228C22×Dic3C22×C411yescharacteristic
229C22×Dic3C22×C411yescharacteristic
230C22×Dic3C22×C411yescharacteristic
231C22×Dic3C22×C411yescharacteristic
232#235—44no—
233#235—44no—
234#235—44no—
235#235—44no—
236C2×D12—22no—
237C2×D12—22no—
238C2×D12—41no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3#4112yes—
250C2×C4×D3#4112yes—
251C2×Dic6—22no—
252C2×Dic6—22no—
253C2×Dic6—41no—
254C2×C3×C8—21no—
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—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—22no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—22no—
270C3×C42—21no—
271C3×C42—21no—
272C3×C42—21no—
273C3×C42—21no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—41no—
277(C2×D3)⋊C4—41no—
278(C2×D3)⋊C4—41no—
279(C2×D3)⋊C4—41no—
280(C2×D3)⋊C4—41no—
281(C2×D3)⋊C4—41no—
282C4×Dic3—21no—
283C4×Dic3—21no—
284C4×Dic3—21no—
285C4×Dic3—21no—
286C4×Dic3—41no—
287C4×Dic3—41no—
288C2×C3⋊C8—21no—
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⋊C8C2×D412yes—
299C2×C3⋊C8C2×D412yes—
300ΓL(1,𝔽25)—44no—
301D3×C8—44no—
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—62no—
318C2×M16—62no—
319C2×M16—121no—
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—22no—
332#117—22no—
333C2×C4⋊C4C4×D311yescharacteristic
334C2×C4⋊C4C4×D311yescharacteristic
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—22no—
359C22⋊C8—34no—
360C22⋊C8—62no—
361C22⋊C8—62no—
362C22⋊C8—62no—
363C22⋊C8—62no—
364C22⋊C8—62no—
365C22⋊C8—121no—
366C22⋊C8—121no—
367#97—62no—
368#97—121no—
369#97—121no—
370C4×C8—62no—
371#95—31no—
372#95—31no—
373#95—31no—
374#95—31no—
375#95—31no—
376#95—31no—
377#95—31no—
378#95—31no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3C4×D412yes—
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×D3#11712yes—
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×C4C4×D412yes—
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×Dic3—44no—
445C2×Dic3—44no—
446C2×Dic3#11712yes—
447C2×Dic3#13112yes—
448D12—44no—
449C4×D3—22no—
450C4×D3—22no—
451C4×D3—22no—
452C4×D3—22no—
453C4×D3—41no—
454C4×D3—41no—
455C4×D3—41no—
456C4×D3—41no—
457Dic6—44no—
458C3×C8—41no—
459C3×C8—41no—
460C3×C8—41no—
461C3×C8—41no—
462C3⋊C8—22no—
463C3⋊C8—22no—
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×C4D3×D412yes—
519C22×C4#23712yes—
520C22×C4C23×D311yescharacteristic
521M16—124no—
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—21no—
534C2×C8—32no—
535C2×C8—32no—
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—61no—
546C2×C8—124no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—62no—
552C22⋊C4—62no—
553C22⋊C4—121no—
554C22⋊C4—121no—
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#67⋊C412yes—
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#67⋊C412yes—
685C2×C4C2×D3×D411yescharacteristic
686C2×C4C2×#23711yescharacteristic
687C2×C4D3×#4111yescharacteristic
688C2×C4D3×#4111yescharacteristic
689C2×C4#100911yescharacteristic
690C2×C4#100911yescharacteristic
691C8—41no—
692C8—41no—
693C8—41no—
694C8—41no—
695C8—62no—
696C8—62no—
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×#67⋊C411yescharacteristic
731C22D3×#11711yescharacteristic
732C22#552111yescharacteristic
733C22D3×#13111yescharacteristic
734C22#575011yescharacteristic
735C22#575011yescharacteristic
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#565411yescharacteristic
749C4#565411yescharacteristic
750C4#565811yescharacteristic
751C4#565811yescharacteristic
752C3#2256111yescharacteristic, complemented, Sylow
753C2—42no—
754C2—122no—
755C2—241no—
756C2#7412211yescharacteristic
757C2#7865811yescharacteristic
758C2#7866011yescharacteristic
759C2#7937311yescharacteristic
760C2#7937511yescharacteristic
761C2#7937611yescharacteristic
762C2#7937811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1818C2
prime radicalC22×#235C22
cosocleC22×C3×C4C24
hypercenter#1818D3
hypocenterC3#22561
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
2. C2×#5000C2semidirect
4. C3×#1818C2semidirect
6. #69908C2semidirect
7. #69906C2semidirect
8. #68667C2semidirect
9. #68666C2semidirect
10. #68658C2semidirect
11. #68657C2semidirect
12. #68649C2semidirect
13. #68648C2semidirect
14. #68616C2semidirect
15. #68616C2semidirect
71. #1818D3semidirect
752. C3#22561semidirect

Maximal subgroups

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

subgroupindex
#822282
C2×#50002
C2×#47272
C3×#18182
#699562
#699082
#699062
#686672
#686662
#686582
#686572
#686492
#686482
#686162
#225613