Finite Group Databasebeta

← #10812201

Subgroups — #10812201

Order 768.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5126C211yesmaximal, characteristic
2C2×#4840C211yesmaximal, characteristic, complemented
3#73561C211yesmaximal, characteristic
4C3×#1851C211yesmaximal, characteristic, complemented
5#71983C211yesmaximal, characteristic, complemented
6#70476C211yesmaximal, characteristic, complemented
7#70449C211yesmaximal, characteristic, complemented
8#70449C211yesmaximal, characteristic, complemented
9#69955C211yesmaximal, characteristic
10#69949C211yesmaximal, characteristic, complemented
11#69450C211yesmaximal, characteristic, complemented
12#68665C211yesmaximal, characteristic, complemented
13#68616C211yesmaximal, characteristic, complemented
14#68616C211yesmaximal, characteristic, complemented
15#68601C211yesmaximal, characteristic, complemented
16#22559—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C22×#208C2211yescharacteristic
20C2×#872C2211yescharacteristic
21C2×#872C2211yescharacteristic
22C2×C3×C4⋊C8C2211yescharacteristic, complemented
23C2×C3×C4⋊C8C2211yescharacteristic, complemented
24C2×C3×C22⋊C8C2211yescharacteristic
25C3×C4×C22⋊C4C2211yescharacteristic
26C4×#217C2211yescharacteristic
27C2×#830C2211yescharacteristic
28#5126—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×#815C2211yescharacteristic, complemented
38C2×#815C2211yescharacteristic, complemented
39C2×C8×Dic3C2211yescharacteristic, complemented
40C2×C8×Dic3C2211yescharacteristic, complemented
41#4955C411yescharacteristic
42#4955C411yescharacteristic
43#4942C411yescharacteristic
44#4942C411yescharacteristic
45C4×(C2×D3)⋊C4C2211yescharacteristic
46C4×(C2×D3)⋊C4C2211yescharacteristic
47C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
48C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
49#4840—24no—
50#4667C411yescharacteristic
51#4667C411yescharacteristic
52#4664C411yescharacteristic
53#4664C411yescharacteristic
54C3×#336C2211yescharacteristic, complemented
55C3×#336C2211yescharacteristic, complemented
56#4550C2211yescharacteristic, complemented
57#4550C2211yescharacteristic, complemented
58#4550C2211yescharacteristic, complemented
59#4550C2211yescharacteristic, complemented
60#4524C2211yescharacteristic, complemented
61#4524C2211yescharacteristic, complemented
62C2×#433—31no—
63C2×#407—31no—
64#2280—31no—
65#1924—31no—
66#1924—31no—
67#1923—31no—
68#1923—31no—
69#1851—31no—
70#1851D311yescharacteristic, complemented
71#1818—31no—
72#1798—31no—
73#1779—31no—
74#1753—31no—
75#1753—31no—
76#1750—31no—
77C24×D3C2×C411yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×Dic3C2×C411yescharacteristic
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3—22no—
84C22×C4×D3—41no—
85C22×C4×D3—41no—
86C22×C4×D3C2×C411yescharacteristic
87C22×C4×D3C2×C411yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C2×C3×M16—22no—
91C2×C3×M16—22no—
92C2×C3×M16—41no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C2×C3×C22⋊C4C2×C411yescharacteristic
98C2×C3×C22⋊C4C2×C411yescharacteristic
99C2×C3×C42C2311yescharacteristic
100C2×C3×C42C2311yescharacteristic
101C2×#217C2×C411yescharacteristic
102C2×#217C2×C411yescharacteristic
103C2×(C2×D3)⋊C4C2×C411yescharacteristic
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×Dic3⋊C4C2×C411yescharacteristic
112C2×Dic3⋊C4C2×C411yescharacteristic
113C2×Dic3⋊C4C2×C411yescharacteristic
114C2×Dic3⋊C4C2×C411yescharacteristic
115C2×C4×Dic3C2311yescharacteristic
116C2×C4×Dic3C2311yescharacteristic
117C2×#208—22no—
118C2×#208—22no—
119C2×#208—41no—
120C22×C3⋊C8C2311yescharacteristic
121C22×C3⋊C8C2311yescharacteristic
122C22×C3⋊C8C2311yescharacteristic
123C22×C3⋊C8C2311yescharacteristic
124#872—22no—
125#872—22no—
126#872—41no—
127#872—41no—
128C3×C4⋊C8—22no—
129C3×C4⋊C8—41no—
130C3×C22⋊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—
148#815—22no—
149#815—41no—
150C8×Dic3—22no—
151C8×Dic3—41no—
152C4⋊(C3⋊C8)—22no—
153C4⋊(C3⋊C8)—41no—
154C24×C4—31no—
155C22×M16—31no—
156C22×M16C2×D311yescharacteristic
157C2×#117—31no—
158C2×#117—31no—
159#433—64no—
160C2×C4⋊C8—31no—
161C2×C4⋊C8—31no—
162C2×C4⋊C8C2×D311yescharacteristic, complemented
163C2×C4⋊C8C2×D311yescharacteristic, complemented
164#407—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×C4×C8—31no—
178C2×C4×C8—31no—
179#381—31no—
180#381—31no—
181#380—31no—
182#380—31no—
183#380—31no—
184#380—31no—
185#379—31no—
186#379—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, complemented
198#336C2×D311yescharacteristic, complemented
199C24×C3C22×C411yescharacteristic
200C23×D3—22no—
201C23×D3—22no—
202C23×D3—22no—
203C23×D3—41no—
204C23×D3—41no—
205C23×D3—41no—
206C23×D3—41no—
207C23×D3C22×C411yescharacteristic
208C23×D3C22×C411yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4C22×C411yescharacteristic
214C22×C3×C4C22×C411yescharacteristic
215C22×C3×C4C22×C411yescharacteristic
216C22×C3×C4C22×C411yescharacteristic
217C22×C3×C4C22×C411yescharacteristic
218C22×C3×C4#4112yes—
219C22×C3×C4#4112yes—
220C22×C3×C4C2411yescharacteristic
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—41no—
224C22×Dic3C22×C411yescharacteristic
225C22×Dic3C22×C411yescharacteristic
226C22×Dic3C22×C411yescharacteristic
227C22×Dic3C22×C411yescharacteristic
228C22×Dic3C22×C411yescharacteristic
229C22×Dic3C22×C411yescharacteristic
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—22no—
235C2×C4×D3—22no—
236C2×C4×D3—22no—
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—44no—
245C2×C4×D3—44no—
246C2×C4×D3—44no—
247C2×C4×D3—44no—
248C2×C4×D3—41no—
249C2×C4×D3—41no—
250C2×C4×D3C2×D412yes—
251C2×C4×D3#4112yes—
252C3×M16—44no—
253C2×C3×C8—21no—
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×C8C2×D412yes—
265C3×C22⋊C4—41no—
266C3×C22⋊C4—41no—
267C3×C42—21no—
268C3×C42—21no—
269C3×C42—21no—
270C3×C42—21no—
271#217—41no—
272#217—41no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—41no—
278(C2×D3)⋊C4—41no—
279(C2×D3)⋊C4—41no—
280(C2×D3)⋊C4—41no—
281Dic3⋊C4—22no—
282Dic3⋊C4—22no—
283Dic3⋊C4—41no—
284Dic3⋊C4—41no—
285C4×Dic3—21no—
286C4×Dic3—21no—
287C4×Dic3—21no—
288C4×Dic3—21no—
289#208—44no—
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—21no—
301C2×C3⋊C8C2×D412yes—
302C25—31no—
303C23×C4—31no—
304C23×C4—31no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—62no—
309C23×C4—62no—
310C23×C4—62no—
311C23×C4—62no—
312C23×C4—121no—
313C23×C4—121no—
314C23×C4C22×D311yescharacteristic
315C2×M16—22no—
316C2×M16—22no—
317C2×M16—41no—
318C2×M16—62no—
319C2×M16—62no—
320C2×M16—121no—
321C22×C8—31no—
322C22×C8—31no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8C22×D311yescharacteristic
326C22×C8C22×D311yescharacteristic
327C22×C8C22×D311yescharacteristic
328C22×C8C22×D311yescharacteristic
329#117—62no—
330#117—62no—
331#117—121no—
332#117—121no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊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⋊C4—31no—
344C2×C22⋊C4—31no—
345C2×C22⋊C4—31no—
346C2×C22⋊C4—31no—
347C2×C22⋊C4C4×D311yescharacteristic
348C2×C22⋊C4C4×D311yescharacteristic
349C2×C42—31no—
350C2×C42—31no—
351C2×C42C22×D311yescharacteristic
352C2×C42C22×D311yescharacteristic
353C4⋊C8—22no—
354C4⋊C8—41no—
355C4⋊C8—62no—
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—62no—
368#97—121no—
369C4×C8—62no—
370C4×C8—121no—
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—44no—
400C22×D3—44no—
401C22×D3—44no—
402C22×D3—44no—
403C22×D3—44no—
404C22×D3—44no—
405C22×D3—44no—
406C22×D3C4×D412yes—
407C22×D3#13112yes—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4#11712yes—
427C2×C3×C4C22×D411yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430C2×C3×C4C2×#4111yescharacteristic
431C2×C3×C4H(5,𝔽2)11yescharacteristic
432C2×C3×C4H(5,𝔽2)11yescharacteristic
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—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—44no—
451C2×Dic3C4×D412yes—
452C4×D3—22no—
453C4×D3—22no—
454C4×D3—22no—
455C4×D3—22no—
456C4×D3—44no—
457C4×D3—44no—
458C4×D3—41no—
459C4×D3—41no—
460C4×D3—41no—
461C4×D3—41no—
462C3×C8—22no—
463C3×C8—41no—
464C3×C8—41no—
465C3×C8—41no—
466C3⋊C8—22no—
467C3⋊C8—41no—
468C3⋊C8—41no—
469C3⋊C8—41no—
470C24—31no—
471C24—31no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—121no—
476C24—121no—
477C24—121no—
478C24—121no—
479C24C2×C4×D311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—31no—
485C22×C4—32no—
486C22×C4—32no—
487C22×C4—31no—
488C22×C4—31no—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4—31no—
492C22×C4—62no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
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—124no—
511C22×C4—124no—
512C22×C4—124no—
513C22×C4—124no—
514C22×C4—121no—
515C22×C4C2×C4×D311yescharacteristic
516C22×C4C2×C4×D311yescharacteristic
517C22×C4C2×C4×D311yescharacteristic
518C22×C4C2×C4×D311yescharacteristic
519C22×C4C2×C4×D311yescharacteristic
520C22×C4#23712yes—
521C22×C4#23912yes—
522C22×C4C23×D311yescharacteristic
523M16—44no—
524M16—124no—
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—21no—
535C2×C8—21no—
536C2×C8—32no—
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—61no—
547C2×C8—61no—
548C2×C8D3×D412yes—
549C4⋊C4—62no—
550C4⋊C4—62no—
551C4⋊C4—121no—
552C4⋊C4—121no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C22⋊C4—62no—
556C22⋊C4—62no—
557C22⋊C4—62no—
558C22⋊C4—62no—
559C22⋊C4—121no—
560C22⋊C4—121no—
561C22⋊C4—121no—
562C22⋊C4—121no—
563C22⋊C4—121no—
564C22⋊C4—121no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—61no—
570C42—61no—
571C42—61no—
572C42—61no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3C2×#11711yescharacteristic
581C22×C3C2×C4×D411yescharacteristic
582C22×C3#51811yescharacteristic
583C22×C3C2×#13111yescharacteristic
584C22×C3#56811yescharacteristic
585C22×C3#56811yescharacteristic
586C22×C3#56811yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—22no—
592C2×D3—22no—
593C2×D3—416no—
594C2×D3—41no—
595C2×D3—41no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
599C2×D3—41no—
600C2×D3—41no—
601C2×D3—41no—
602C3×C4—22no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4#54611yescharacteristic
608C3×C4#54611yescharacteristic
609C3×C4#55111yescharacteristic
610C3×C4#55111yescharacteristic
611Dic3—22no—
612Dic3—41no—
613Dic3—41no—
614Dic3—41no—
615Dic3—41no—
616Dic3—41no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—32no—
624C23—32no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23—61no—
633C23—61no—
634C23—61no—
635C23—61no—
636C23—61no—
637C23—124no—
638C23—124no—
639C23—124no—
640C23—124no—
641C23—124no—
642C23—124no—
643C23—124no—
644C23#89212yes—
645C23C22×C4×D311yescharacteristic
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—32no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—124no—
687C2×C4—124no—
688C2×C4—124no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—121no—
693C2×C4#89212yes—
694C2×C4C2×D3×D411yescharacteristic
695C2×C4C2×#23711yescharacteristic
696C2×C4#100411yescharacteristic
697C2×C4C2×#23911yescharacteristic
698C2×C4D3×#4111yescharacteristic
699C2×C4#100911yescharacteristic
700C8—22no—
701C8—41no—
702C8—41no—
703C8—41no—
704C8—62no—
705C8—121no—
706C8—121no—
707C8—121no—
708C2×C3—42no—
709C2×C3#234211yescharacteristic
710C2×C3#292111yescharacteristic
711C2×C3#292411yescharacteristic
712C2×C3#293011yescharacteristic
713C2×C3#293311yescharacteristic
714C2×C3#297611yescharacteristic
715C2×C3#297811yescharacteristic
716D3—42no—
717D3—42no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—62no—
726C22—62no—
727C22—62no—
728C22—62no—
729C22—62no—
730C22—62no—
731C22—1216no—
732C22—121no—
733C22—121no—
734C22—121no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22C2×#89211yescharacteristic
741C22C4×D3×D411yescharacteristic
742C22#554511yescharacteristic
743C22#574511yescharacteristic
744C22#574511yescharacteristic
745C22D3×#13111yescharacteristic
746C22#575011yescharacteristic
747C4—22no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—62no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4#559111yescharacteristic
759C4#563011yescharacteristic
760C4#563711yescharacteristic
761C4#565811yescharacteristic
762C3#2255911yescharacteristic, complemented, Sylow
763C2—42no—
764C2—122no—
765C2—122no—
766C2#7459511yescharacteristic
767C2#7903911yescharacteristic
768C2#7907211yescharacteristic
769C2#7948211yescharacteristic
770C2#7948811yescharacteristic
771C2#7953711yescharacteristic
772C2#7954511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1851C2
prime radicalC24×D3C2×C4
cosocleC22×C3×C4C24
hypercenter#1851D3
hypocenterC3#22559
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
2. C2×#4840C2semidirect
4. C3×#1851C2semidirect
5. #71983C2semidirect
6. #70476C2semidirect
7. #70449C2semidirect
8. #70449C2semidirect
10. #69949C2semidirect
11. #69450C2semidirect
12. #68665C2semidirect
13. #68616C2semidirect
14. #68616C2semidirect
15. #68601C2semidirect
22. C2×C3×C4⋊C8C22semidirect
23. C2×C3×C4⋊C8C22semidirect
37. C2×#815C22semidirect
38. C2×#815C22semidirect
39. C2×C8×Dic3C22semidirect
40. C2×C8×Dic3C22semidirect
47. C2×C4⋊(C3⋊C8)C22semidirect
48. C2×C4⋊(C3⋊C8)C22semidirect
54. C3×#336C22semidirect
55. C3×#336C22semidirect
56. #4550C22semidirect
57. #4550C22semidirect
58. #4550C22semidirect
59. #4550C22semidirect
60. #4524C22semidirect
61. #4524C22semidirect
70. #1851D3semidirect
162. C2×C4⋊C8C2×D3semidirect
163. C2×C4⋊C8C2×D3semidirect
197. #336C2×D3semidirect
198. #336C2×D3semidirect
762. C3#22559semidirect

Maximal subgroups

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

subgroupindex
C2×#51262
C2×#48402
#735612
C3×#18512
#719832
#704762
#704492
#699552
#699492
#694502
#686652
#686162
#686012
#225593