Finite Group Databasebeta

← #10812225

Subgroups — #10812225

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
1C3×#2297C211yesmaximal, characteristic
2C2×#5234C211yesmaximal, characteristic
3C2×#5000C211yesmaximal, characteristic, complemented
4#72136C211yesmaximal, characteristic
5#71584C211yesmaximal, characteristic, complemented
6#71530C211yesmaximal, characteristic, complemented
7#71529C211yesmaximal, characteristic, complemented
8#69452C211yesmaximal, characteristic, complemented
9#69452C211yesmaximal, characteristic, complemented
10#69452C211yesmaximal, characteristic, complemented
11#69451C211yesmaximal, characteristic, complemented
12#69450C211yesmaximal, characteristic, complemented
13#69449C211yesmaximal, characteristic, complemented
14#69448C211yesmaximal, characteristic, complemented
15#69447C211yesmaximal, characteristic, complemented
16#22561—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×C3×#117C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×#208C2211yescharacteristic
21C23×C3⋊C8C2211yescharacteristic
22C3×#391C411yescharacteristic
23C3×#391C411yescharacteristic
24C3×#390C411yescharacteristic
25C3×#390C411yescharacteristic
26C3×#386C411yescharacteristic
27C3×#386C411yescharacteristic
28C3×#386C411yescharacteristic
29C3×#386C411yescharacteristic
30C3×C4×C22⋊C4C2211yescharacteristic
31C3×C4×C22⋊C4C2211yescharacteristic
32C3×C4×C22⋊C4C2211yescharacteristic
33C3×C4×C22⋊C4C2211yescharacteristic
34#5234—24no—
35C2×#830C2211yescharacteristic
36C2×#830C2211yescharacteristic
37C2×#830C2211yescharacteristic
38C2×#830C2211yescharacteristic
39C2×#830C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#830C2211yescharacteristic
45#5000—24no—
46C2×C4⋊(C3⋊C8)C2211yescharacteristic
47C2×C4⋊(C3⋊C8)C2211yescharacteristic
48C2×C4⋊(C3⋊C8)C2211yescharacteristic
49C2×C4⋊(C3⋊C8)C2211yescharacteristic
50C2×#803C2211yescharacteristic
51C2×#803C2211yescharacteristic
52C2×#803C2211yescharacteristic
53C2×C4×C3⋊C8C2211yescharacteristic
54#4524C2211yescharacteristic
55#4524C2211yescharacteristic
56#4524C2211yescharacteristic
57#4524C2211yescharacteristic
58#4524C2211yescharacteristic
59#4524C2211yescharacteristic
60#4524C2211yescharacteristic
61#4524C2211yescharacteristic
62C2×#433—31no—
63C2×#408—31no—
64#2297D311yescharacteristic
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#1753—31no—
75#1752—31no—
76#1749—31no—
77C2×C3×#41—22no—
78C2×C3×#41—22no—
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—41no—
82C2×C3×#41—41no—
83C22×C3×Q8C2×C411yescharacteristic
84C22×C3×D4C2×C411yescharacteristic
85C22×C3×D4C2×C411yescharacteristic
86C22×C3×D4C2×C411yescharacteristic
87C23×C3×C4C2×C411yescharacteristic
88C23×C3×C4C2×C411yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C3×#117—22no—
93C3×#117—22no—
94C2×C3×C4⋊C4C2×C411yescharacteristic
95C2×C3×C4⋊C4C2×C411yescharacteristic
96C2×C3×C22⋊C4C2×C411yescharacteristic
97C2×C3×C22⋊C4C2×C411yescharacteristic
98C2×C3×C22⋊C4C2×C411yescharacteristic
99C2×C3×C22⋊C4C2×C411yescharacteristic
100C2×C3×C22⋊C4C2×C411yescharacteristic
101C2×C3×C22⋊C4C2×C411yescharacteristic
102C2×C3×C22⋊C4C2×C411yescharacteristic
103C2×C3×C22⋊C4C2×C411yescharacteristic
104C2×C3×C22⋊C4C2×C411yescharacteristic
105C2×C3×C22⋊C4C2×C411yescharacteristic
106C2×C3×C42—41no—
107C2×C3×C42—41no—
108C2×C3×C42C2×C411yescharacteristic
109C2×C3×C42C2×C411yescharacteristic
110C2×C3×C42C2311yescharacteristic
111C2×C3×C42C2311yescharacteristic
112C2×C3×C42C2311yescharacteristic
113C2×C3×C42C2311yescharacteristic
114C2×#208—22no—
115C2×#208—22no—
116C2×#208—41no—
117C22×C3⋊C8—22no—
118C22×C3⋊C8—22no—
119C22×C3⋊C8—41no—
120C22×C3⋊C8C2311yescharacteristic
121C22×C3⋊C8C2311yescharacteristic
122C22×C3⋊C8C2311yescharacteristic
123C22×C3⋊C8C2311yescharacteristic
124C22×C3⋊C8C2311yescharacteristic
125C22×C3⋊C8C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128C3×#95C2×C411yescharacteristic
129C3×#95C2×C411yescharacteristic
130C3×#95C2×C411yescharacteristic
131C3×#95C2×C411yescharacteristic
132C3×#95C2×C411yescharacteristic
133C3×#95C2×C411yescharacteristic
134C3×#95C2×C411yescharacteristic
135C3×#95C2×C411yescharacteristic
136#830—22no—
137#830—22no—
138#830—22no—
139#830—22no—
140#830—22no—
141#830—22no—
142#830—22no—
143#830—41no—
144#830—41no—
145#830D414yes—
146C4⋊(C3⋊C8)—22no—
147C4⋊(C3⋊C8)—22no—
148C4⋊(C3⋊C8)—41no—
149C4⋊(C3⋊C8)—41no—
150#803—22no—
151#803—41no—
152#803—41no—
153C4×C3⋊C8—22no—
154C22×#41C2×D311yescharacteristic
155C22×M16—31no—
156C23×C8—31no—
157C2×#117C2×D311yescharacteristic
158C22×C42C2×D311yescharacteristic
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⋊C8—31no—
175C2×#97—31no—
176C2×#97—31no—
177C2×#97—31no—
178C2×C4×C8—31no—
179#391Dic311yescharacteristic
180#391Dic311yescharacteristic
181#390Dic311yescharacteristic
182#390Dic311yescharacteristic
183#386Dic311yescharacteristic
184#386Dic311yescharacteristic
185#386Dic311yescharacteristic
186#386Dic311yescharacteristic
187C4×C22⋊C4C2×D311yescharacteristic
188C4×C22⋊C4C2×D311yescharacteristic
189C4×C22⋊C4C2×D311yescharacteristic
190C4×C22⋊C4C2×D311yescharacteristic
191#336—31no—
192#336—31no—
193#336—31no—
194#336—31no—
195#336—31no—
196#336—31no—
197#336—31no—
198#336—31no—
199C24×C3C22×C411yescharacteristic
200C24×C3C22×C411yescharacteristic
201C24×C3C22×C411yescharacteristic
202C3×#41—44no—
203C3×#41—44no—
204C3×#41—44no—
205C3×#41—44no—
206C2×C3×Q8—22no—
207C2×C3×Q8—22no—
208C2×C3×Q8—41no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—22no—
214C2×C3×D4—22no—
215C2×C3×D4—41no—
216C2×C3×D4—41no—
217C2×C3×D4—41no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—41no—
234C22×C3×C4—41no—
235C22×C3×C4—41no—
236C22×C3×C4—41no—
237C22×C3×C4—41no—
238C22×C3×C4C22×C411yescharacteristic
239C22×C3×C4C22×C411yescharacteristic
240C22×C3×C4C22×C411yescharacteristic
241C22×C3×C4C22×C411yescharacteristic
242C22×C3×C4C22×C411yescharacteristic
243C22×C3×C4C22×C411yescharacteristic
244C22×C3×C4C22×C411yescharacteristic
245C22×C3×C4C22×C411yescharacteristic
246C22×C3×C4C22×C411yescharacteristic
247C22×C3×C4C22×C411yescharacteristic
248C22×C3×C4C22×C411yescharacteristic
249C22×C3×C4C2×D412yes—
250C22×C3×C4#4112yes—
251C22×C3×C4#4112yes—
252C22×C3×C4#4112yes—
253C22×C3×C4C2411yescharacteristic
254C3×C4⋊C4—22no—
255C3×C4⋊C4—22no—
256C3×C22⋊C4—22no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—22no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—41no—
261C3×C22⋊C4—41no—
262C3×C22⋊C4—41no—
263C3×C22⋊C4—41no—
264C3×C22⋊C4—41no—
265C3×C22⋊C4—41no—
266C3×C42—21no—
267C3×C42—21no—
268C3×C42—21no—
269C3×C42—21no—
270C3×C42—21no—
271C3×C42—21no—
272C3×C42—21no—
273C3×C42—21no—
274C3×C42—41no—
275C3×C42—41no—
276#208—44no—
277C2×C3⋊C8—21no—
278C2×C3⋊C8—21no—
279C2×C3⋊C8—21no—
280C2×C3⋊C8—21no—
281C2×C3⋊C8—21no—
282C2×C3⋊C8—21no—
283C2×C3⋊C8—21no—
284C2×C3⋊C8—21no—
285C2×C3⋊C8—21no—
286C2×C3⋊C8—21no—
287C2×C3⋊C8—21no—
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⋊C8—21no—
299C2×C3⋊C8—44no—
300C2×C3⋊C8C2×D412yes—
301C2×C3⋊C8C2×D412yes—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—41no—
307C2×#41—41no—
308C22×Q8C2×Dic311yescharacteristic
309C22×D4C2×Dic311yescharacteristic
310C22×D4C2×Dic311yescharacteristic
311C22×D4C2×Dic311yescharacteristic
312C23×C4C2×Dic311yescharacteristic
313C23×C4C2×Dic311yescharacteristic
314C23×C4C22×D311yescharacteristic
315C23×C4C22×D311yescharacteristic
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—31no—
325C22×C8—31no—
326C22×C8—31no—
327C22×C8—31no—
328C22×C8—62no—
329C22×C8—62no—
330C22×C8—121no—
331#117—22no—
332#117—22no—
333C2×C4⋊C4C2×Dic311yescharacteristic
334C2×C4⋊C4C2×Dic311yescharacteristic
335C2×C22⋊C4C2×Dic311yescharacteristic
336C2×C22⋊C4C2×Dic311yescharacteristic
337C2×C22⋊C4C2×Dic311yescharacteristic
338C2×C22⋊C4C2×Dic311yescharacteristic
339C2×C22⋊C4C2×Dic311yescharacteristic
340C2×C22⋊C4C2×Dic311yescharacteristic
341C2×C22⋊C4C2×Dic311yescharacteristic
342C2×C22⋊C4C2×Dic311yescharacteristic
343C2×C22⋊C4C2×Dic311yescharacteristic
344C2×C22⋊C4C2×Dic311yescharacteristic
345C2×C42—41no—
346C2×C42—41no—
347C2×C42C2×Dic311yescharacteristic
348C2×C42C2×Dic311yescharacteristic
349C2×C42C22×D311yescharacteristic
350C2×C42C22×D311yescharacteristic
351C2×C42C22×D311yescharacteristic
352C2×C42C22×D311yescharacteristic
353C4⋊C8—62no—
354C4⋊C8—62no—
355C4⋊C8—121no—
356C4⋊C8—121no—
357C22⋊C8—34no—
358C22⋊C8—62no—
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—
369#97—121no—
370C4×C8—62no—
371#95C2×Dic311yescharacteristic
372#95C2×Dic311yescharacteristic
373#95C2×Dic311yescharacteristic
374#95C2×Dic311yescharacteristic
375#95C2×Dic311yescharacteristic
376#95C2×Dic311yescharacteristic
377#95C2×Dic311yescharacteristic
378#95C2×Dic311yescharacteristic
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3#11712yes—
399C23×C3C4×D412yes—
400C23×C3C23×C411yescharacteristic
401C3×Q8—44no—
402C3×D4—44no—
403C3×D4—44no—
404C3×D4—44no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
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—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—44no—
444C2×C3×C4—44no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4#11712yes—
450C2×C3×C4C4×D412yes—
451C2×C3×C4#13112yes—
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4H(5,𝔽2)11yescharacteristic
457C2×C3×C4H(5,𝔽2)11yescharacteristic
458C3⋊C8—22no—
459C3⋊C8—22no—
460C3⋊C8—41no—
461C3⋊C8—41no—
462C3⋊C8—41no—
463C3⋊C8—41no—
464C3⋊C8—41no—
465C3⋊C8—41no—
466C24C22×Dic311yescharacteristic
467C24C22×Dic311yescharacteristic
468C24C22×Dic311yescharacteristic
469#41—44no—
470#41—44no—
471#41—44no—
472#41—44no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—41no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4#23512yes—
506C22×C4#23512yes—
507C22×C4D3×D412yes—
508C22×C4#23712yes—
509C22×C4C22×Dic311yescharacteristic
510C22×C4C22×Dic311yescharacteristic
511C22×C4C22×Dic311yescharacteristic
512C22×C4C22×Dic311yescharacteristic
513C22×C4C22×Dic311yescharacteristic
514C22×C4C22×Dic311yescharacteristic
515C22×C4C22×Dic311yescharacteristic
516C22×C4C22×Dic311yescharacteristic
517C22×C4C22×Dic311yescharacteristic
518C22×C4C22×Dic311yescharacteristic
519C22×C4C22×Dic311yescharacteristic
520C22×C4C23×D311yescharacteristic
521M16—124no—
522C2×C8—32no—
523C2×C8—32no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C2×C8—61no—
528C2×C8—61no—
529C2×C8—61no—
530C2×C8—61no—
531C2×C8—61no—
532C2×C8—61no—
533C2×C8—61no—
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—61no—
546C2×C8—124no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—41no—
568C42—41no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3C2×#11711yescharacteristic
591C22×C3C2×C4×D411yescharacteristic
592C22×C3#51811yescharacteristic
593C22×C3C2×#13111yescharacteristic
594C22×C3#56811yescharacteristic
595C22×C3#56811yescharacteristic
596C22×C3#56811yescharacteristic
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—22no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4#54611yescharacteristic
609C3×C4#54611yescharacteristic
610C3×C4#55111yescharacteristic
611C3×C4#55111yescharacteristic
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23#92612yes—
632C23D4×Dic312yes—
633C23C23×Dic311yescharacteristic
634Q8—44no—
635D4—44no—
636D4—44no—
637D4—44no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
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—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4#92612yes—
683C2×C4D4×Dic312yes—
684C2×C4#94812yes—
685C2×C4C2×#23511yescharacteristic
686C2×C4C2×#23511yescharacteristic
687C2×C4C2×D3×D411yescharacteristic
688C2×C4C2×#23711yescharacteristic
689C2×C4#100411yescharacteristic
690C2×C4#100411yescharacteristic
691C8—62no—
692C8—62no—
693C8—121no—
694C8—121no—
695C8—121no—
696C8—121no—
697C8—121no—
698C8—121no—
699C2×C3—42no—
700C2×C3—42no—
701C2×C3—81no—
702C2×C3#234211yescharacteristic
703C2×C3#292311yescharacteristic
704C2×C3#292511yescharacteristic
705C2×C3#293211yescharacteristic
706C2×C3#293511yescharacteristic
707C2×C3#297611yescharacteristic
708C2×C3#297811yescharacteristic
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22C2×#92611yescharacteristic
731C22C2×D4×Dic311yescharacteristic
732C22#579811yescharacteristic
733C22C2×#94811yescharacteristic
734C22#581911yescharacteristic
735C22#581911yescharacteristic
736C22#581911yescharacteristic
737C4—22no—
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4#549011yescharacteristic
749C4#549011yescharacteristic
750C4#549511yescharacteristic
751C4#549511yescharacteristic
752C3#2256111yescharacteristic, complemented, Sylow
753C2—42no—
754C2—42no—
755C2—81no—
756C2#8209711yescharacteristic
757C2#8251411yescharacteristic
758C2#8251511yescharacteristic
759C2#8291911yescharacteristic
760C2#8292111yescharacteristic
761C2#8327611yescharacteristic
762C2#8327711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#2297C2
prime radicalC22×C3×#41C22
cosocleC22×C3×C4C24
hypercenter#2297D3
hypocenterC3#22561
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #2297

Complements

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

NH ≅ G/Ntype
3. C2×#5000C2semidirect
5. #71584C2semidirect
6. #71530C2semidirect
7. #71529C2semidirect
8. #69452C2semidirect
9. #69452C2semidirect
10. #69452C2semidirect
11. #69451C2semidirect
12. #69450C2semidirect
13. #69449C2semidirect
14. #69448C2semidirect
15. #69447C2semidirect
752. C3#22561semidirect

Maximal subgroups

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

subgroupindex
C3×#22972
C2×#52342
C2×#50002
#721362
#715842
#715302
#715292
#694522
#694512
#694502
#694492
#694482
#694472
#225613