Finite Group Databasebeta

← #14770811

Subgroups — #14770811

Order 2816.

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×#10622613C211yesmaximal, characteristic, complemented
2C2×#10622847C211yesmaximal, characteristic
3#13069231C211yesmaximal, characteristic, complemented
4#13069231C211yesmaximal, characteristic, complemented
5#13069231C211yesmaximal, characteristic, complemented
6#13069224C211yesmaximal, characteristic, complemented
7#13068801C211yesmaximal, characteristic, complemented
8#13068796C211yesmaximal, characteristic, complemented
9#13068687C211yesmaximal, characteristic, complemented
10#13068596C211yesmaximal, characteristic, complemented
11#13068528C211yesmaximal, characteristic
12#13068400C211yesmaximal, characteristic, complemented
13#13068394C211yesmaximal, characteristic, complemented
14#13068378C211yesmaximal, characteristic, complemented
15C11×#2297C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C11×#391C411yescharacteristic
22C11×#391C411yescharacteristic
23C11×#390C411yescharacteristic
24C11×#390C411yescharacteristic
25C11×#386C411yescharacteristic
26C11×#386C411yescharacteristic
27C11×#386C411yescharacteristic
28C11×#386C411yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33#10622847—24no—
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622613—24no—
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2×C411yescharacteristic
68C22×D4×C11C2×C411yescharacteristic
69C22×D4×C11C2×C411yescharacteristic
70C22×D4×C11C2×C411yescharacteristic
71C23×C4×C11C2×C411yescharacteristic
72C23×C4×C11C2×C411yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C11×#117—22no—
77C11×#117—22no—
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C11×C22⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C42×C11—41no—
91C2×C42×C11—41no—
92C2×C42×C11C2×C411yescharacteristic
93C2×C42×C11C2×C411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×#4318—22no—
99C2×#4318—22no—
100C2×#4318—41no—
101C22×C11⋊C8—22no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8—41no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C11×#95C2×C411yescharacteristic
113C11×#95C2×C411yescharacteristic
114C11×#95C2×C411yescharacteristic
115C11×#95C2×C411yescharacteristic
116C11×#95C2×C411yescharacteristic
117C11×#95C2×C411yescharacteristic
118C11×#95C2×C411yescharacteristic
119C11×#95C2×C411yescharacteristic
120C22⋊(C11⋊C8)—22no—
121C22⋊(C11⋊C8)—22no—
122C22⋊(C11⋊C8)—22no—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—22no—
126C22⋊(C11⋊C8)—22no—
127C22⋊(C11⋊C8)—41no—
128C22⋊(C11⋊C8)—41no—
129C22⋊(C11⋊C8)D414yes—
130C4⋊(C11⋊C8)—22no—
131C4⋊(C11⋊C8)—22no—
132C4⋊(C11⋊C8)—41no—
133C4⋊(C11⋊C8)—41no—
134#66867—22no—
135#66867—41no—
136#66867—41no—
137C4×C11⋊C8—22no—
138#22561—111nomaximal, Sylow
139C24×C11C22×C411yescharacteristic
140C24×C11C22×C411yescharacteristic
141C24×C11C22×C411yescharacteristic
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11—41no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—22no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—41no—
174C22×C4×C11—41no—
175C22×C4×C11—41no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C22×C411yescharacteristic
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C22×C411yescharacteristic
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C22×C411yescharacteristic
187C22×C4×C11C22×C411yescharacteristic
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11#4112yes—
191C22×C4×C11#4112yes—
192C22×C4×C11#4112yes—
193C22×C4×C11C2411yescharacteristic
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—41no—
215C42×C11—41no—
216#4318—44no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—44no—
240C2×C11⋊C8C2×D412yes—
241C2×C11⋊C8C2×D412yes—
242C2×#433—111no—
243C2×#408—111no—
244#2297D1111yescharacteristic
245#1924—111no—
246#1924—111no—
247#1924—111no—
248#1923—111no—
249#1851—111no—
250#1850—111no—
251#1818—111no—
252#1797—111no—
253#1780—111no—
254#1753—111no—
255#1752—111no—
256#1749—111no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11#11712yes—
277C23×C11C4×D412yes—
278C23×C11C23×C411yescharacteristic
279Q8×C11—44no—
280D4×C11—44no—
281D4×C11—44no—
282D4×C11—44no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—44no—
322C2×C4×C11—44no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11#11712yes—
328C2×C4×C11C4×D412yes—
329C2×C4×C11#13112yes—
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C11⋊C8—22no—
337C11⋊C8—22no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C11⋊C8—41no—
342C11⋊C8—41no—
343C11⋊C8—41no—
344C22×#41C2×D1111yescharacteristic
345C22×M16—111no—
346C23×C8—111no—
347C2×#117C2×D1111yescharacteristic
348C22×C42C2×D1111yescharacteristic
349#433—224no—
350C2×C4⋊C8—111no—
351C2×C4⋊C8—111no—
352C2×C4⋊C8—111no—
353C2×C4⋊C8—111no—
354#408—224no—
355C2×C22⋊C8—111no—
356C2×C22⋊C8—111no—
357C2×C22⋊C8—111no—
358C2×C22⋊C8—111no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8—111no—
362C2×C22⋊C8—111no—
363C2×C22⋊C8—111no—
364C2×C22⋊C8—111no—
365C2×#97—111no—
366C2×#97—111no—
367C2×#97—111no—
368C2×C4×C8—111no—
369#391Dic1111yescharacteristic
370#391Dic1111yescharacteristic
371#390Dic1111yescharacteristic
372#390Dic1111yescharacteristic
373#386Dic1111yescharacteristic
374#386Dic1111yescharacteristic
375#386Dic1111yescharacteristic
376#386Dic1111yescharacteristic
377C4×C22⋊C4C2×D1111yescharacteristic
378C4×C22⋊C4C2×D1111yescharacteristic
379C4×C22⋊C4C2×D1111yescharacteristic
380C4×C22⋊C4C2×D1111yescharacteristic
381#336—111no—
382#336—111no—
383#336—111no—
384#336—111no—
385#336—111no—
386#336—111no—
387#336—111no—
388#336—111no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11C2×#11711yescharacteristic
411C22×C11C2×C4×D411yescharacteristic
412C22×C11#51811yescharacteristic
413C22×C11C2×#13111yescharacteristic
414C22×C11#56811yescharacteristic
415C22×C11#56811yescharacteristic
416C22×C11#56811yescharacteristic
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—41no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11#54611yescharacteristic
429C4×C11#54611yescharacteristic
430C4×C11#55111yescharacteristic
431C4×C11#55111yescharacteristic
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—41no—
437C2×#41—41no—
438C22×Q8C2×Dic1111yescharacteristic
439C22×D4C2×Dic1111yescharacteristic
440C22×D4C2×Dic1111yescharacteristic
441C22×D4C2×Dic1111yescharacteristic
442C23×C4C2×Dic1111yescharacteristic
443C23×C4C2×Dic1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1111yescharacteristic
447C2×M16—222no—
448C2×M16—222no—
449C2×M16—441no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—111no—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—222no—
459C22×C8—222no—
460C22×C8—441no—
461#117—22no—
462#117—22no—
463C2×C4⋊C4C2×Dic1111yescharacteristic
464C2×C4⋊C4C2×Dic1111yescharacteristic
465C2×C22⋊C4C2×Dic1111yescharacteristic
466C2×C22⋊C4C2×Dic1111yescharacteristic
467C2×C22⋊C4C2×Dic1111yescharacteristic
468C2×C22⋊C4C2×Dic1111yescharacteristic
469C2×C22⋊C4C2×Dic1111yescharacteristic
470C2×C22⋊C4C2×Dic1111yescharacteristic
471C2×C22⋊C4C2×Dic1111yescharacteristic
472C2×C22⋊C4C2×Dic1111yescharacteristic
473C2×C22⋊C4C2×Dic1111yescharacteristic
474C2×C22⋊C4C2×Dic1111yescharacteristic
475C2×C42—41no—
476C2×C42—41no—
477C2×C42C2×Dic1111yescharacteristic
478C2×C42C2×Dic1111yescharacteristic
479C2×C42C22×D1111yescharacteristic
480C2×C42C22×D1111yescharacteristic
481C2×C42C22×D1111yescharacteristic
482C2×C42C22×D1111yescharacteristic
483C4⋊C8—222no—
484C4⋊C8—222no—
485C4⋊C8—441no—
486C4⋊C8—441no—
487C22⋊C8—114no—
488C22⋊C8—222no—
489C22⋊C8—222no—
490C22⋊C8—222no—
491C22⋊C8—222no—
492C22⋊C8—222no—
493C22⋊C8—222no—
494C22⋊C8—222no—
495C22⋊C8—441no—
496C22⋊C8—441no—
497#97—222no—
498#97—441no—
499#97—441no—
500C4×C8—222no—
501#95C2×Dic1111yescharacteristic
502#95C2×Dic1111yescharacteristic
503#95C2×Dic1111yescharacteristic
504#95C2×Dic1111yescharacteristic
505#95C2×Dic1111yescharacteristic
506#95C2×Dic1111yescharacteristic
507#95C2×Dic1111yescharacteristic
508#95C2×Dic1111yescharacteristic
509C2×C11—42no—
510C2×C11—42no—
511C2×C11—81no—
512C2×C11#234211yescharacteristic
513C2×C11#292311yescharacteristic
514C2×C11#292511yescharacteristic
515C2×C11#293211yescharacteristic
516C2×C11#293511yescharacteristic
517C2×C11#297611yescharacteristic
518C2×C11#297811yescharacteristic
519C24C22×Dic1111yescharacteristic
520C24C22×Dic1111yescharacteristic
521C24C22×Dic1111yescharacteristic
522#41—44no—
523#41—44no—
524#41—44no—
525#41—44no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—41no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4#433912yes—
559C22×C4#433912yes—
560C22×C4D4×D1112yes—
561C22×C4#434112yes—
562C22×C4C22×Dic1111yescharacteristic
563C22×C4C22×Dic1111yescharacteristic
564C22×C4C22×Dic1111yescharacteristic
565C22×C4C22×Dic1111yescharacteristic
566C22×C4C22×Dic1111yescharacteristic
567C22×C4C22×Dic1111yescharacteristic
568C22×C4C22×Dic1111yescharacteristic
569C22×C4C22×Dic1111yescharacteristic
570C22×C4C22×Dic1111yescharacteristic
571C22×C4C22×Dic1111yescharacteristic
572C22×C4C22×Dic1111yescharacteristic
573C22×C4C23×D1111yescharacteristic
574M16—444no—
575C2×C8—112no—
576C2×C8—112no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—444no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—41no—
621C42—41no—
622C11#2256111yescharacteristic, complemented, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23#6697912yes—
643C23D4×Dic1112yes—
644C23C23×Dic1111yescharacteristic
645Q8—44no—
646D4—44no—
647D4—44no—
648D4—44no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
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—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4#6697912yes—
694C2×C4D4×Dic1112yes—
695C2×C4#6700112yes—
696C2×C4C2×#433911yescharacteristic
697C2×C4C2×#433911yescharacteristic
698C2×C4C2×D4×D1111yescharacteristic
699C2×C4C2×#434111yescharacteristic
700C2×C4#6703711yescharacteristic
701C2×C4#6703711yescharacteristic
702C8—222no—
703C8—222no—
704C8—441no—
705C8—441no—
706C8—441no—
707C8—441no—
708C8—441no—
709C8—441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
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—
730C22—41no—
731C22C2×#6697911yescharacteristic
732C22C2×D4×Dic1111yescharacteristic
733C22#1062332911yescharacteristic
734C22C2×#6700111yescharacteristic
735C22#1062335011yescharacteristic
736C22#1062335011yescharacteristic
737C22#1062335011yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4#1062302111yescharacteristic
750C4#1062302111yescharacteristic
751C4#1062302611yescharacteristic
752C4#1062302611yescharacteristic
753C2—42no—
754C2—42no—
755C2—81no—
756C2#1307146511yescharacteristic
757C2#1307726711yescharacteristic
758C2#1307728211yescharacteristic
759C2#1307733411yescharacteristic
760C2#1307736011yescharacteristic
761C2#1307766411yescharacteristic
762C2#1307767811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#2297C2
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#2297D11
hypocenterC11#22561
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2297

Complements

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

NH ≅ G/Ntype
1. C2×#10622613C2semidirect
3. #13069231C2semidirect
4. #13069231C2semidirect
5. #13069231C2semidirect
6. #13069224C2semidirect
7. #13068801C2semidirect
8. #13068796C2semidirect
9. #13068687C2semidirect
10. #13068596C2semidirect
12. #13068400C2semidirect
13. #13068394C2semidirect
14. #13068378C2semidirect
622. C11#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#106226132
C2×#106228472
#130692312
#130692242
#130688012
#130687962
#130686872
#130685962
#130685282
#130684002
#130683942
#130683782
C11×#22972
#2256111