Finite Group Databasebeta

← #14759893

Subgroups — #14759893

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622741C211yesmaximal, characteristic, complemented
2C2×#10622724C211yesmaximal, characteristic, complemented
3C2×#10622714C211yesmaximal, characteristic, complemented
4#13071858C211yesmaximal, characteristic
5#13069412C211yesmaximal, characteristic, complemented
6#13069336C211yesmaximal, characteristic, complemented
7#13069232C211yesmaximal, characteristic, complemented
8#13069228C211yesmaximal, characteristic, complemented
9#13068914C211yesmaximal, characteristic, complemented
10#13068911C211yesmaximal, characteristic, complemented
11#13068598C211yesmaximal, characteristic, complemented
12#13068484C211yesmaximal, characteristic, complemented
13#13068401C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24C11×#435—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29#10622836C411yescharacteristic
30#10622835C411yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622741—24no—
36#10622724—24no—
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40#10622714—24no—
41C2×#66879C2211yescharacteristic
42C2×#66879C2211yescharacteristic
43C2×#66879C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×Dic11⋊C8C2211yescharacteristic
46C2×Dic11⋊C8C2211yescharacteristic
47C2×C8×Dic11C2211yescharacteristic
48C2×C8×Dic11C2211yescharacteristic
49#10622607C411yescharacteristic
50#10622597C411yescharacteristic
51#10622574C411yescharacteristic
52#10622572C411yescharacteristic
53#10622565C411yescharacteristic
54#10622561C411yescharacteristic
55C4×(C2×D11)⋊C4C2211yescharacteristic
56C4×Dic11⋊C4C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11D414yescomplemented
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90C2×C22⋊Dic11C2×C411yescharacteristic
91C4×C22⋊D11—22no—
92C4×C22⋊D11—22no—
93C4×C22⋊D11—22no—
94C4×C22⋊D11—22no—
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99#66979—22no—
100#66979—22no—
101C2×C4⋊Dic11C2×C411yescharacteristic
102C2×C4⋊Dic11C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×Dic11⋊C4C2×C411yescharacteristic
106C2×Dic11⋊C4C2×C411yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C2×#4318—22no—
111C2×#4318—22no—
112C2×#4318—22no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C2×#4313—22no—
118C2×#4313—22no—
119C2×#4313—22no—
120C11×C4⋊C8—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C11×#97—22no—
124C11⋊#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—22no—
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—22no—
136#66879—22no—
137#66879—22no—
138#66879—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141Dic11⋊C8—22no—
142C8×Dic11—22no—
143C8×Dic11D414yescomplemented
144#21493—111nomaximal, Sylow
145C24×C11C22×C411yescharacteristic
146C24×C11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
148C2×D4×C11—22no—
149C2×D4×C11—41no—
150C2×D4×C11—41no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11#4112yes—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—22no—
169C2×C22⋊D11—22no—
170C2×C22⋊D11—41no—
171C2×C22⋊D11—41no—
172C2×C22⋊D11—41no—
173C2×C22⋊D11—41no—
174C22×Dic11C22×C411yescharacteristic
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C22×Dic11C22×C411yescharacteristic
180C22×Dic11C22×C411yescharacteristic
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C11×M16—44no—
188C2×C8×C11—28no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11C2×D412yes—
198C2×C8×C11C2×D412yes—
199C2×C8×C11C2×D412yes—
200C2×C8×C11#4112yes—
201C11×C4⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C42×C11—21no—
205C42×C11—21no—
206C22⋊Dic11—22no—
207C22⋊Dic11—22no—
208C22⋊Dic11—22no—
209C22⋊Dic11—22no—
210C22⋊Dic11—41no—
211C22⋊Dic11—41no—
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4—22no—
214(C2×D11)⋊C4—41no—
215(C2×D11)⋊C4—41no—
216C4⋊Dic11—22no—
217C4⋊Dic11—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—22no—
220Dic11⋊C4—41no—
221Dic11⋊C4—41no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11C2×D412yes—
227C4×Dic11#4112yes—
228#4318—28no—
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⋊C8C2×D412yes—
240C2×C11⋊C8#4112yes—
241#4313—44no—
242C2×#436—111no—
243C2×#435—111no—
244C2×#435D1111yescharacteristic, complemented
245C2×#405—111no—
246#2392—111no—
247#1955—111no—
248#1940—111no—
249#1924—111no—
250#1924—111no—
251#1870—111no—
252#1870—111no—
253#1798—111no—
254#1770—111no—
255#1753—111no—
256#1753—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×C11C4×D412yes—
271C23×C11C23×C411yescharacteristic
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279D4×C11—44no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11C4×D412yes—
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C22⋊D11—44no—
307C22⋊D11—44no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11C4×D412yes—
328C2×Dic11C4×D412yes—
329C4×D11—41no—
330C4×D11—41no—
331C4×D11—41no—
332C4×D11—41no—
333C8×C11—22no—
334C8×C11—41no—
335C8×C11—41no—
336C8×C11#12114yes—
337C11⋊C8—22no—
338C11⋊C8—22no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C22×M16—111no—
342C22×M16—111no—
343C22×M16C2×D1111yescharacteristic
344C23×C8C2×D1111yescharacteristic
345C2×C4×D4—111no—
346C2×C4×D4—111no—
347C2×C4×D4C2×D1111yescharacteristic
348C2×#117—111no—
349#436—224no—
350#435—24no—
351#435—224no—
352C2×C4⋊C8—111no—
353C2×C4⋊C8—111no—
354C2×C4⋊C8—111no—
355C2×C4⋊C8C2×D1111yescharacteristic
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⋊C8C2×D1111yescharacteristic
363C2×C22⋊C8C2×D1111yescharacteristic
364#405—224no—
365C2×#97—111no—
366C2×#97—111no—
367C2×#97—111no—
368C2×#97C2×D1111yescharacteristic
369C2×C4×C8—111no—
370C2×C4×C8—111no—
371#398—111no—
372#397—111no—
373#396—111no—
374#396—111no—
375#394—111no—
376#394—111no—
377#394—111no—
378#392—111no—
379C4×C4⋊C4—111no—
380C4×C22⋊C4—111no—
381C4×C22⋊C4—111no—
382#336—111no—
383#336—111no—
384#336—111no—
385#336—111no—
386#336—111no—
387#336—111no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11C2×C4×D411yescharacteristic
403C22×C11C2×C4×D411yescharacteristic
404C22×C11C4×#4111yescharacteristic
405C22×C11#56811yescharacteristic
406C22×C11#56811yescharacteristic
407C22×C11#56811yescharacteristic
408C22×C11#56811yescharacteristic
409C2×D11—41no—
410C2×D11—41no—
411C2×D11—41no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11—41no—
416C4×C11—22no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11C2×#12111yescharacteristic
421C4×C11#52511yescharacteristic
422C4×C11#52911yescharacteristic
423C4×C11#53211yescharacteristic
424Dic11—22no—
425Dic11—22no—
426Dic11—41no—
427Dic11—41no—
428Dic11—41no—
429Dic11—41no—
430Dic11—41no—
431C22×D4—111no—
432C22×D4—111no—
433C22×D4C4×D1111yescharacteristic
434C23×C4—111no—
435C23×C4C22×D1111yescharacteristic
436C23×C4C22×D1111yescharacteristic
437C2×M16—22no—
438C2×M16—22no—
439C2×M16—22no—
440C2×M16—222no—
441C2×M16—222no—
442C2×M16—222no—
443C2×M16—222no—
444C2×M16—222no—
445C2×M16—222no—
446C22×C8—22no—
447C22×C8—22no—
448C22×C8—111no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8C22⋊D1114yescomplemented
453C22×C8C22×D1111yescharacteristic
454C22×C8C22×D1111yescharacteristic
455C22×C8C22×D1111yescharacteristic
456C22×C8C22×D1111yescharacteristic
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—222no—
460C4×D4—222no—
461C4×D4—222no—
462C4×D4—222no—
463#117—222no—
464#117—222no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4C4×D1111yescharacteristic
472C2×C22⋊C4—111no—
473C2×C22⋊C4—111no—
474C2×C22⋊C4—111no—
475C2×C22⋊C4—111no—
476C2×C22⋊C4—111no—
477C2×C22⋊C4—111no—
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4C4×D1111yescharacteristic
483C2×C22⋊C4C4×D1111yescharacteristic
484C2×C42—111no—
485C2×C42—111no—
486C2×C42—111no—
487C2×C42C22×D1111yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—222no—
490C4⋊C8—222no—
491C4⋊C8—222no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—222no—
495C22⋊C8—222no—
496C22⋊C8—222no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—222no—
500#97—22no—
501#97—222no—
502#97—222no—
503#97—222no—
504C4×C8—114no—
505C4×C8—222no—
506#95—111no—
507#95—111no—
508#95—111no—
509#95—111no—
510#95—111no—
511#95—111no—
512C2×C11—42no—
513C2×C11—81no—
514C2×C11C4×#12111yescharacteristic
515C2×C11#293011yescharacteristic
516C2×C11#293011yescharacteristic
517C2×C11#293011yescharacteristic
518C2×C11#293211yescharacteristic
519C2×C11#296711yescharacteristic
520C2×C11#296711yescharacteristic
521D11—81no—
522C24—111no—
523C24C2×C4×D1111yescharacteristic
524C24C2×C4×D1111yescharacteristic
525C2×D4—22no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—222no—
529C2×D4—222no—
530C2×D4—441no—
531C2×D4—441no—
532C2×D4—441no—
533C2×D4—441no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—111no—
545C22×C4—111no—
546C22×C4—111no—
547C22×C4—111no—
548C22×C4—111no—
549C22×C4—111no—
550C22×C4—111no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4C2×C4×D1111yescharacteristic
558C22×C4C2×C4×D1111yescharacteristic
559C22×C4C2×C4×D1111yescharacteristic
560C22×C4C2×C4×D1111yescharacteristic
561C22×C4#433912yes—
562C22×C4C2×C22⋊D1112yes—
563C22×C4C23×D1111yescharacteristic
564M16—44no—
565M16—228no—
566M16—444no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—28no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—112no—
577C2×C8—112no—
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×C8D4×D1112yes—
589C2×C8#434112yes—
590C2×C8C2×C22⋊D1112yes—
591C2×C8C2×C22⋊D1112yes—
592C4⋊C4—22no—
593C4⋊C4—222no—
594C4⋊C4—222no—
595C4⋊C4—222no—
596C4⋊C4—222no—
597C4⋊C4—441no—
598C4⋊C4—441no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—222no—
602C22⋊C4—222no—
603C22⋊C4—222no—
604C22⋊C4—222no—
605C22⋊C4—222no—
606C22⋊C4—222no—
607C22⋊C4—441no—
608C22⋊C4—441no—
609C22⋊C4—441no—
610C22⋊C4—441no—
611C42—21no—
612C42—21no—
613C42—112no—
614C42—112no—
615C42—221no—
616C42—221no—
617C42—221no—
618C42—221no—
619C11#2149311yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23C4×C22⋊D1112yes—
641C23C22×C4×D1111yescharacteristic
642D4—44no—
643D4—444no—
644D4—444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
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—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—112no—
665C2×C4—112no—
666C2×C4—221no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4C4×C22⋊D1112yes—
690C2×C4C2×#433911yescharacteristic
691C2×C4C2×D4×D1111yescharacteristic
692C2×C4C2×#434111yescharacteristic
693C2×C4#41×D1111yescharacteristic
694C2×C4#41×D1111yescharacteristic
695C2×C4C22×C22⋊D1111yescharacteristic
696C8—22no—
697C8—41no—
698C8—41no—
699C8—222no—
700C8—222no—
701C8—441no—
702C8—441no—
703C8#6699214yes—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—441no—
719C22—441no—
720C22—441no—
721C22—441no—
722C22—441no—
723C22—441no—
724C22—441no—
725C22C4×#434111yescharacteristic
726C22C4×D4×D1111yescharacteristic
727C22#1062327611yescharacteristic
728C22#1062327611yescharacteristic
729C22#1062328111yescharacteristic
730C22#1062328111yescharacteristic
731C22C2×C4×C22⋊D1111yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—222no—
737C4—222no—
738C4—441no—
739C4—441no—
740C4—441no—
741C4—441no—
742C4—441no—
743C4#1062306911yescharacteristic
744C4#1062307811yescharacteristic
745C4C2×#6699211yescharacteristic
746C4#1062336311yescharacteristic
747C2—42no—
748C2—81no—
749C2—881no—
750C2C4×#6699211yescharacteristic
751C2#1307731411yescharacteristic
752C2#1307731711yescharacteristic
753C2#1307731911yescharacteristic
754C2#1307733011yescharacteristic
755C2#1307759511yescharacteristic
756C2#1307759811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#435C2
prime radical#10622836C4
cosocleC22×C4×C11C24
hypercenterC2×#435D11
hypocenterC11#21493
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#10622741C2semidirect
2. C2×#10622724C2semidirect
3. C2×#10622714C2semidirect
5. #13069412C2semidirect
6. #13069336C2semidirect
7. #13069232C2semidirect
8. #13069228C2semidirect
9. #13068914C2semidirect
10. #13068911C2semidirect
11. #13068598C2semidirect
12. #13068484C2semidirect
13. #13068401C2semidirect
14. #13068397C2semidirect
15. C2×C11×#435C2semidirect
74. C22×C8×C11D4semidirect
143. C8×Dic11D4semidirect
244. C2×#435D11semidirect
452. C22×C8C22⋊D11semidirect
619. C11#21493semidirect

Maximal subgroups

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

subgroupindex
C2×#106227412
C2×#106227242
C2×#106227142
#130718582
#130694122
#130693362
#130692322
#130692282
#130689142
#130689112
#130685982
#130684842
#130684012
#130683972
C2×C11×#4352
#2149311