Finite Group Databasebeta

← #14769863

Subgroups — #14769863

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C211yesmaximal, characteristic, complemented
2C2×#10622624C211yesmaximal, characteristic, complemented
3#13069557C211yesmaximal, characteristic, complemented
4#13069553C211yesmaximal, characteristic, complemented
5#13068914C211yesmaximal, characteristic, complemented
6#13068914C211yesmaximal, characteristic, complemented
7#13068914C211yesmaximal, characteristic, complemented
8#13068909C211yesmaximal, characteristic, complemented
9#13068687C211yesmaximal, characteristic, complemented
10#13068684C211yesmaximal, characteristic, complemented
11#13068600C211yesmaximal, characteristic, complemented
12#13068382C211yesmaximal, characteristic, complemented
13#13068313C211yesmaximal, characteristic, complemented
14#13068310C211yesmaximal, characteristic, complemented
15C2×C11×#529C211yesmaximal, characteristic
16C11×#529—24no—
17C11×#529—24no—
18C2×C11×#126C411yescharacteristic
19C2×C11×#126C411yescharacteristic
20C2×C11×#125C411yescharacteristic
21C2×C11×#124C411yescharacteristic
22C2×C11×#123C411yescharacteristic
23C2×C11×#123C411yescharacteristic
24C2×C11×C22⋊Q8C411yescharacteristic
25C2×C11×#121C411yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic
32C22×C42×C11C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35C22×#4318C2211yescharacteristic
36C23×C11⋊C8C2211yescharacteristic
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
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622625—24no—
46#10622624—24no—
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622162C2211yescharacteristic
52#10622162C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2×C411yescharacteristic
64C22×D4×C11C2×C411yescharacteristic
65C22×D4×C11C2×C411yescharacteristic
66C22×D4×C11C2×C411yescharacteristic
67C23×C4×C11C2×C411yescharacteristic
68C23×C4×C11C2×C411yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C11×#126—24no—
73C11×#126—24no—
74C11×#125—24no—
75C11×#124—24no—
76C11×#123—24no—
77C11×#123—24no—
78C11×C22⋊Q8—24no—
79C11×#121—24no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11D414yes—
87C4×D4×C11D414yes—
88C11×#117—22no—
89C11×#117—22no—
90C11×#117—22no—
91C11×#117—22no—
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C11×C4⋊C4C2×C411yescharacteristic
94C2×C11×C4⋊C4C2×C411yescharacteristic
95C2×C11×C4⋊C4C2×C411yescharacteristic
96C2×C11×C4⋊C4C2×C411yescharacteristic
97C2×C11×C4⋊C4C2×C411yescharacteristic
98C2×C11×C4⋊C4C2×C411yescharacteristic
99C2×C11×C4⋊C4C2×C411yescharacteristic
100C2×C11×C4⋊C4C2×C411yescharacteristic
101C2×C11×C4⋊C4C2×C411yescharacteristic
102C2×C11×C22⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C11×C22⋊C4C2×C411yescharacteristic
106C2×C11×C22⋊C4C2×C411yescharacteristic
107C2×C11×C22⋊C4C2×C411yescharacteristic
108C2×C11×C22⋊C4C2×C411yescharacteristic
109C2×C11×C22⋊C4C2×C411yescharacteristic
110C2×C11×C22⋊C4C2×C411yescharacteristic
111C2×C11×C22⋊C4C2×C411yescharacteristic
112C2×C42×C11—22no—
113C2×C42×C11—22no—
114C2×C42×C11C2×C411yescharacteristic
115C2×C42×C11C2×C411yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×#4318—22no—
121C2×#4318—22no—
122C2×#4318—22no—
123C2×#4318—22no—
124C2×#4318—22no—
125C2×#4318—22no—
126C2×#4318—41no—
127C2×#4318—41no—
128C2×#4318—41no—
129C22×C11⋊C8—22no—
130C22×C11⋊C8—22no—
131C22×C11⋊C8—41no—
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—22no—
142C22⋊(C11⋊C8)—22no—
143C22⋊(C11⋊C8)—22no—
144C22⋊(C11⋊C8)—22no—
145C22⋊(C11⋊C8)—22no—
146C22⋊(C11⋊C8)—41no—
147C22⋊(C11⋊C8)—41no—
148C4⋊(C11⋊C8)—22no—
149C4⋊(C11⋊C8)—22no—
150#66867—22no—
151C4×C11⋊C8—22no—
152#22472—111nomaximal, Sylow
153C24×C11C22×C411yescharacteristic
154C24×C11C22×C411yescharacteristic
155C24×C11C22×C411yescharacteristic
156C2×Q8×C11—22no—
157C2×Q8×C11—22no—
158C2×Q8×C11—41no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11—41no—
167C2×D4×C11C22⋊C414yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—41no—
186C22×C4×C11—41no—
187C22×C4×C11—41no—
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C22×C411yescharacteristic
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C22×C411yescharacteristic
192C22×C4×C11C22×C411yescharacteristic
193C22×C4×C11C22×C411yescharacteristic
194C22×C4×C11C22×C411yescharacteristic
195C22×C4×C11C22×C411yescharacteristic
196C22×C4×C11C22×C411yescharacteristic
197C22×C4×C11C22×C411yescharacteristic
198C22×C4×C11C22×C411yescharacteristic
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2411yescharacteristic
204C11×C4⋊C4—22no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4C22⋊C414yes—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4C22⋊C414yes—
223C11×C22⋊C4C22⋊C414yes—
224C42×C11—22no—
225C42×C11—22no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11C2×D412yes—
233C42×C11C2×D412yes—
234#4318—44no—
235#4318—44no—
236#4318—44no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—44no—
260C2×C11⋊C8#4112yes—
261C2×C11⋊C8#4112yes—
262C2×#529D1111yescharacteristic
263C2×#436—111no—
264C2×#435—111no—
265#1985—111no—
266#1984—111no—
267#1870—111no—
268#1870—111no—
269#1870—111no—
270#1869—111no—
271#1818—111no—
272#1817—111no—
273#1798—111no—
274#1750—111no—
275#1729—111no—
276#1728—111no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11C2×C22⋊C412yes—
297C23×C11C2×C22⋊C412yes—
298C23×C11C23×C411yescharacteristic
299Q8×C11—44no—
300D4×C11—44no—
301D4×C11—44no—
302D4×C11—44no—
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—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—44no—
340C2×C4×C11—44no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11C2×C22⋊C412yes—
346C2×C4×C11C2×C22⋊C412yes—
347C2×C4×C11C2×C22⋊C412yes—
348C2×C4×C11C2×C22⋊C412yes—
349C2×C4×C11#13112yes—
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C2×#4111yescharacteristic
353C2×C4×C11C2×#4111yescharacteristic
354C2×C4×C11H(5,𝔽2)11yescharacteristic
355C2×C4×C112−1+411yescharacteristic
356C11⋊C8—22no—
357C11⋊C8—22no—
358C11⋊C8—41no—
359C11⋊C8—41no—
360C11⋊C8—41no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C11⋊C8—41no—
364C22×M16—111no—
365C22×M16—111no—
366C22×M16—111no—
367C23×C8—111no—
368#529—24no—
369#529—24no—
370C2×#126Dic1111yescharacteristic
371C2×#126Dic1111yescharacteristic
372C2×#125Dic1111yescharacteristic
373C2×#124Dic1111yescharacteristic
374C2×#123Dic1111yescharacteristic
375C2×#123Dic1111yescharacteristic
376C2×C22⋊Q8Dic1111yescharacteristic
377C2×#121Dic1111yescharacteristic
378C2×C4×Q8C2×D1111yescharacteristic
379C2×C4×D4C2×D1111yescharacteristic
380C2×C4×D4C2×D1111yescharacteristic
381C2×C4×D4C2×D1111yescharacteristic
382C2×#117C2×D1111yescharacteristic
383C2×#117C2×D1111yescharacteristic
384C22×C42C2×D1111yescharacteristic
385#436—224no—
386#435—224no—
387C2×C4⋊C8—111no—
388C2×C4⋊C8—111no—
389C2×C22⋊C8—111no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—111no—
392C2×C22⋊C8—111no—
393C2×C22⋊C8—111no—
394C2×C22⋊C8—111no—
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
397C2×#97—111no—
398C2×C4×C8—111no—
399#336—111no—
400#336—111no—
401#336—111no—
402#336—111no—
403#336—111no—
404#336—111no—
405#336—111no—
406#336—111no—
407#336—111no—
408#336—111no—
409#336—111no—
410#336—111no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11C22×C22⋊C411yescharacteristic
433C22×C11C4×#4111yescharacteristic
434C22×C11#52011yescharacteristic
435C22×C11C2×#13111yescharacteristic
436C22×C11#56811yescharacteristic
437C22×C11#56811yescharacteristic
438C22×C11#56811yescharacteristic
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—22no—
444C4×C11—41no—
445C4×C11—41no—
446C4×C11—41no—
447C4×C11—41no—
448C4×C11—41no—
449C4×C11—41no—
450C4×C11#54611yescharacteristic
451C4×C11#54611yescharacteristic
452C4×C11#54711yescharacteristic
453C4×C11#54711yescharacteristic
454C22×Q8C2×Dic1111yescharacteristic
455C22×D4C2×Dic1111yescharacteristic
456C22×D4C2×Dic1111yescharacteristic
457C22×D4C2×Dic1111yescharacteristic
458C23×C4C2×Dic1111yescharacteristic
459C23×C4C2×Dic1111yescharacteristic
460C23×C4C22×D1111yescharacteristic
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1111yescharacteristic
463C2×M16—222no—
464C2×M16—222no—
465C2×M16—222no—
466C2×M16—222no—
467C2×M16—222no—
468C2×M16—222no—
469C2×M16—441no—
470C2×M16—441no—
471C2×M16—441no—
472C22×C8—111no—
473C22×C8—111no—
474C22×C8—111no—
475C22×C8—111no—
476C22×C8—111no—
477C22×C8—111no—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8—222no—
481C22×C8—222no—
482C22×C8—441no—
483#126—24no—
484#126—24no—
485#125—24no—
486#124—24no—
487#123—24no—
488#123—24no—
489C22⋊Q8—24no—
490#121—24no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4C22⋊D1114yes—
498C4×D4C22⋊D1114yes—
499#117—22no—
500#117—22no—
501#117—22no—
502#117—22no—
503C2×C4⋊C4C2×Dic1111yescharacteristic
504C2×C4⋊C4C2×Dic1111yescharacteristic
505C2×C4⋊C4C2×Dic1111yescharacteristic
506C2×C4⋊C4C2×Dic1111yescharacteristic
507C2×C4⋊C4C2×Dic1111yescharacteristic
508C2×C4⋊C4C2×Dic1111yescharacteristic
509C2×C4⋊C4C2×Dic1111yescharacteristic
510C2×C4⋊C4C2×Dic1111yescharacteristic
511C2×C4⋊C4C2×Dic1111yescharacteristic
512C2×C4⋊C4C2×Dic1111yescharacteristic
513C2×C22⋊C4C2×Dic1111yescharacteristic
514C2×C22⋊C4C2×Dic1111yescharacteristic
515C2×C22⋊C4C2×Dic1111yescharacteristic
516C2×C22⋊C4C2×Dic1111yescharacteristic
517C2×C22⋊C4C2×Dic1111yescharacteristic
518C2×C22⋊C4C2×Dic1111yescharacteristic
519C2×C22⋊C4C2×Dic1111yescharacteristic
520C2×C22⋊C4C2×Dic1111yescharacteristic
521C2×C22⋊C4C2×Dic1111yescharacteristic
522C2×C22⋊C4C2×Dic1111yescharacteristic
523C2×C42—22no—
524C2×C42—22no—
525C2×C42C2×Dic1111yescharacteristic
526C2×C42C2×Dic1111yescharacteristic
527C2×C42C22×D1111yescharacteristic
528C2×C42C22×D1111yescharacteristic
529C2×C42C22×D1111yescharacteristic
530C2×C42C22×D1111yescharacteristic
531C4⋊C8—222no—
532C4⋊C8—222no—
533C22⋊C8—222no—
534C22⋊C8—222no—
535C22⋊C8—222no—
536C22⋊C8—222no—
537C22⋊C8—222no—
538C22⋊C8—222no—
539C22⋊C8—441no—
540C22⋊C8—441no—
541#97—222no—
542C4×C8—222no—
543C2×C11—42no—
544C2×C11—42no—
545C2×C11—81no—
546C2×C11#233911yescharacteristic
547C2×C11#287911yescharacteristic
548C2×C11#288011yescharacteristic
549C2×C11#296711yescharacteristic
550C2×C11#296911yescharacteristic
551C2×C11#299311yescharacteristic
552C2×C11#299511yescharacteristic
553C24C22×Dic1111yescharacteristic
554C24C22×Dic1111yescharacteristic
555C24C22×Dic1111yescharacteristic
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—41no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4C22⋊Dic1114yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4C22×Dic1111yescharacteristic
589C22×C4C22×Dic1111yescharacteristic
590C22×C4C22×Dic1111yescharacteristic
591C22×C4C22×Dic1111yescharacteristic
592C22×C4C22×Dic1111yescharacteristic
593C22×C4C22×Dic1111yescharacteristic
594C22×C4C22×Dic1111yescharacteristic
595C22×C4C22×Dic1111yescharacteristic
596C22×C4C22×Dic1111yescharacteristic
597C22×C4C22×Dic1111yescharacteristic
598C22×C4C22×Dic1111yescharacteristic
599C22×C4C2×C22⋊D1112yes—
600C22×C4C2×C22⋊D1112yes—
601C22×C4C2×C22⋊D1112yes—
602C22×C4C2×C22⋊D1112yes—
603C22×C4C23×D1111yescharacteristic
604M16—444no—
605M16—444no—
606M16—444no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8—221no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—221no—
615C2×C8—221no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—221no—
631C2×C8—444no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4C22⋊Dic1114yes—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4C22⋊Dic1114yes—
651C22⋊C4C22⋊Dic1114yes—
652C42—22no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42C2×C22⋊D1112yes—
661C42C2×C22⋊D1112yes—
662C11#2247211yescharacteristic, complemented, Sylow
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23C2×C22⋊Dic1112yes—
683C23C2×C22⋊Dic1112yes—
684C23C23×Dic1111yescharacteristic
685Q8—44no—
686D4—44no—
687D4—44no—
688D4—44no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4#6700112yes—
732C2×C4C2×C22⋊Dic1112yes—
733C2×C4C2×C22⋊Dic1112yes—
734C2×C4C2×C22⋊Dic1112yes—
735C2×C4C2×C22⋊Dic1112yes—
736C2×C4#41×D1111yescharacteristic
737C2×C4#41×D1111yescharacteristic
738C2×C4#6704211yescharacteristic
739C2×C4#6704311yescharacteristic
740C2×C4C22×C22⋊D1111yescharacteristic
741C2×C4C22×C22⋊D1111yescharacteristic
742C8—222no—
743C8—222no—
744C8—441no—
745C8—441no—
746C8—441no—
747C8—441no—
748C8—441no—
749C8—441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22C2×#6700111yescharacteristic
772C22#1062335011yescharacteristic
773C22#1062335011yescharacteristic
774C22#1062335011yescharacteristic
775C22#41×Dic1111yescharacteristic
776C22#1062335811yescharacteristic
777C22C22×C22⋊Dic1111yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4#1062335511yescharacteristic
790C4#1062335511yescharacteristic
791C4#1062336011yescharacteristic
792C4#1062336011yescharacteristic
793C2—42no—
794C2—42no—
795C2—81no—
796C2#1307144611yescharacteristic
797C2#1307706111yescharacteristic
798C2#1307706511yescharacteristic
799C2#1307760311yescharacteristic
800C2#1307762111yescharacteristic
801C2#1307776511yescharacteristic
802C2#1307778611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#529C2
prime radicalC2×C11×#121C4
cosocleC22×C4×C11C24
hypercenterC2×#529D11
hypocenterC11#22472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#10622625C2semidirect
2. C2×#10622624C2semidirect
3. #13069557C2semidirect
4. #13069553C2semidirect
5. #13068914C2semidirect
6. #13068914C2semidirect
7. #13068914C2semidirect
8. #13068909C2semidirect
9. #13068687C2semidirect
10. #13068684C2semidirect
11. #13068600C2semidirect
12. #13068382C2semidirect
13. #13068313C2semidirect
14. #13068310C2semidirect
662. C11#22472semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×#106226242
#130695572
#130695532
#130689142
#130689092
#130686872
#130686842
#130686002
#130683822
#130683132
#130683102
C2×C11×#5292
#2247211