Finite Group Databasebeta

← C2×#13073682 #14923860

Subgroups — C2×#13073682 #14923860

Order 2816.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66929C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic, complemented
3#13073682C2116yesmaximal, direct product factor
4C2×#10622597C211yesmaximal, characteristic, complemented
5C2×#10622289C211yesmaximal, characteristic, complemented
6C2×#10622572C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic
8C2×#10622601C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622283C211yesmaximal, characteristic, complemented
12C2×#10622557C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66936—28no—
47C2×#66936C2218yescomplemented
48C2×#66929—28no—
49C2×#66929C2218yescomplemented
50C11×#388C2218yescomplemented
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622601C2218yescomplemented
58#10622597C2218yescomplemented
59#10622573C2218yes—
60#10622572C2218yescomplemented
61#10622570C2218yescomplemented
62#10622570C2218yescomplemented
63#10622557C2218yescomplemented
64C4×(C2×D11)⋊C4C2218yescomplemented
65#10622289C2218yescomplemented
66#10622283C2218yescomplemented
67#10622278C2218yescomplemented
68#10622262C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—24no—
79C22×C22⋊D11—24no—
80C22×C22⋊D11—24no—
81C22×C22⋊D11—42no—
82C22×C22⋊D11—42no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11C2314yes—
85C22×C22⋊D11C2314yes—
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C22×D44—24no—
93C22×D44—24no—
94C22×D44—42no—
95C22×D44C2314yes—
96C22×C4×D11—24no—
97C22×C4×D11—24no—
98C22×C4×D11—42no—
99C22×C4×D11C2314yes—
100C2×C11×C4⋊C4—42no—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4—24no—
104C2×C11×C22⋊C4—42no—
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C42×C11—24no—
109C2×C42×C11C2314yes—
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×C4⋊Dic11—24no—
133C2×C4⋊Dic11C2314yes—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4—42no—
138C2×Dic11⋊C4D418yescomplemented
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×C4×Dic11—24no—
145C2×C4×Dic11—42no—
146C2×C4×Dic11—42no—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2314yes—
150#66936—232no—
151#66929—232no—
152C11×#95C2314yes—
153C11×#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2554—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11#4114yes—
182C23×D11C2412yes—
183C23×D11C2412yes—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11C2×D414yes—
201C22×C4×C11#4114yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C2×C22⋊D11—28no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—28no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—416no—
215C2×C22⋊D11—416no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11C2×D414yes—
231C22×Dic11C2×D414yes—
232C22×Dic11#4114yes—
233C22×Dic11#4114yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C2×D44—28no—
241C2×D44—28no—
242C2×D44—44no—
243C2×D44—416no—
244C2×C4×D11—28no—
245C2×C4×D11—28no—
246C2×C4×D11—44no—
247C2×C4×D11—416no—
248C11×C4⋊C4—44no—
249C11×C22⋊C4—28no—
250C11×C22⋊C4—28no—
251C11×C22⋊C4—44no—
252C42×C11—28no—
253C22⋊Dic11—28no—
254C22⋊Dic11—28no—
255(C2×D11)⋊C4—28no—
256(C2×D11)⋊C4—28no—
257(C2×D11)⋊C4—28no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264C4⋊Dic11—28no—
265Dic11⋊C4—28no—
266Dic11⋊C4—28no—
267Dic11⋊C4—28no—
268Dic11⋊C4—44no—
269Dic11⋊C4C2×D4116yescomplemented
270C4×Dic11—28no—
271C4×Dic11—44no—
272C4×Dic11—44no—
273C22×#126—111no—
274C22×#123—111no—
275#2554—1116no—
276C2×#398—111no—
277C2×#396—111no—
278C2×#394—111no—
279C2×#392—111no—
280C2×#390—111no—
281C2×#390—111no—
282C2×#390—111no—
283C2×#388—111no—
284C2×#388—111no—
285C2×#388D1111yescharacteristic, complemented
286C2×#386—111no—
287C2×C4×C4⋊C4—111no—
288C2×C4×C22⋊C4—111no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11—44no—
299C23×C11—44no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11C22×D412yes—
304C23×C11C2×#4112yes—
305C23×C11C2×#4112yes—
306C23×C11C2×#4112yes—
307C23×C11C2×#4112yes—
308C23×C11H(5,𝔽2)12yes—
309C23×C11H(5,𝔽2)12yes—
310C23×C11C2511yescharacteristic
311C22×D11—28no—
312C22×D11—28no—
313C22×D11—28no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—44no—
328C22×D11—44no—
329C22×D11—44no—
330C22×D11—44no—
331C22×D11—44no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11C2×#4114yes—
339C2×C4×C11—28no—
340C2×C4×C11—28no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—44no—
358C2×C4×C11—44no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11C22×D414yes—
362C2×C4×C11C2×#4114yes—
363C22⋊D11—416no—
364C22⋊D11—416no—
365C2×Dic11—28no—
366C2×Dic11—28no—
367C2×Dic11—28no—
368C2×Dic11—28no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—44no—
384C2×Dic11—44no—
385C2×Dic11C22×D414yes—
386C2×Dic11C22×D414yes—
387C2×Dic11C2×#4114yes—
388C2×Dic11C2×#4114yes—
389D44—416no—
390C4×D11—416no—
391C23×D4—111no—
392C23×D4—111no—
393C23×D4—111no—
394C24×C4—111no—
395C2×#126—118no—
396C2×#126—228no—
397C2×#123—118no—
398C2×#123—228no—
399C22×C4⋊C4—111no—
400C22×C4⋊C4—111no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊C4C2×D1111yescharacteristic
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4C2×D1111yescharacteristic
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C42—111no—
421C22×C42—111no—
422C22×C42—111no—
423C22×C42C2×D1111yescharacteristic
424#398—118no—
425#396—118no—
426#394—118no—
427#392—118no—
428#390—118no—
429#390—118no—
430#390—118no—
431#388—118no—
432#388—118no—
433#388C2×D1118yescomplemented
434#386—118no—
435C4×C4⋊C4—118no—
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95C2×D1111yescharacteristic
442C2×#95C2×D1111yescharacteristic
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—88no—
451C22×C11#52914yes—
452C22×C11#53214yes—
453C22×C11#53814yes—
454C22×C11#54614yes—
455C22×C11#55014yes—
456C22×C11#55114yes—
457C22×C11#55314yes—
458C22×C11C23×D411yescharacteristic
459C22×C11C22×#4111yescharacteristic
460C22×C11C22×#4111yescharacteristic
461C22×C11C22×#4111yescharacteristic
462C22×C11C22×#4111yescharacteristic
463C22×C11C2×H(5,𝔽2)11yescharacteristic
464C22×C11C2×H(5,𝔽2)11yescharacteristic
465C2×D11—24no—
466C2×D11—24no—
467C2×D11—24no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—416no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—88no—
481C4×C11—24no—
482C4×C11—24no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11—42no—
487Dic11—24no—
488Dic11—24no—
489Dic11—24no—
490Dic11—24no—
491Dic11—42no—
492Dic11—42no—
493C25—111no—
494C25—111no—
495C25C22×D1111yescharacteristic
496C22×D4—114no—
497C22×D4—114no—
498C22×D4—114no—
499C22×D4—224no—
500C22×D4—224no—
501C22×D4—224no—
502C22×D4—224no—
503C22×D4—224no—
504C22×D4—442no—
505C22×D4—442no—
506C22×D4—442no—
507C22×D4—442no—
508C23×C4—111no—
509C23×C4—111no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—114no—
515C23×C4—224no—
516C23×C4—224no—
517C23×C4—442no—
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524#126—2232no—
525#123—2232no—
526C2×C4⋊C4—42no—
527C2×C4⋊C4—118no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—114no—
530C2×C4⋊C4—114no—
531C2×C4⋊C4—114no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—224no—
535C2×C4⋊C4—224no—
536C2×C4⋊C4—224no—
537C2×C4⋊C4—224no—
538C2×C4⋊C4—442no—
539C2×C4⋊C4C22×D1114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—224no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—442no—
564C2×C22⋊C4—442no—
565C2×C22⋊C4C22×D1114yes—
566C2×C22⋊C4C22×D1114yes—
567C2×C22⋊C4C22×D1114yes—
568C2×C42—24no—
569C2×C42—114no—
570C2×C42—114no—
571C2×C42—114no—
572C2×C42—224no—
573C2×C42—442no—
574C2×C42—442no—
575C2×C42C22×D1114yes—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95C22×D1114yes—
581#95C22×D1114yes—
582C2×C11—82no—
583C2×C11#255418yescomplemented
584C2×C11C2×#52911yescharacteristic
585C2×C11C2×#53211yescharacteristic
586C2×C11C2×#53811yescharacteristic
587C2×C11C2×#54611yescharacteristic
588C2×C11C2×#55011yescharacteristic
589C2×C11C2×#55111yescharacteristic
590C2×C11C2×#55311yescharacteristic
591D11—44no—
592D11—82no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—114no—
601C24—112no—
602C24—112no—
603C24—222no—
604C24—222no—
605C24—222no—
606C24—222no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24C23×D1112yes—
617C24C23×D1111yescharacteristic
618C2×D4—228no—
619C2×D4—228no—
620C2×D4—228no—
621C2×D4—228no—
622C2×D4—228no—
623C2×D4—444no—
624C2×D4—4416no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—4416no—
629C2×D4—4416no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—114no—
647C22×C4—114no—
648C22×C4—114no—
649C22×C4—114no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—228no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—228no—
672C22×C4—444no—
673C22×C4—4416no—
674C22×C4#433914yes—
675C22×C4D4×D1114yes—
676C22×C4C23×D1112yes—
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1112yes—
681C22×C4C23×D1112yes—
682C4⋊C4—44no—
683C4⋊C4—1116no—
684C4⋊C4—228no—
685C4⋊C4—228no—
686C4⋊C4—228no—
687C4⋊C4—228no—
688C4⋊C4—444no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—44no—
692C22⋊C4—228no—
693C22⋊C4—228no—
694C22⋊C4—228no—
695C22⋊C4—228no—
696C22⋊C4—228no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C42—28no—
704C42—228no—
705C42—444no—
706C42—444no—
707C11C2×#255411yescharacteristic, complemented, Sylow
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—114no—
723C23—228no—
724C23—228no—
725C23—228no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—444no—
740C23—444no—
741C23—444no—
742C23—444no—
743C23—444no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23C2×#433912yes—
751C23C2×D4×D1112yes—
752C23#6703712yes—
753C23#41×D1112yes—
754C23#41×D1112yes—
755C23#41×D1112yes—
756C23#6704212yes—
757C23C24×D1111yescharacteristic
758D4—4416no—
759D4—4416no—
760D4—4416no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—114no—
784C2×C4—114no—
785C2×C4—114no—
786C2×C4—114no—
787C2×C4—228no—
788C2×C4—228no—
789C2×C4—228no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—228no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—4416no—
806C2×C4—444no—
807C2×C4—444no—
808C2×C4C2×#433914yes—
809C2×C4C2×D4×D1114yes—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—88no—
818C22—224no—
819C22—224no—
820C22—224no—
821C22—4416no—
822C22—442no—
823C22—442no—
824C22—442no—
825C22—442no—
826C22—442no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—888no—
834C22#1062306114yes—
835C22#1062307914yes—
836C22#1062308714yes—
837C22#1062313014yes—
838C22#1062318514yes—
839C22#1062320914yes—
840C22#1062323714yes—
841C22C22×#433911yescharacteristic
842C22C22×D4×D1111yescharacteristic
843C22C2×#6703711yescharacteristic
844C22C2×#41×D1111yescharacteristic
845C22C2×#41×D1111yescharacteristic
846C22C2×#41×D1111yescharacteristic
847C22C2×#6704211yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—224no—
855C4—224no—
856C4—224no—
857C4—224no—
858C4—442no—
859C4—442no—
860C2—82no—
861C2—444no—
862C2—882no—
863C2#1307368218yesdirect product factor
864C2C2×#1062323711yescharacteristic
865C2C2×#1062307911yescharacteristic
866C2C2×#1062320911yescharacteristic
867C2C2×#1062318511yescharacteristic
868C2C2×#1062313011yescharacteristic
869C2C2×#1062308711yescharacteristic
870C2C2×#1062306111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#388D11
hypocenterC11C2×#2554
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66929C2semidirect
2. C22×#66936C2semidirect
3. #13073682C2direct (N × H)
4. C2×#10622597C2semidirect
5. C2×#10622289C2semidirect
6. C2×#10622572C2semidirect
8. C2×#10622601C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622283C2semidirect
12. C2×#10622557C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622262C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#388C2semidirect
47. C2×#66936C22semidirect
49. C2×#66929C22semidirect
50. C11×#388C22semidirect
57. #10622601C22semidirect
58. #10622597C22semidirect
60. #10622572C22semidirect
61. #10622570C22semidirect
62. #10622570C22semidirect
63. #10622557C22semidirect
64. C4×(C2×D11)⋊C4C22semidirect
65. #10622289C22semidirect
66. #10622283C22semidirect
67. #10622278C22semidirect
68. #10622262C22semidirect
138. C2×Dic11⋊C4D4semidirect
269. Dic11⋊C4C2×D4semidirect
285. C2×#388D11semidirect
433. #388C2×D11semidirect
583. C2×C11#2554semidirect
707. C11C2×#2554semidirect
863. C2#13073682direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669292
C22×#669362
#130736822
C2×#106225972
C2×#106222892
C2×#106225722
C2×#106225732
C2×#106226012
C2×#106225702
C2×#106222832
C2×#106225572
C2×#106222782
C2×#106222622
C2×C4×(C2×D11)⋊C42
C2×C11×#3882
C2×#255411