Finite Group Databasebeta

← #14780321

Subgroups — #14780321

Order 2816.

944 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66993C211yesmaximal, characteristic
2#13068914C211yesmaximal, characteristic, complemented
3#13068912C211yesmaximal, characteristic, complemented
4#13068911C211yesmaximal, characteristic, complemented
5#13068911C211yesmaximal, characteristic, complemented
6#13068910C211yesmaximal, characteristic, complemented
7#13068910C211yesmaximal, characteristic, complemented
8#13068908C211yesmaximal, characteristic, complemented
9#13068908C211yesmaximal, characteristic, complemented
10#13068907C211yesmaximal, characteristic, complemented
11#13068905C211yesmaximal, characteristic, complemented
12#13068905C211yesmaximal, characteristic, complemented
13#13068758C211yesmaximal, characteristic, complemented
14#13068758C211yesmaximal, characteristic, complemented
15C11×#1869C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66993C411yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C22×#4313C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26C2×C4×D44C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30#10622834C411yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40#10622601C411yescharacteristic
41#10622589C411yescharacteristic
42#10622570C411yescharacteristic
43#10622570C411yescharacteristic
44#10622570C411yescharacteristic
45#10622570C411yescharacteristic
46C42×Dic11C2211yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11C2×C411yescharacteristic
63C22×C22⋊D11C2×C411yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C22×C8×C11—41no—
70C22×C8×C11—41no—
71C22×C8×C11—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C4×D4×C11—41no—
77C4×D4×C11—41no—
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86#66993—24no—
87C4×C22⋊D11—41no—
88C4×C22⋊D11—41no—
89C4×C22⋊D11—41no—
90C4×C22⋊D11—41no—
91C4×C22⋊D11—41no—
92C4×C22⋊D11—41no—
93C4×C22⋊D11—41no—
94C4×C22⋊D11—41no—
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×C4⋊Dic11C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×Dic11⋊C4C2×C411yescharacteristic
106C2×C4×Dic11C2×C411yescharacteristic
107C2×C4×Dic11C2×C411yescharacteristic
108C2×C4×Dic11C2×C411yescharacteristic
109C2×C4×Dic11C2×C411yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C2×#4318—41no—
113C2×#4318—41no—
114C2×#4318—41no—
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C2×#4313—41no—
120C2×#4313—41no—
121C2×#4313—41no—
122C2×C8×D11—41no—
123C2×C8×D11—41no—
124C2×C8×D11—41no—
125C4×D44—41no—
126C4×D44—41no—
127C11×C22⋊C8—41no—
128C11×C22⋊C8—41no—
129C11×C22⋊C8—41no—
130C22⋊(C11⋊C8)—41no—
131C22⋊(C11⋊C8)—41no—
132C22⋊(C11⋊C8)—41no—
133(C2×D11)⋊C8—41no—
134(C2×D11)⋊C8—41no—
135(C2×D11)⋊C8—41no—
136(C2×D11)⋊C8—41no—
137(C2×D11)⋊C8—41no—
138(C2×D11)⋊C8—41no—
139#23356—111nomaximal, Sylow
140C24×C11C22×C411yescharacteristic
141C24×C11C22×C411yescharacteristic
142C23×D11C22×C411yescharacteristic
143C23×D11C22×C411yescharacteristic
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—41no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
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×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C2×C22⋊D11—22no—
165C2×C22⋊D11—22no—
166C2×C22⋊D11—22no—
167C2×C22⋊D11—22no—
168C2×C22⋊D11—22no—
169C2×C22⋊D11—41no—
170C2×C22⋊D11—41no—
171C2×C22⋊D11—41no—
172C2×C22⋊D11—41no—
173C2×C22⋊D11—41no—
174C2×C22⋊D11—41no—
175C2×C22⋊D11M1614yescomplemented
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C22×Dic11C22×C411yescharacteristic
180C22×Dic11C22×C411yescharacteristic
181C22×Dic11C22×C411yescharacteristic
182C2×D44—22no—
183C2×D44—22no—
184C2×D44—41no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—44no—
210C11×C4⋊C4—41no—
211C11×C22⋊C4—41no—
212C11×C22⋊C4—41no—
213C42×C11—21no—
214C42×C11—21no—
215C22⋊Dic11—41no—
216C22⋊Dic11—41no—
217C22⋊Dic11—41no—
218C22⋊Dic11—41no—
219(C2×D11)⋊C4—41no—
220(C2×D11)⋊C4—41no—
221(C2×D11)⋊C4—41no—
222(C2×D11)⋊C4—41no—
223(C2×D11)⋊C4—41no—
224(C2×D11)⋊C4—41no—
225C4⋊Dic11—41no—
226Dic11⋊C4—41no—
227Dic11⋊C4—41no—
228Dic11⋊C4—41no—
229Dic11⋊C4—41no—
230C4×Dic11—22no—
231C4×Dic11—22no—
232C4×Dic11—22no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—21no—
237C4×Dic11—41no—
238#4318—44no—
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—
251#4313—44no—
252C8×D11—44no—
253C4×#127—111no—
254#1870—111no—
255#1870—111no—
256#1870—111no—
257#1870—111no—
258#1870—111no—
259#1870—111no—
260#1869—111no—
261#1869—111no—
262#1869—111no—
263#1869—111no—
264#1869—111no—
265#1869D1111yescharacteristic, complemented
266#1839—111no—
267#1839—111no—
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—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11C2×M1612yes—
282C23×C11C23×C411yescharacteristic
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11C2×M1612yes—
297D4×C11—44no—
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—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11#13112yes—
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C22⋊D11—44no—
325C22⋊D11—44no—
326C22⋊D11—44no—
327C22⋊D11—44no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11C2×M1612yes—
345C2×Dic11#13112yes—
346D44—44no—
347C4×D11—41no—
348C4×D11—41no—
349C4×D11—41no—
350C4×D11—41no—
351C4×D11—41no—
352C4×D11—41no—
353C4×D11—41no—
354C4×D11—41no—
355C8×C11—41no—
356C8×C11—41no—
357C8×C11—41no—
358C8×C11—41no—
359C11⋊C8—41no—
360C11⋊C8—41no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C22×M16—111no—
364C22×M16—111no—
365C23×C8—111no—
366C23×C8C2×D1111yescharacteristic
367C2×#127—111no—
368C2×C4×D4—111no—
369C2×C4×D4—111no—
370C2×C4×D4—111no—
371C2×C4×D4—111no—
372C2×C4×D4—111no—
373C2×C4×D4C2×D1111yescharacteristic
374C2×C22⋊C8—111no—
375C2×C22⋊C8—111no—
376C2×C22⋊C8—111no—
377C2×C22⋊C8—111no—
378C2×C22⋊C8—111no—
379C2×C22⋊C8—111no—
380C2×C22⋊C8—111no—
381C2×C22⋊C8—111no—
382C2×C22⋊C8—111no—
383C2×C22⋊C8C2×D1111yescharacteristic
384C2×C22⋊C8C2×D1111yescharacteristic
385C2×C22⋊C8C2×D1111yescharacteristic
386#390—111no—
387#390—111no—
388#390—111no—
389#390—111no—
390#390—111no—
391#390—111no—
392#384—111no—
393C43—111no—
394#336—111no—
395#336—111no—
396#336—111no—
397#336—111no—
398#336—111no—
399#336—111no—
400#336—111no—
401#336—111no—
402#336—111no—
403#336—111no—
404#336C2×D1111yescharacteristic
405#336C2×D1111yescharacteristic
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11#51811yescharacteristic
421C22×C11#51811yescharacteristic
422C22×C11#51811yescharacteristic
423C22×C11C22×M1611yescharacteristic
424C22×C11C2×#13111yescharacteristic
425C22×C11C2×#13111yescharacteristic
426C22×C11#56811yescharacteristic
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—41no—
431C2×D11—41no—
432C2×D11—41no—
433C2×D11—41no—
434C2×D11—41no—
435C2×D11—41no—
436C2×D11—41no—
437C2×D11—41no—
438C2×D11—41no—
439C2×D11—41no—
440C2×D11—41no—
441C4×C11—22no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11—41no—
445C4×C11#56011yescharacteristic
446C4×C11#56011yescharacteristic
447C4×C11#56011yescharacteristic
448C4×C11#56011yescharacteristic
449Dic11—22no—
450Dic11—22no—
451Dic11—41no—
452Dic11—41no—
453Dic11—41no—
454Dic11—41no—
455C22×D4—111no—
456C22×D4—111no—
457C22×D4—111no—
458C22×D4—111no—
459C22×D4—111no—
460C22×D4C4×D1111yescharacteristic
461C23×C4—111no—
462C23×C4—111no—
463C23×C4C22×D1111yescharacteristic
464C23×C4C22×D1111yescharacteristic
465C2×M16—441no—
466C2×M16—441no—
467C2×M16—441no—
468C2×M16—441no—
469C2×M16—441no—
470C2×M16—441no—
471C22×C8—41no—
472C22×C8—41no—
473C22×C8—41no—
474C22×C8—111no—
475C22×C8—111no—
476C22×C8—111no—
477C22×C8—111no—
478C22×C8—441no—
479C22×C8—441no—
480C22×C8—441no—
481C22×C8C22×D1111yescharacteristic
482C22×C8C22×D1111yescharacteristic
483C22×C8C22×D1111yescharacteristic
484C22×C8C22×D1111yescharacteristic
485#127—224no—
486C4×D4—41no—
487C4×D4—41no—
488C4×D4—441no—
489C4×D4—441no—
490C4×D4—441no—
491C4×D4—441no—
492C4×D4—441no—
493C4×D4—441no—
494C4×D4—441no—
495C4×D4—441no—
496C4×D4—441no—
497C4×D4—441no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4C4×D1111yescharacteristic
504C2×C22⋊C4—111no—
505C2×C22⋊C4—111no—
506C2×C22⋊C4—111no—
507C2×C22⋊C4—111no—
508C2×C22⋊C4—111no—
509C2×C22⋊C4—111no—
510C2×C22⋊C4—111no—
511C2×C22⋊C4—111no—
512C2×C22⋊C4—111no—
513C2×C22⋊C4—111no—
514C2×C22⋊C4C4×D1111yescharacteristic
515C2×C22⋊C4C4×D1111yescharacteristic
516C2×C42—111no—
517C2×C42—111no—
518C2×C42—111no—
519C2×C42—111no—
520C2×C42—111no—
521C2×C42—111no—
522C2×C42C22×D1111yescharacteristic
523C22⋊C8—41no—
524C22⋊C8—41no—
525C22⋊C8—41no—
526C22⋊C8—441no—
527C22⋊C8—441no—
528C22⋊C8—441no—
529C22⋊C8—441no—
530C22⋊C8—441no—
531C22⋊C8—441no—
532C22⋊C8—441no—
533C22⋊C8—441no—
534C22⋊C8—441no—
535C2×C11—42no—
536C2×C11—81no—
537C2×C11#238011yescharacteristic
538C2×C11#297311yescharacteristic
539C2×C11#297411yescharacteristic
540C2×C11#297411yescharacteristic
541C2×C11#297911yescharacteristic
542C2×C11#298111yescharacteristic
543C2×C11#298111yescharacteristic
544D11—42no—
545D11—81no—
546C24—111no—
547C24—111no—
548C24C2×C4×D1111yescharacteristic
549C24C2×C4×D1111yescharacteristic
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—41no—
553C2×D4—114no—
554C2×D4—222no—
555C2×D4—222no—
556C2×D4—222no—
557C2×D4—222no—
558C2×D4—222no—
559C2×D4—222no—
560C2×D4—222no—
561C2×D4—441no—
562C2×D4—441no—
563C2×D4—441no—
564C2×D4—441no—
565C2×D4—441no—
566C2×D4—441no—
567C2×D4—441no—
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—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—111no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—111no—
584C22×C4—111no—
585C22×C4—111no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4C2×C4×D1111yescharacteristic
599C22×C4C2×C4×D1111yescharacteristic
600C22×C4C2×C4×D1111yescharacteristic
601C22×C4C2×C4×D1111yescharacteristic
602C22×C4C23×D1111yescharacteristic
603M16—444no—
604M16—444no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—44no—
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—444no—
631C4⋊C4—41no—
632C4⋊C4—441no—
633C4⋊C4—441no—
634C4⋊C4—441no—
635C4⋊C4—441no—
636C4⋊C4—441no—
637C22⋊C4—41no—
638C22⋊C4—41no—
639C22⋊C4—441no—
640C22⋊C4—441no—
641C22⋊C4—441no—
642C22⋊C4—441no—
643C22⋊C4—441no—
644C22⋊C4—441no—
645C22⋊C4—441no—
646C22⋊C4—441no—
647C22⋊C4—441no—
648C22⋊C4—441no—
649C42—21no—
650C42—21no—
651C42—222no—
652C42—222no—
653C42—222no—
654C42—221no—
655C42—221no—
656C42—221no—
657C42—221no—
658C42—441no—
659C11#2335611yescharacteristic, complemented, Sylow
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—112no—
674C23—221no—
675C23—221no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23—221no—
681C23—221no—
682C23—221no—
683C23—221no—
684C23—221no—
685C23—221no—
686C23—221no—
687C23M16×D1112yes—
688C23C22×C4×D1111yescharacteristic
689D4—44no—
690D4—444no—
691D4—444no—
692D4—444no—
693D4—444no—
694D4—444no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—112no—
715C2×C4—112no—
716C2×C4—221no—
717C2×C4—221no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—221no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—221no—
731C2×C4—221no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4#6695412yes—
741C2×C4#6703711yescharacteristic
742C2×C4#6703711yescharacteristic
743C2×C4#6703711yescharacteristic
744C2×C4#6703711yescharacteristic
745C2×C4#6704211yescharacteristic
746C2×C4#6704211yescharacteristic
747C8—41no—
748C8—41no—
749C8—41no—
750C8—41no—
751C8—441no—
752C8—441no—
753C8—441no—
754C8—441no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—222no—
770C22—222no—
771C22—222no—
772C22—441no—
773C22—441no—
774C22—441no—
775C22—441no—
776C22—441no—
777C22—441no—
778C22—441no—
779C22—441no—
780C22—441no—
781C22—441no—
782C22—441no—
783C22#1062301711yescharacteristic
784C22#1062307611yescharacteristic
785C22#1062307611yescharacteristic
786C22C2×#6695411yescharacteristic
787C22C2×M16×D1111yescharacteristic
788C22D11×#13111yescharacteristic
789C22#1062328111yescharacteristic
790C4—22no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—222no—
795C4—222no—
796C4—441no—
797C4—441no—
798C4—441no—
799C4—441no—
800C4#1062312611yescharacteristic
801C4#1062315111yescharacteristic
802C4#1062315111yescharacteristic
803C4#1062319711yescharacteristic
804C2—42no—
805C2—81no—
806C2—442no—
807C2—881no—
808C2#1307179111yescharacteristic
809C2#1307764111yescharacteristic
810C2#1307764611yescharacteristic
811C2#1307764711yescharacteristic
812C2#1307767911yescharacteristic
813C2#1307768911yescharacteristic
814C2#1307769011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1869C2
prime radicalC2×#66993C4
cosocleC22×C4×C11C24
hypercenter#1869D11
hypocenterC11#23356
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #13068914C2semidirect
3. #13068912C2semidirect
4. #13068911C2semidirect
5. #13068911C2semidirect
6. #13068910C2semidirect
7. #13068910C2semidirect
8. #13068908C2semidirect
9. #13068908C2semidirect
10. #13068907C2semidirect
11. #13068905C2semidirect
12. #13068905C2semidirect
13. #13068758C2semidirect
14. #13068758C2semidirect
15. C11×#1869C2semidirect
175. C2×C22⋊D11M16semidirect
265. #1869D11semidirect
659. C11#23356semidirect

Maximal subgroups

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

subgroupindex
C4×#669932
#130689142
#130689122
#130689112
#130689102
#130689082
#130689072
#130689052
#130687582
C11×#18692
#2335611