Finite Group Databasebeta

← #14764893

Subgroups — #14764893

Order 2816.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622741C211yesmaximal, characteristic, complemented
2C2×#10622742C211yesmaximal, characteristic, complemented
3#13071832C211yesmaximal, characteristic
4#13069414C211yesmaximal, characteristic, complemented
5#13069410C211yesmaximal, characteristic, complemented
6#13069229C211yesmaximal, characteristic, complemented
7#13069223C211yesmaximal, characteristic, complemented
8#13069223C211yesmaximal, characteristic, complemented
9#13069222C211yesmaximal, characteristic, complemented
10#13068912C211yesmaximal, characteristic, complemented
11#13068912C211yesmaximal, characteristic, complemented
12#13068906C211yesmaximal, characteristic, complemented
13#13068796C211yesmaximal, characteristic, complemented
14#13068527C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28#10622742—24no—
29#10622741—24no—
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622574C411yescharacteristic
44#10622574C411yescharacteristic
45#10622573C411yescharacteristic
46#10622573C411yescharacteristic
47C4×(C2×D11)⋊C4C2211yescharacteristic
48C4×(C2×D11)⋊C4C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622286C411yescharacteristic
52#10622285C411yescharacteristic
53#10622284C411yescharacteristic
54#10622269C411yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11C2×C411yescharacteristic
63C22×C22⋊D11C2×C411yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C2×#4339—22no—
66C2×#4339—22no—
67C2×#4339—41no—
68C2×#4339—41no—
69C2×#4339—41no—
70C2×#4339—41no—
71C22×D44C2×C411yescharacteristic
72C22×D44C2×C411yescharacteristic
73C22×D44C2×C411yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×C4×D11C2311yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×Dic22C2×C411yescharacteristic
78C2×C11×M16—41no—
79C2×C11×M16—41no—
80C2×C11×M16D414yescomplemented
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90C4×C22⋊D11—22no—
91C4×C22⋊D11—22no—
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
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×C4⋊Dic11C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8—22no—
106C22×C11⋊C8—41no—
107C22×C11⋊C8—41no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C2×#4313—22no—
113C2×#4313—41no—
114C2×#4313—41no—
115C4×D44—41no—
116C4×D44—41no—
117C4×D44—41no—
118C4×D44—41no—
119C11×C22⋊C8—22no—
120C11×#97—41no—
121C4×C8×C11—41no—
122C11×#95C2×C411yescharacteristic
123C11×#95C2×C411yescharacteristic
124C11⋊#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C22⋊(C11⋊C8)—22no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
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(C2×D11)⋊C8—41no—
140Dic11⋊C8—22no—
141C8×Dic11—22no—
142C4⋊(C11⋊C8)—41no—
143C4⋊(C11⋊C8)—41no—
144#22039—111nomaximal, Sylow
145C24×C11C22×C411yescharacteristic
146C23×D11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
148C23×D11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—22no—
162C2×C22⋊D11—22no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11—22no—
165C2×C22⋊D11—41no—
166C2×C22⋊D11—41no—
167C2×C22⋊D11—41no—
168C2×C22⋊D11—41no—
169C2×C22⋊D11—41no—
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C411yescharacteristic
172C22×Dic11C22×C411yescharacteristic
173C22×Dic11C22×C411yescharacteristic
174C22×Dic11C22×C411yescharacteristic
175#4339—44no—
176#4339—44no—
177#4339—44no—
178#4339—44no—
179C2×D44—22no—
180C2×D44—22no—
181C2×D44—41no—
182C2×D44—41no—
183C2×D44—41no—
184C2×D44—41no—
185C2×D44—41no—
186C2×D44—41no—
187C2×D44—41no—
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×C4×D11—21no—
198C2×C4×D11—21no—
199C2×C4×D11—21no—
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×Dic22—22no—
207C2×Dic22—41no—
208C2×Dic22—41no—
209C11×M16—44no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11C2×D412yes—
221C2×C8×C11C2×D412yes—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—41no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—21no—
228C22⋊Dic11—22no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—22no—
231(C2×D11)⋊C4—22no—
232(C2×D11)⋊C4—22no—
233(C2×D11)⋊C4—41no—
234(C2×D11)⋊C4—41no—
235(C2×D11)⋊C4—41no—
236(C2×D11)⋊C4—41no—
237(C2×D11)⋊C4—41no—
238C4⋊Dic11—41no—
239C4⋊Dic11—41no—
240Dic11⋊C4—22no—
241C4×Dic11—21no—
242C4×Dic11—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—44no—
256#4313—44no—
257C2×#436—111no—
258C2×#408—111no—
259#2388—111no—
260#1955—111no—
261#1954—111no—
262#1924—111no—
263#1923—111no—
264#1923—111no—
265#1923—111no—
266#1870—111no—
267#1870—111no—
268#1869—111no—
269#1850—111no—
270#1780—111no—
271#1753D1111yescharacteristic, complemented
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11C4×D412yes—
279C23×C11C23×C411yescharacteristic
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
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×D11—21no—
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
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×C11C4×D412yes—
319C2×C4×C11#13112yes—
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C22⋊D11—44no—
327C22⋊D11—44no—
328C22⋊D11—44no—
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#13112yes—
344D44—44no—
345D44—44no—
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—
355C4×D11—41no—
356C4×D11—41no—
357C4×D11—41no—
358C4×D11—41no—
359Dic22—44no—
360C8×C11—22no—
361C8×C11—22no—
362C8×C11—41no—
363C8×C11—41no—
364C11⋊C8—41no—
365C11⋊C8—41no—
366C11⋊C8—41no—
367C11⋊C8—41no—
368C22×#41—111no—
369C22×M16—111no—
370C22×M16C2×D1111yescharacteristic
371C23×C8—111no—
372C2×C4×D4—111no—
373C2×C4×D4—111no—
374C2×C4×D4—111no—
375#436—224no—
376C2×C4⋊C8—111no—
377C2×C4⋊C8—111no—
378C2×C4⋊C8—111no—
379#408—224no—
380C2×C22⋊C8—111no—
381C2×C22⋊C8—111no—
382C2×C22⋊C8—111no—
383C2×C22⋊C8—111no—
384C2×C22⋊C8—111no—
385C2×C22⋊C8—111no—
386C2×C22⋊C8—111no—
387C2×C22⋊C8—111no—
388C2×C22⋊C8—111no—
389C2×C22⋊C8—111no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—111no—
392C2×C22⋊C8C2×D1111yescharacteristic
393C2×#97C2×D1111yescharacteristic
394C2×C4×C8—111no—
395C2×C4×C8C2×D1111yescharacteristic
396#395—111no—
397#394—111no—
398#394—111no—
399#394—111no—
400#393—111no—
401#392—111no—
402#392—111no—
403#392—111no—
404C4×C22⋊C4—111no—
405C4×C22⋊C4—111no—
406C4×C22⋊C4C2×D1111yescharacteristic
407#336—111no—
408#336—111no—
409#336—111no—
410#336—111no—
411#336C2×D1111yescharacteristic
412#336C2×D1111yescharacteristic
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11C2×C4×D411yescharacteristic
421C22×C11#51811yescharacteristic
422C22×C11#51811yescharacteristic
423C22×C11C2×#13111yescharacteristic
424C22×C11C2×#13111yescharacteristic
425C22×C11#56811yescharacteristic
426C22×C11#56811yescharacteristic
427C2×D11—41no—
428C2×D11—41no—
429C2×D11—41no—
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—
441C2×D11—41no—
442C2×D11—41no—
443C2×D11—41no—
444C2×D11—41no—
445C2×D11—41no—
446C2×D11—41no—
447C2×D11—41no—
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—41no—
451C4×C11—41no—
452C4×C11—41no—
453C4×C11#53411yescharacteristic
454C4×C11#53511yescharacteristic
455C4×C11#53811yescharacteristic
456C4×C11#53811yescharacteristic
457Dic11—22no—
458Dic11—41no—
459Dic11—41no—
460Dic11—41no—
461Dic11—41no—
462C2×#41—222no—
463C2×#41—222no—
464C2×#41—441no—
465C2×#41—441no—
466C2×#41—441no—
467C2×#41—441no—
468C22×Q8—111no—
469C22×D4—111no—
470C22×D4—111no—
471C22×D4—111no—
472C22×D4—111no—
473C22×D4—111no—
474C22×D4—111no—
475C23×C4—111no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4C22×D1111yescharacteristic
479C2×M16—41no—
480C2×M16—41no—
481C2×M16—222no—
482C2×M16—441no—
483C2×M16—441no—
484C2×M16D4414yescomplemented
485C22×C8—111no—
486C22×C8—111no—
487C22×C8—111no—
488C22×C8—111no—
489C22×C8—222no—
490C22×C8—441no—
491C22×C8—441no—
492C22×C8C22×D1111yescharacteristic
493C22×C8C22×D1111yescharacteristic
494C22×C8C22×D1111yescharacteristic
495C22×C8C22×D1111yescharacteristic
496C4×D4—222no—
497C4×D4—222no—
498C4×D4—441no—
499C4×D4—441no—
500C4×D4—441no—
501C4×D4—441no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊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⋊C4—111no—
515C2×C22⋊C4C4×D1111yescharacteristic
516C2×C22⋊C4C4×D1111yescharacteristic
517C2×C42—111no—
518C2×C42C22×D1111yescharacteristic
519C2×C42C22×D1111yescharacteristic
520C4⋊C8—222no—
521C4⋊C8—441no—
522C4⋊C8—441no—
523C22⋊C8—22no—
524C22⋊C8—222no—
525C22⋊C8—222no—
526C22⋊C8—222no—
527C22⋊C8—222no—
528C22⋊C8—222no—
529C22⋊C8—222no—
530C22⋊C8—441no—
531C22⋊C8—441no—
532C22⋊C8—441no—
533C22⋊C8—441no—
534C22⋊C8—441no—
535C22⋊C8—441no—
536#97—41no—
537C4×C8—41no—
538C4×C8—222no—
539#95—111no—
540#95—111no—
541#95—111no—
542#95—111no—
543#95C4×D1111yescharacteristic
544#95C4×D1111yescharacteristic
545C2×C11—42no—
546C2×C11#232111yescharacteristic
547C2×C11#293311yescharacteristic
548C2×C11#293511yescharacteristic
549C2×C11#297611yescharacteristic
550C2×C11#297811yescharacteristic
551C2×C11#297911yescharacteristic
552C2×C11#298111yescharacteristic
553D11—81no—
554D11—81no—
555D11—81no—
556C24—111no—
557C24—111no—
558C24—111no—
559C24C2×C4×D1111yescharacteristic
560#41—444no—
561#41—444no—
562#41—444no—
563#41—444no—
564C2×Q8—222no—
565C2×Q8—441no—
566C2×Q8—441no—
567C2×D4—222no—
568C2×D4—222no—
569C2×D4—222no—
570C2×D4—222no—
571C2×D4—222no—
572C2×D4—222no—
573C2×D4—441no—
574C2×D4—441no—
575C2×D4—441no—
576C2×D4—441no—
577C2×D4—441no—
578C2×D4—441no—
579C2×D4—441no—
580C2×D4—441no—
581C2×D4—441no—
582C2×D4—441no—
583C2×D4—441no—
584C2×D4—441no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—111no—
590C22×C4—111no—
591C22×C4—111no—
592C22×C4—111no—
593C22×C4—111no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4C2×C4×D1111yescharacteristic
613C22×C4C2×C4×D1111yescharacteristic
614C22×C4C2×C4×D1111yescharacteristic
615C22×C4C2×C4×D1111yescharacteristic
616C22×C4C2×C4×D1111yescharacteristic
617C22×C4C2×D4412yes—
618C22×C4#433912yes—
619C22×C4C23×D1111yescharacteristic
620M16—44no—
621M16—444no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—221no—
633C2×C8—221no—
634C2×C8—221no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—444no—
645C2×C8C2×D4412yes—
646C2×C8C2×D4412yes—
647C4⋊C4—222no—
648C4⋊C4—441no—
649C4⋊C4—441no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—222no—
653C22⋊C4—222no—
654C22⋊C4—222no—
655C22⋊C4—222no—
656C22⋊C4—222no—
657C22⋊C4—441no—
658C22⋊C4—441no—
659C22⋊C4—441no—
660C22⋊C4—441no—
661C22⋊C4—441no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—221no—
667C42—221no—
668C11#2203911yescharacteristic, complemented, Sylow
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—221no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23—221no—
681C23—221no—
682C23—221no—
683C23—221no—
684C23—221no—
685C23—221no—
686C23—221no—
687C23—221no—
688C23—221no—
689C23—221no—
690C23—221no—
691C23—221no—
692C23—221no—
693C23—221no—
694C23—221no—
695C23—221no—
696C23C4×D4412yes—
697C23C22×C4×D1111yescharacteristic
698Q8—444no—
699D4—444no—
700D4—444no—
701D4—444no—
702D4—444no—
703D4—444no—
704D4—444no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
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—112no—
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—221no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—221no—
736C2×C4—221no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4C4×D4412yes—
750C2×C4#6696012yes—
751C2×C4C22×D4411yescharacteristic
752C2×C4C2×#433911yescharacteristic
753C2×C4#6703711yescharacteristic
754C2×C4#6703711yescharacteristic
755C2×C4#6704211yescharacteristic
756C2×C4#6704211yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C8—441no—
762C8—441no—
763C8—441no—
764C8—441no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—441no—
773C22—441no—
774C22—441no—
775C22—441no—
776C22—441no—
777C22—441no—
778C22—441no—
779C22—441no—
780C22—441no—
781C22—441no—
782C22—441no—
783C22—441no—
784C22—441no—
785C22—441no—
786C22—441no—
787C22—441no—
788C22—441no—
789C22—441no—
790C22—441no—
791C22—441no—
792C22—441no—
793C22C2×C4×D4411yescharacteristic
794C22#1062307611yescharacteristic
795C22#1062307611yescharacteristic
796C22C2×#6696011yescharacteristic
797C22#1062327611yescharacteristic
798C22D11×#13111yescharacteristic
799C22#1062328111yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—222no—
806C4—441no—
807C4—441no—
808C4—441no—
809C4—441no—
810C4#1062302411yescharacteristic
811C4#1062305611yescharacteristic
812C4#1062309111yescharacteristic
813C4#1062309111yescharacteristic
814C2—42no—
815C2—881no—
816C2—881no—
817C2—881no—
818C2#1307127611yescharacteristic
819C2#1307734411yescharacteristic
820C2#1307736211yescharacteristic
821C2#1307766511yescharacteristic
822C2#1307767311yescharacteristic
823C2#1307768111yescharacteristic
824C2#1307768811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1753C2
prime radical#13071832C2
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#22039
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#10622741C2semidirect
2. C2×#10622742C2semidirect
4. #13069414C2semidirect
5. #13069410C2semidirect
6. #13069229C2semidirect
7. #13069223C2semidirect
8. #13069223C2semidirect
9. #13069222C2semidirect
10. #13068912C2semidirect
11. #13068912C2semidirect
12. #13068906C2semidirect
13. #13068796C2semidirect
14. #13068527C2semidirect
15. C11×#1753C2semidirect
80. C2×C11×M16D4semidirect
271. #1753D11semidirect
484. C2×M16D44semidirect
668. C11#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#106227412
C2×#106227422
#130718322
#130694142
#130694102
#130692292
#130692232
#130692222
#130689122
#130689062
#130687962
#130685272
C11×#17532
#2203911