Finite Group Databasebeta

← #14772029

Subgroups — #14772029

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4318C211yesmaximal, characteristic
2C2×#10622624C211yesmaximal, characteristic
3C2×#10622737C211yesmaximal, characteristic, complemented
4C22×#66886C211yesmaximal, characteristic, complemented
5#13069391C211yesmaximal, characteristic, complemented
6#13069389C211yesmaximal, characteristic, complemented
7#13068821C211yesmaximal, characteristic, complemented
8#13068821C211yesmaximal, characteristic, complemented
9#13068820C211yesmaximal, characteristic, complemented
10#13068820C211yesmaximal, characteristic, complemented
11#13068790C211yesmaximal, characteristic, complemented
12#13068656C211yesmaximal, characteristic, complemented
13#13068652C211yesmaximal, characteristic, complemented
14#13068523C211yesmaximal, characteristic, complemented
15D4×C11×M16C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C11×#436—21no—
24C11×#435—21no—
25C11×#435—21no—
26C8×D4×C11—21no—
27C11×#423C2211yescharacteristic
28C11×#407C2211yescharacteristic
29C11×#407C2211yescharacteristic
30C4×C11×M16C2211yescharacteristic
31#10622820C2211yescharacteristic
32#10622820C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622737—24no—
36C2×#66886—24no—
37C2×#66886C2211yescharacteristic
38C2×#66886C2211yescharacteristic
39C2×#66886C2211yescharacteristic
40C2×#66886C2211yescharacteristic
41C2×#66886C2211yescharacteristic
42C2×#66886C2211yescharacteristic
43C2×#66886C2211yescharacteristic
44C2×#66886C2211yescharacteristic
45C2×#66886C2211yescharacteristic
46C2×#66886C2211yescharacteristic
47#10622625—21no—
48#10622624—21no—
49#10622624—21no—
50#10622624C412yes—
51#10622624C412yes—
52#10622624C412yes—
53#10622624C412yes—
54D4×C11⋊C8—21no—
55#10622537C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2211yescharacteristic
57C4×#4318C2211yescharacteristic
58C2×#66867C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622196C2211yescharacteristic
62#10622196C2211yescharacteristic
63#10622196C2211yescharacteristic
64#10622196C2211yescharacteristic
65C22×D4×C11Q811yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—41no—
73C2×C11×M16—41no—
74C2×C11×M16C2311yescharacteristic
75C2×C11×M16C2311yescharacteristic
76C2×C11×M16C2311yescharacteristic
77C2×C11×M16C2311yescharacteristic
78C22×C8×C11—21no—
79C22×C8×C11—21no—
80C4×D4×C11C2×C411yescharacteristic
81C4×D4×C11C2×C411yescharacteristic
82C4×D4×C11C2×C411yescharacteristic
83C4×D4×C11C2×C411yescharacteristic
84C4×D4×C11D411yescharacteristic
85C4×D4×C11D411yescharacteristic
86C4×D4×C11D411yescharacteristic
87C4×D4×C11D411yescharacteristic
88C2×C11×C4⋊C4Q811yescharacteristic
89C2×C11×C22⋊C4Q811yescharacteristic
90C2×C11×C22⋊C4Q811yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×#4318—21no—
93C2×#4318—21no—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318—41no—
99C2×#4318—41no—
100C2×#4318C2×C412yes—
101C2×#4318C2×C412yes—
102C2×#4318C2311yescharacteristic
103C2×#4318C2311yescharacteristic
104C2×#4318C2311yescharacteristic
105C2×#4318C2311yescharacteristic
106C22×C11⋊C8—22no—
107C22×C11⋊C8—22no—
108C22×C11⋊C8—21no—
109C22×C11⋊C8—21no—
110C22×C11⋊C8C2×C412yes—
111C22×C11⋊C8C2×C412yes—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C11×C4⋊C8—21no—
117C11×C4⋊C8—21no—
118C11×C22⋊C8—21no—
119C11×C22⋊C8—21no—
120C11×C22⋊C8—21no—
121C11×C22⋊C8—21no—
122C11×#97—21no—
123C4×C8×C11—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127C22⋊(C11⋊C8)—21no—
128C22⋊(C11⋊C8)C2×C412yes—
129C22⋊(C11⋊C8)C2×C412yes—
130C22⋊(C11⋊C8)C2×C412yes—
131C22⋊(C11⋊C8)C2×C412yes—
132#66886—22no—
133#66886—22no—
134#66886—22no—
135#66886—22no—
136#66886—22no—
137#66886—22no—
138#66886—22no—
139#66886—41no—
140#66886—41no—
141#66886D414yescomplemented
142C4⋊(C11⋊C8)—21no—
143C4⋊(C11⋊C8)—21no—
144C4⋊(C11⋊C8)C2×C412yes—
145C4⋊(C11⋊C8)C2×C412yes—
146#66867—21no—
147#66867C2×C412yes—
148#66867C2×C412yes—
149C4×C11⋊C8—21no—
150#22668—111nomaximal, Sylow
151C24×C11C2×Q811yescharacteristic
152C24×C11C2×Q811yescharacteristic
153C2×D4×C11—42no—
154C2×D4×C11C4⋊C411yescharacteristic
155C2×D4×C11C4⋊C411yescharacteristic
156C2×D4×C11C4⋊C411yescharacteristic
157C2×D4×C11C4⋊C411yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C22×C411yescharacteristic
169C22×C4×C11C22×C411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×Q811yescharacteristic
175C22×C4×C11C2×Q811yescharacteristic
176C22×C4×C11C2×Q811yescharacteristic
177C22×C4×C11C2×Q811yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C11×M16—21no—
180C11×M16—21no—
181C11×M16—21no—
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—21no—
186C11×M16—42no—
187C11×M16—42no—
188C11×M16C2×D412yes—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—42no—
194C2×C8×C11—42no—
195C11×C4⋊C4C4⋊C411yescharacteristic
196C11×C4⋊C4C4⋊C411yescharacteristic
197C11×C4⋊C4C4⋊C411yescharacteristic
198C11×C4⋊C4C4⋊C411yescharacteristic
199C11×C22⋊C4C4⋊C411yescharacteristic
200C11×C22⋊C4C4⋊C411yescharacteristic
201C11×C22⋊C4C4⋊C411yescharacteristic
202C11×C22⋊C4C4⋊C411yescharacteristic
203C11×C22⋊C4C4⋊C411yescharacteristic
204C11×C22⋊C4C4⋊C411yescharacteristic
205C11×C22⋊C4C4⋊C411yescharacteristic
206C11×C22⋊C4C4⋊C411yescharacteristic
207C42×C11C22×C411yescharacteristic
208C42×C11C22×C411yescharacteristic
209C42×C11C2×D411yescharacteristic
210C42×C11C2×D411yescharacteristic
211#4318—24no—
212#4318—24no—
213#4318—21no—
214#4318—21no—
215#4318—21no—
216#4318—21no—
217#4318—21no—
218#4318—21no—
219#4318—21no—
220#4318—42no—
221#4318—42no—
222#4318C2×D412yes—
223C2×C11⋊C8—24no—
224C2×C11⋊C8—24no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
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—42no—
236C2×C11⋊C8—42no—
237C2×C11⋊C8C22×C412yes—
238C2×C11⋊C8C22×C412yes—
239C2×C11⋊C8C22×C412yes—
240C2×C11⋊C8C22×C412yes—
241C2×C11⋊C8C2×D412yes—
242C2×C11⋊C8#4112yes—
243D4×M16—111no—
244D4×M16D1111yescharacteristic
245C2×#435—111no—
246C2×#430—111no—
247C22×#108—111no—
248#1950—111no—
249#1950—111no—
250#1855—111no—
251#1855—111no—
252#1855—111no—
253#1855—111no—
254#1849—111no—
255#1811—111no—
256#1810—111no—
257#1778—111no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—22no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11C2×C4⋊C411yescharacteristic
267C23×C11C2×C4⋊C411yescharacteristic
268C23×C11C2×C4⋊C411yescharacteristic
269C23×C11C2×C4⋊C411yescharacteristic
270C23×C11C22×Q811yescharacteristic
271D4×C11—22no—
272D4×C11—22no—
273D4×C11—41no—
274D4×C11—41no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
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×C11C2×C4⋊C411yescharacteristic
298C2×C4×C11C2×C4⋊C411yescharacteristic
299C2×C4×C11C2×C4⋊C411yescharacteristic
300C2×C4×C11C2×C4⋊C411yescharacteristic
301C2×C4×C11C2×C4⋊C411yescharacteristic
302C2×C4×C11C2×C4⋊C411yescharacteristic
303C2×C4×C11C2×C4⋊C411yescharacteristic
304C2×C4×C11C2×C4⋊C411yescharacteristic
305C2×C4×C11C23×C411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C112−1+411yescharacteristic
311C8×C11—22no—
312C8×C11—41no—
313C8×C11—41no—
314C8×C11—41no—
315C11⋊C8—22no—
316C11⋊C8—22no—
317C11⋊C8—22no—
318C11⋊C8—22no—
319C11⋊C8—41no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C11⋊C8C4×D414yes—
323C22×M16—111no—
324C22×M16—111no—
325C22×M16—111no—
326C22×M16C2×D1111yescharacteristic
327C22×M16C2×D1111yescharacteristic
328C23×C8—111no—
329C2×C4×D4C2×D1111yescharacteristic
330#436—21no—
331#436—221no—
332#435—21no—
333#435—21no—
334#435—112no—
335#435—112no—
336#435—112no—
337#435—112no—
338#435—221no—
339#435—221no—
340C8×D4—21no—
341C8×D4—221no—
342#430—224no—
343C2×#108—111no—
344C2×#108—111no—
345C2×#108—111no—
346C2×#108—111no—
347C2×#108—111no—
348C2×#108—111no—
349C2×#108—111no—
350C2×#108—111no—
351C2×#108—111no—
352C2×#108—111no—
353C2×#108—224no—
354#423—111no—
355#423C2×D1111yescharacteristic
356C2×C4⋊C8—111no—
357#407—111no—
358#407—111no—
359#407C2×D1111yescharacteristic
360#407C2×D1111yescharacteristic
361C2×C22⋊C8—111no—
362C2×C22⋊C8—111no—
363C4×M16—111no—
364C4×M16C2×D1111yescharacteristic
365C2×#97—111no—
366#341—111no—
367#341—111no—
368#341—111no—
369#341—111no—
370#341—111no—
371#341—111no—
372C22×C11—21no—
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—21no—
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—21no—
383C22×C11—21no—
384C22×C11—21no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11#43012yescomplemented
390C22×C11C22×C4⋊C411yescharacteristic
391C22×C11D4×Q811yescharacteristic
392C22×C11#55411yescharacteristic
393C4×C11—21no—
394C4×C11—21no—
395C4×C11—21no—
396C4×C11—21no—
397C4×C11—21no—
398C4×C11—21no—
399C4×C11—21no—
400C4×C11—21no—
401C4×C11C2×C4×D411yescharacteristic
402C4×C11#52011yescharacteristic
403C4×C11D4211yescharacteristic
404C4×C11#54711yescharacteristic
405C22×D4Dic2211yescharacteristic
406C23×C4C22×D1111yescharacteristic
407C23×C4C22×D1111yescharacteristic
408C2×M16—21no—
409C2×M16—21no—
410C2×M16—22no—
411C2×M16—22no—
412C2×M16—41no—
413C2×M16—41no—
414C2×M16—112no—
415C2×M16—112no—
416C2×M16—111no—
417C2×M16—111no—
418C2×M16—111no—
419C2×M16—111no—
420C2×M16—222no—
421C2×M16—222no—
422C2×M16—221no—
423C2×M16—221no—
424C2×M16—222no—
425C2×M16—222no—
426C2×M16—441no—
427C2×M16—441no—
428C2×M16C22×D1111yescharacteristic
429C2×M16C22×D1111yescharacteristic
430C2×M16C22×D1111yescharacteristic
431C2×M16C22×D1111yescharacteristic
432C22×C8—21no—
433C22×C8—21no—
434C22×C8—111no—
435C22×C8—112no—
436C22×C8—112no—
437C22×C8—111no—
438C22×C8—111no—
439C22×C8—111no—
440C22×C8—222no—
441C22×C8—222no—
442C22×C8—221no—
443C22×C8—221no—
444C4×D4C4×D1111yescharacteristic
445C4×D4C4×D1111yescharacteristic
446C4×D4C4×D1111yescharacteristic
447C4×D4C4×D1111yescharacteristic
448C4×D4C22⋊D1111yescharacteristic
449C4×D4C22⋊D1111yescharacteristic
450C4×D4C22⋊D1111yescharacteristic
451C4×D4C22⋊D1111yescharacteristic
452C2×C4⋊C4Dic2211yescharacteristic
453C2×C22⋊C4Dic2211yescharacteristic
454C2×C22⋊C4Dic2211yescharacteristic
455C2×C42C22×D1111yescharacteristic
456#108—114no—
457#108—222no—
458#108—222no—
459#108—222no—
460#108—222no—
461#108—222no—
462#108—222no—
463#108—222no—
464#108—441no—
465#108—441no—
466C4⋊C8—21no—
467C4⋊C8—21no—
468C4⋊C8—112no—
469C4⋊C8—112no—
470C4⋊C8—221no—
471C4⋊C8—221no—
472C22⋊C8—21no—
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—21no—
476C22⋊C8—112no—
477C22⋊C8—112no—
478C22⋊C8—112no—
479C22⋊C8—112no—
480C22⋊C8—221no—
481C22⋊C8—221no—
482C22⋊C8—221no—
483C22⋊C8—221no—
484#97—21no—
485#97—112no—
486#97—112no—
487#97—221no—
488C4×C8—21no—
489C4×C8—221no—
490C2×C11—21no—
491C2×C11—21no—
492C2×C11—22no—
493C2×C11—41no—
494C2×C11—41no—
495C2×C11—41no—
496C2×C11D4×C4⋊C411yescharacteristic
497C2×C11C2×#43011yescharacteristic
498C2×C11#291611yescharacteristic
499C24C2×Dic2211yescharacteristic
500C24C2×Dic2211yescharacteristic
501C2×D4—42no—
502C2×D4Dic11⋊C411yescharacteristic
503C2×D4Dic11⋊C411yescharacteristic
504C2×D4Dic11⋊C411yescharacteristic
505C2×D4Dic11⋊C411yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4C2×Dic2211yescharacteristic
515C22×C4C2×Dic2211yescharacteristic
516C22×C4C2×Dic2211yescharacteristic
517C22×C4C2×Dic2211yescharacteristic
518C22×C4C2×C4×D1111yescharacteristic
519C22×C4C2×C4×D1111yescharacteristic
520C22×C4C2×C4×D1111yescharacteristic
521C22×C4C2×C4×D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C2×C22⋊D1111yescharacteristic
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C2×C22⋊D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—42no—
535M16—42no—
536M16—112no—
537M16—224no—
538M16—224no—
539M16—221no—
540M16—221no—
541M16—221no—
542M16—221no—
543M16—221no—
544M16—221no—
545M16—221no—
546M16—442no—
547M16—442no—
548M16D4×D1112yes—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—42no—
554C2×C8—42no—
555C2×C8—112no—
556C2×C8—112no—
557C2×C8—112no—
558C2×C8—112no—
559C2×C8—112no—
560C2×C8—112no—
561C2×C8—224no—
562C2×C8—224no—
563C2×C8—221no—
564C2×C8—221no—
565C2×C8—221no—
566C2×C8—221no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—442no—
574C2×C8—442no—
575C4⋊C4Dic11⋊C411yescharacteristic
576C4⋊C4Dic11⋊C411yescharacteristic
577C4⋊C4Dic11⋊C411yescharacteristic
578C4⋊C4Dic11⋊C411yescharacteristic
579C22⋊C4Dic11⋊C411yescharacteristic
580C22⋊C4Dic11⋊C411yescharacteristic
581C22⋊C4Dic11⋊C411yescharacteristic
582C22⋊C4Dic11⋊C411yescharacteristic
583C22⋊C4Dic11⋊C411yescharacteristic
584C22⋊C4Dic11⋊C411yescharacteristic
585C22⋊C4Dic11⋊C411yescharacteristic
586C22⋊C4Dic11⋊C411yescharacteristic
587C42C2×C4×D1111yescharacteristic
588C42C2×C4×D1111yescharacteristic
589C42C2×C22⋊D1111yescharacteristic
590C42C2×C22⋊D1111yescharacteristic
591C11#2266811yescharacteristic, complemented, Sylow
592C23—22no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×Dic11⋊C411yescharacteristic
601C23C2×Dic11⋊C411yescharacteristic
602C23C2×Dic11⋊C411yescharacteristic
603C23C2×Dic11⋊C411yescharacteristic
604C23C22×Dic2211yescharacteristic
605D4—22no—
606D4—22no—
607D4—41no—
608D4—41no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4C2×Dic11⋊C411yescharacteristic
632C2×C4C2×Dic11⋊C411yescharacteristic
633C2×C4C2×Dic11⋊C411yescharacteristic
634C2×C4C2×Dic11⋊C411yescharacteristic
635C2×C4C2×Dic11⋊C411yescharacteristic
636C2×C4C2×Dic11⋊C411yescharacteristic
637C2×C4C2×Dic11⋊C411yescharacteristic
638C2×C4C2×Dic11⋊C411yescharacteristic
639C2×C4C22×C4×D1111yescharacteristic
640C2×C4C2×D4×D1111yescharacteristic
641C2×C4#6703711yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C2×C4#6704311yescharacteristic
644C2×C4C22×C22⋊D1111yescharacteristic
645C8—22no—
646C8—41no—
647C8—41no—
648C8—41no—
649C8—114no—
650C8—222no—
651C8—222no—
652C8—222no—
653C8—222no—
654C8—441no—
655C8—441no—
656C8—441no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—42no—
671C22—42no—
672C22—81no—
673C22—81no—
674C22#1062273712yescomplemented
675C22D4×Dic2211yescharacteristic
676C22#1062307011yescharacteristic
677C22C22×Dic11⋊C411yescharacteristic
678C4—21no—
679C4—21no—
680C4—21no—
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—21no—
686C4C4×D4×D1111yescharacteristic
687C4#1062307711yescharacteristic
688C4D4×C22⋊D1111yescharacteristic
689C4#1062335511yescharacteristic
690C2—21no—
691C2—21no—
692C2—22no—
693C2—41no—
694C2—41no—
695C2—41no—
696C2D4×Dic11⋊C411yescharacteristic
697C2C2×#1062273711yescharacteristic
698C2#1307722511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×M16C2
socleC22×C11C22×C4⋊C4
prime radicalC22×D4×C11Q8
cosocleC22×C4×C11C24
hypercenterD4×M16D11
hypocenterC11#22668
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
3. C2×#10622737C2semidirect
4. C22×#66886C2semidirect
5. #13069391C2semidirect
6. #13069389C2semidirect
7. #13068821C2semidirect
8. #13068821C2semidirect
9. #13068820C2semidirect
10. #13068820C2semidirect
11. #13068790C2semidirect
12. #13068656C2semidirect
13. #13068652C2semidirect
14. #13068523C2semidirect
141. #66886D4semidirect
389. C22×C11#430semidirect
591. C11#22668semidirect
674. C22#10622737semidirect

Maximal subgroups

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

subgroupindex
D4×#43182
C2×#106226242
C2×#106227372
C22×#668862
#130693912
#130693892
#130688212
#130688202
#130687902
#130686562
#130686522
#130685232
D4×C11×M162
#2266811