Finite Group Databasebeta

← #14770506

Subgroups — #14770506

Order 2816.

1364 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×C4×#4341C211yesmaximal, characteristic
2C2×#10622441C211yesmaximal, characteristic, complemented
3C2×#10622314C211yesmaximal, characteristic, complemented
4#13069415C211yesmaximal, characteristic, complemented
5#13069412C211yesmaximal, characteristic, complemented
6#13069412C211yesmaximal, characteristic, complemented
7#13069408C211yesmaximal, characteristic, complemented
8#13069408C211yesmaximal, characteristic, complemented
9#13068594C211yesmaximal, characteristic, complemented
10#13068594C211yesmaximal, characteristic, complemented
11#13068593C211yesmaximal, characteristic, complemented
12#13068380C211yesmaximal, characteristic, complemented
13#13068379C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
15C11×#1955C211yesmaximal, characteristic, complemented
16C22×#4341C411yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C411yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C4×#4341—24no—
24C4×#4341—24no—
25C2×#66945C411yescharacteristic
26C2×#66940C411yescharacteristic
27C2×(C22⋊D11)⋊C4C411yescharacteristic
28C2×(C22⋊D11)⋊C4C411yescharacteristic
29C2×#66930C411yescharacteristic
30C2×#66930C411yescharacteristic
31C2×C42×D11C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×#97C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×#66879C2211yescharacteristic
48C2×#66879C2211yescharacteristic
49C2×Dic11⋊C8C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
51C2×Dic11⋊C8C2211yescharacteristic
52C2×Dic11⋊C8C2211yescharacteristic
53C2×C8×Dic11C2211yescharacteristic
54C2×C8×Dic11C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622441—24no—
58#10622314—24no—
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C23×Dic11C2×C411yescharacteristic
70C23×Dic11C2×C411yescharacteristic
71C23×Dic11C2×C411yescharacteristic
72C2×#4341—24no—
73C2×#4341—24no—
74C2×#4341—24no—
75C22×C4×D11C2×C411yescharacteristic
76C22×C4×D11C2×C411yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×Dic22C2×C411yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C2×C11×C4⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90C2×C22⋊Dic11C2×C411yescharacteristic
91D4×Dic11—24no—
92C4×C22⋊D11—22no—
93C4×C22⋊D11—22no—
94C4×C22⋊D11—22no—
95C4×C22⋊D11—22no—
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×C4⋊Dic11C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×Dic11⋊C4C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11C2×C411yescharacteristic
108C2×C4×Dic11C2×C411yescharacteristic
109C2×C4×Dic11C2×C411yescharacteristic
110C2×C4×Dic11C2×C411yescharacteristic
111C2×C4×Dic11C2×C411yescharacteristic
112C2×C4×Dic11C2×C411yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120#66945—24no—
121#66940—24no—
122(C22⋊D11)⋊C4—24no—
123(C22⋊D11)⋊C4—24no—
124#66930—24no—
125#66930—24no—
126C42×D11—22no—
127C42×D11—22no—
128C4×Dic22D414yes—
129C4×Dic22D414yes—
130C11×C4⋊C8—22no—
131C11×C22⋊C8—22no—
132C11×C22⋊C8—22no—
133C11×C22⋊C8—41no—
134C11×C22⋊C8—41no—
135C11×#97—22no—
136C22⋊(C11⋊C8)—22no—
137C22⋊(C11⋊C8)—22no—
138C22⋊(C11⋊C8)—41no—
139C22⋊(C11⋊C8)—41no—
140(C2×D11)⋊C8—22no—
141(C2×D11)⋊C8—22no—
142(C2×D11)⋊C8—41no—
143(C2×D11)⋊C8—41no—
144#66879—22no—
145#66879—22no—
146Dic11⋊C8—22no—
147Dic11⋊C8—22no—
148Dic11⋊C8—22no—
149Dic11⋊C8—22no—
150C8×Dic11—22no—
151C8×Dic11—22no—
152C4⋊(C11⋊C8)—22no—
153#66867—22no—
154#22532—111nomaximal, Sylow
155C24×C11C22×C411yescharacteristic
156C24×C11C22×C411yescharacteristic
157C23×D11C22×C411yescharacteristic
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—22no—
179C2×C22⋊D11—22no—
180C2×C22⋊D11—22no—
181C2×C22⋊D11—22no—
182C2×C22⋊D11—22no—
183C2×C22⋊D11M1614yes—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—41no—
194C22×Dic11—41no—
195C22×Dic11M1614yes—
196C22×Dic11C22×C411yescharacteristic
197C22×Dic11C22×C411yescharacteristic
198C22×Dic11C22×C411yescharacteristic
199C22×Dic11C22×C411yescharacteristic
200C22×Dic11C22×C411yescharacteristic
201C22×Dic11C22×C411yescharacteristic
202C22×Dic11C22×C411yescharacteristic
203#4341—232no—
204C2×C4×D11—22no—
205C2×C4×D11—22no—
206C2×C4×D11—22no—
207C2×C4×D11—22no—
208C2×C4×D11—22no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—21no—
212C2×C4×D11—21no—
213C2×C4×D11—21no—
214C2×C4×D11—21no—
215C2×C4×D11—41no—
216C2×Dic22—22no—
217C2×Dic22—22no—
218C2×Dic22C22⋊C414yes—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11#4112yescomplemented
231C11×C4⋊C4—22no—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—22no—
234C42×C11C2×D412yes—
235C42×C11C2×D412yes—
236C22⋊Dic11—22no—
237C22⋊Dic11—22no—
238(C2×D11)⋊C4—22no—
239(C2×D11)⋊C4—22no—
240C4⋊Dic11C22⋊C414yes—
241Dic11⋊C4—22no—
242Dic11⋊C4—22no—
243Dic11⋊C4C22⋊C414yes—
244Dic11⋊C4C22⋊C414yes—
245C4×Dic11—22no—
246C4×Dic11—22no—
247C4×Dic11—22no—
248C4×Dic11—22no—
249C4×Dic11—22no—
250C4×Dic11—22no—
251C4×Dic11—21no—
252C4×Dic11—21no—
253C4×Dic11C2×D412yes—
254C4×Dic11C2×D412yes—
255C4×Dic11C2×D412yes—
256C4×Dic11C2×D412yes—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8#4112yescomplemented
269C2×C4×#41—111no—
270C2×#446—111no—
271C2×#446—111no—
272#1955—111no—
273#1955—111no—
274#1955—111no—
275#1955D1111yescharacteristic, complemented
276#1954—111no—
277#1954—111no—
278#1797—111no—
279#1797—111no—
280#1797—111no—
281#1749—111no—
282#1749—111no—
283C4×C22⋊C8—111no—
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×M1612yes—
297C23×C11C2×M1612yes—
298C23×C11C23×C411yescharacteristic
299C22×D11—21no—
300C22×D11—21no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—21no—
305C22×D11C2×M1612yes—
306D4×C11—28no—
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—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11C2×C22⋊C412yes—
326C2×C4×C11C2×C22⋊C412yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×C4×C112−1+411yescharacteristic
333C22⋊D11—28no—
334C22⋊D11—28no—
335C2×Dic11—28no—
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×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—28no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—44no—
351C2×Dic11—44no—
352C2×Dic11C2×C22⋊C412yes—
353C2×Dic11C2×C22⋊C412yes—
354C2×Dic11C2×C22⋊C412yes—
355C2×Dic11C2×C22⋊C412yes—
356C2×Dic11C2×M1612yes—
357C2×Dic11C2×M1612yes—
358C2×Dic11C2×M1612yes—
359C2×Dic11#13112yes—
360C4×D11—28no—
361C4×D11—44no—
362C4×D11—41no—
363C4×D11—41no—
364C4×D11—41no—
365C4×D11—41no—
366Dic22—28no—
367C8×C11—22no—
368C8×C11—41no—
369C8×C11—41no—
370C8×C11—41no—
371C11⋊C8—22no—
372C11⋊C8—41no—
373C11⋊C8—41no—
374C11⋊C8—41no—
375C22×#41—111no—
376C4×#41—224no—
377C4×#41—224no—
378C2×C4×Q8—111no—
379C2×C4×Q8—111no—
380C2×C4×D4—111no—
381C2×C4×D4—111no—
382C2×C4×D4—111no—
383C2×C4×D4—111no—
384C2×C4×D4—111no—
385C2×C4×D4C2×D1111yescharacteristic
386C2×#117—111no—
387C2×#117—111no—
388C2×#117—111no—
389C22×C42—111no—
390C22×C42—111no—
391C22×C42—111no—
392#446—224no—
393#446—224no—
394C2×C4⋊C8—111no—
395C2×C4⋊C8—111no—
396C2×C4⋊C8—111no—
397C2×C4⋊C8—111no—
398C2×C4⋊C8—111no—
399C2×C4⋊C8C2×D1111yescharacteristic
400C2×C22⋊C8—111no—
401C2×C22⋊C8—111no—
402C2×C22⋊C8—111no—
403C2×C22⋊C8—111no—
404C2×C22⋊C8—111no—
405C2×C22⋊C8—111no—
406C2×C22⋊C8—111no—
407C2×C22⋊C8—111no—
408C2×C22⋊C8C2×D1111yescharacteristic
409C2×C22⋊C8C2×D1111yescharacteristic
410C2×C22⋊C8C2×D1111yescharacteristic
411C2×C22⋊C8C2×D1111yescharacteristic
412C2×#97—111no—
413C2×#97—111no—
414C2×#97—111no—
415C2×#97C2×D1111yescharacteristic
416C2×C4×C8—111no—
417C2×C4×C8—111no—
418#336—111no—
419#336—111no—
420#336—111no—
421#336—111no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11C22×C22⋊C411yescharacteristic
437C22×C11C4×#4111yescharacteristic
438C22×C11#52011yescharacteristic
439C22×C11C22×M1611yescharacteristic
440C22×C11C22×M1611yescharacteristic
441C22×C11C2×#13111yescharacteristic
442C22×C11#56811yescharacteristic
443C2×D11—22no—
444C2×D11—22no—
445C2×D11—22no—
446C2×D11—41no—
447C2×D11—41no—
448C2×D11—41no—
449C2×D11—41no—
450C4×C11—22no—
451C4×C11—22no—
452C4×C11—41no—
453C4×C11—41no—
454C4×C11#54811yescharacteristic
455C4×C11#54811yescharacteristic
456C4×C11#55011yescharacteristic
457C4×C11#55011yescharacteristic
458Dic11—22no—
459Dic11—22no—
460Dic11—22no—
461Dic11—22no—
462Dic11—22no—
463Dic11—41no—
464Dic11#40714yes—
465C2×#41—224no—
466C2×#41—224no—
467C2×#41—224no—
468C22×Q8—111no—
469C22×D4—111no—
470C22×D4—111no—
471C22×D4C4×D1111yescharacteristic
472C23×C4—111no—
473C23×C4—111no—
474C23×C4—111no—
475C23×C4—111no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—111no—
479C23×C4C22×D1111yescharacteristic
480C23×C4C22×D1111yescharacteristic
481C22×C8—111no—
482C22×C8—111no—
483C22×C8—111no—
484C22×C8—111no—
485C22×C8C22×D1111yescharacteristic
486C22×C8C22×D1111yescharacteristic
487C22×C8C22×D1111yescharacteristic
488C22×C8C22×D1111yescharacteristic
489C4×Q8—114no—
490C4×Q8—114no—
491C4×Q8—224no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—222no—
495C4×D4—222no—
496C4×D4—222no—
497C4×D4—222no—
498C4×D4—224no—
499C4×D4—224no—
500C4×D4—224no—
501#117—224no—
502#117—224no—
503#117—224no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4C4×D1111yescharacteristic
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×C42—111no—
523C2×C42—111no—
524C2×C42—111no—
525C2×C42—222no—
526C2×C42—222no—
527C2×C42—222no—
528C2×C42—222no—
529C2×C42—222no—
530C2×C42—222no—
531C2×C42C22×D1111yescharacteristic
532C4⋊C8—22no—
533C4⋊C8—222no—
534C4⋊C8—222no—
535C4⋊C8—222no—
536C4⋊C8—222no—
537C4⋊C8—222no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—41no—
541C22⋊C8—41no—
542C22⋊C8—222no—
543C22⋊C8—222no—
544C22⋊C8—222no—
545C22⋊C8—222no—
546C22⋊C8—441no—
547C22⋊C8—441no—
548C22⋊C8—441no—
549C22⋊C8—441no—
550#97—22no—
551#97—222no—
552#97—222no—
553#97—222no—
554C4×C8—222no—
555C4×C8—222no—
556C2×C11—42no—
557C2×C11—42no—
558C2×C11#234111yescharacteristic
559C2×C11C2×#40711yescharacteristic
560C2×C11#288011yescharacteristic
561C2×C11#296511yescharacteristic
562C2×C11#297011yescharacteristic
563C2×C11#298911yescharacteristic
564C2×C11#299011yescharacteristic
565D11—42no—
566C24—111no—
567C24C2×C4×D1111yescharacteristic
568C24C2×C4×D1111yescharacteristic
569#41—2232no—
570C2×Q8—114no—
571C2×Q8—222no—
572C2×Q8—222no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—114no—
577C2×D4—222no—
578C2×D4—222no—
579C2×D4—222no—
580C2×D4—222no—
581C2×D4—222no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—111no—
595C22×C4—114no—
596C22×C4—111no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—441no—
623C22×C4—441no—
624C22×C4—441no—
625C22×C4C2×C4×D1111yescharacteristic
626C22×C4C2×C4×D1111yescharacteristic
627C22×C4C2×C4×D1111yescharacteristic
628C22×C4C2×C4×D1111yescharacteristic
629C22×C4C23×D1111yescharacteristic
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—112no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—221no—
645C2×C8—221no—
646C2×C8—221no—
647C2×C8—221no—
648C2×C8—221no—
649C2×C8—221no—
650C2×C8—221no—
651C2×C8—221no—
652C2×C8—221no—
653C2×C8#434112yescomplemented
654C4⋊C4—22no—
655C4⋊C4—114no—
656C4⋊C4—114no—
657C4⋊C4—114no—
658C4⋊C4—222no—
659C4⋊C4—222no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—222no—
663C22⋊C4—222no—
664C22⋊C4—222no—
665C22⋊C4—222no—
666C42—112no—
667C42—112no—
668C42—112no—
669C42—112no—
670C42—222no—
671C42—222no—
672C42—222no—
673C42—222no—
674C42—222no—
675C42—222no—
676C42—221no—
677C42—221no—
678C42D4×D1112yes—
679C42D4×D1112yes—
680C11#2253211yescharacteristic, complemented, Sylow
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—112no—
694C23—221no—
695C23—221no—
696C23—221no—
697C23—221no—
698C23—221no—
699C23—221no—
700C23M16×D1112yes—
701C23M16×D1112yes—
702C23C22×C4×D1111yescharacteristic
703Q8—228no—
704D4—28no—
705D4—228no—
706D4—228no—
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—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—112no—
726C2×C4—112no—
727C2×C4—112no—
728C2×C4—112no—
729C2×C4—112no—
730C2×C4—112no—
731C2×C4—112no—
732C2×C4—112no—
733C2×C4—228no—
734C2×C4—228no—
735C2×C4—228no—
736C2×C4—221no—
737C2×C4—221no—
738C2×C4—221no—
739C2×C4—221no—
740C2×C4—221no—
741C2×C4—221no—
742C2×C4—221no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—221no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—444no—
750C2×C4—444no—
751C2×C4—444no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4C22⋊C4×D1112yes—
757C2×C4C22⋊C4×D1112yes—
758C2×C4C2×D4×D1111yescharacteristic
759C2×C4C2×D4×D1111yescharacteristic
760C2×C4C2×#434111yescharacteristic
761C2×C4#6703711yescharacteristic
762C2×C4#41×D1111yescharacteristic
763C2×C4#6704311yescharacteristic
764C8—22no—
765C8—41no—
766C8—41no—
767C8—41no—
768C8—222no—
769C8—441no—
770C8—441no—
771C8—441no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—222no—
787C22—222no—
788C22—222no—
789C22—441no—
790C22—441no—
791C22—441no—
792C22—441no—
793C22C2×C22⋊C4×D1111yescharacteristic
794C22C4×#434111yescharacteristic
795C22#1062307711yescharacteristic
796C22C2×M16×D1111yescharacteristic
797C22C2×M16×D1111yescharacteristic
798C22D11×#13111yescharacteristic
799C22#1062328111yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—114no—
805C4—222no—
806C4—222no—
807C4—222no—
808C4—222no—
809C4—222no—
810C4—441no—
811C4#1062312911yescharacteristic
812C4#1062313011yescharacteristic
813C4#1062320811yescharacteristic
814C4#1062324911yescharacteristic
815C2—42no—
816C2—42no—
817C2—442no—
818C2#1307145511yescharacteristic
819C2D11×#40711yescharacteristic
820C2#1307706411yescharacteristic
821C2#1307757611yescharacteristic
822C2#1307762611yescharacteristic
823C2#1307772811yescharacteristic
824C2#1307773611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1955C2
prime radicalC22×#4341C4
cosocleC22×C4×C11C24
hypercenter#1955D11
hypocenterC11#22532
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#10622441C2semidirect
3. C2×#10622314C2semidirect
4. #13069415C2semidirect
5. #13069412C2semidirect
6. #13069412C2semidirect
7. #13069408C2semidirect
8. #13069408C2semidirect
9. #13068594C2semidirect
10. #13068594C2semidirect
11. #13068593C2semidirect
12. #13068380C2semidirect
13. #13068379C2semidirect
14. C22⋊C8×Dic11C2semidirect
15. C11×#1955C2semidirect
230. C2×C8×C11#41semidirect
268. C2×C11⋊C8#41semidirect
275. #1955D11semidirect
653. C2×C8#4341semidirect
680. C11#22532semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
C2×#106224412
C2×#106223142
#130694152
#130694122
#130694082
#130685942
#130685932
#130683802
#130683792
C22⋊C8×Dic112
C11×#19552
#2253211