Finite Group Databasebeta

← #14759334

Subgroups — #14759334

Order 2816.

1456 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66954C211yesmaximal, characteristic, complemented
2C2×#10622625C211yesmaximal, characteristic, complemented
3C2×#10622342C211yesmaximal, characteristic, complemented
4C2×#10622341C211yesmaximal, characteristic, complemented
5#13071831C211yesmaximal, characteristic
6#13068910C211yesmaximal, characteristic, complemented
7#13068905C211yesmaximal, characteristic, complemented
8#13068800C211yesmaximal, characteristic, complemented
9#13068795C211yesmaximal, characteristic, complemented
10#13068794C211yesmaximal, characteristic, complemented
11#13068527C211yesmaximal, characteristic, complemented
12#13068402C211yesmaximal, characteristic, complemented
13#13068396C211yesmaximal, characteristic, complemented
14#13068386C211yesmaximal, characteristic, complemented
15C11×#1869C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C2×#66954—24no—
24C2×#66954—24no—
25C2×#66954—24no—
26C22×#4313C2211yescharacteristic
27C22×#4313C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33#10622836C411yescharacteristic
34#10622836C411yescharacteristic
35C4×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×#66879C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×C8×Dic11C2211yescharacteristic
46#10622625—24no—
47#10622604C411yescharacteristic
48#10622592C411yescharacteristic
49#10622573C411yescharacteristic
50#10622572C411yescharacteristic
51#10622572C411yescharacteristic
52#10622560C411yescharacteristic
53C4×(C2×D11)⋊C4C2211yescharacteristic
54C4×(C2×D11)⋊C4C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622342—24no—
58#10622341—24no—
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622188C2211yescharacteristic
65C22×D4×C11C2×C411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11C2×C411yescharacteristic
69C22×C22⋊D11C2×C411yescharacteristic
70C22×C22⋊D11C2×C411yescharacteristic
71C22×C22⋊D11C2×C411yescharacteristic
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339—22no—
76C2×#4339—22no—
77C2×#4339—22no—
78C22×D44C2×C411yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×Dic22C2×C411yescharacteristic
82C22×C8×C11—22no—
83C22×C8×C11—22no—
84C22×C8×C11—22no—
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C11×C22⋊C4C2×C411yescharacteristic
93C2×C11×C22⋊C4C2×C411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11C2×C411yescharacteristic
96C2×C22⋊Dic11C2×C411yescharacteristic
97C2×C22⋊Dic11C2×C411yescharacteristic
98C2×C22⋊Dic11C2×C411yescharacteristic
99C4×C22⋊D11—22no—
100C4×C22⋊D11—22no—
101C4×C22⋊D11—22no—
102C4×C22⋊D11—22no—
103C2×(C2×D11)⋊C4C2×C411yescharacteristic
104C2×(C2×D11)⋊C4C2×C411yescharacteristic
105C2×(C2×D11)⋊C4C2×C411yescharacteristic
106C2×(C2×D11)⋊C4C2×C411yescharacteristic
107C2×(C2×D11)⋊C4C2×C411yescharacteristic
108C2×(C2×D11)⋊C4C2×C411yescharacteristic
109C2×Dic11⋊C4C2×C411yescharacteristic
110C2×Dic11⋊C4C2×C411yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C2×C4×Dic11C2311yescharacteristic
113C2×#4318—22no—
114C2×#4318—22no—
115C2×#4318—22no—
116C2×#4318—22no—
117C2×#4318—22no—
118C2×#4318D414yescomplemented
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123#66954—232no—
124C2×#4313—22no—
125C2×#4313—22no—
126C2×#4313—22no—
127C2×#4313—22no—
128C2×#4313—22no—
129C2×#4313D414yescomplemented
130C2×C8×D11—22no—
131C2×C8×D11—22no—
132C2×C8×D11—22no—
133C2×C8×D11—22no—
134C2×C8×D11—22no—
135C2×C8×D11D414yescomplemented
136C11×C22⋊C8—22no—
137C11×C22⋊C8—22no—
138C11×C22⋊C8—22no—
139C11⋊#95C2×C411yescharacteristic
140C11⋊#95C2×C411yescharacteristic
141C11⋊#95C2×C411yescharacteristic
142C11⋊#95C2×C411yescharacteristic
143C11⋊#95C2×C411yescharacteristic
144C11⋊#95C2×C411yescharacteristic
145C22⋊(C11⋊C8)—22no—
146C22⋊(C11⋊C8)—22no—
147(C2×D11)⋊C8—22no—
148(C2×D11)⋊C8—22no—
149(C2×D11)⋊C8—22no—
150(C2×D11)⋊C8—22no—
151#66879—22no—
152Dic11⋊C8—22no—
153Dic11⋊C8—22no—
154C8×Dic11—22no—
155C4⋊(C11⋊C8)—22no—
156C4×C11⋊C8—22no—
157#21445—111nomaximal, Sylow
158C24×C11C22×C411yescharacteristic
159C24×C11C22×C411yescharacteristic
160C23×D11C22×C411yescharacteristic
161C23×D11C22×C411yescharacteristic
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—41no—
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×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C2×D412yes—
180C22×C4×C11#4112yes—
181C22×C4×C11C2411yescharacteristic
182C2×C22⋊D11—22no—
183C2×C22⋊D11—22no—
184C2×C22⋊D11—22no—
185C2×C22⋊D11—22no—
186C2×C22⋊D11—22no—
187C2×C22⋊D11—22no—
188C2×C22⋊D11—22no—
189C2×C22⋊D11—22no—
190C2×C22⋊D11—22no—
191C2×C22⋊D11—41no—
192C2×C22⋊D11—41no—
193C2×C22⋊D11—41no—
194C22×Dic11C22×C411yescharacteristic
195C22×Dic11C22×C411yescharacteristic
196C22×Dic11C22×C411yescharacteristic
197C22×Dic11C22×C411yescharacteristic
198C22×Dic11C22×C411yescharacteristic
199C22×Dic11C22×C411yescharacteristic
200#4339—28no—
201#4339—28no—
202#4339—28no—
203#4339—28no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44—22no—
207C2×C4×D11—21no—
208C2×C4×D11—21no—
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×D11C2×D412yes—
216C2×C4×D11C2×D412yes—
217C2×C4×D11#4112yes—
218C2×C4×D11#4112yes—
219C2×Dic22—22no—
220C2×Dic22—22no—
221C2×Dic22—22no—
222C2×C8×C11—28no—
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—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11C2×D412yes—
234C2×C8×C11C2×D412yes—
235C11×C4⋊C4—22no—
236C11×C22⋊C4—22no—
237C11×C22⋊C4—22no—
238C42×C11—21no—
239C42×C11—21no—
240C22⋊Dic11—22no—
241C22⋊Dic11—22no—
242C22⋊Dic11—22no—
243C22⋊Dic11—41no—
244(C2×D11)⋊C4—22no—
245(C2×D11)⋊C4—22no—
246(C2×D11)⋊C4—22no—
247(C2×D11)⋊C4—22no—
248(C2×D11)⋊C4—22no—
249(C2×D11)⋊C4—41no—
250Dic11⋊C4—22no—
251Dic11⋊C4—22no—
252C4×Dic11—21no—
253C4×Dic11—21no—
254C4×Dic11—21no—
255C4×Dic11—21no—
256#4318—28no—
257#4318—44no—
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⋊C8C2×D412yes—
267C2×C11⋊C8C2×D412yes—
268C2×C11⋊C8C2×D412yes—
269C2×C11⋊C8C2×D412yes—
270#4313—28no—
271#4313—28no—
272C8×D11—28no—
273C8×D11—28no—
274C22×#131—111no—
275C2×#436—111no—
276C2×#436—111no—
277C2×#435—111no—
278#2388—111no—
279#1870—111no—
280#1869—111no—
281#1869D1111yescharacteristic, complemented
282#1851—111no—
283#1850—111no—
284#1850—111no—
285#1780—111no—
286#1753—111no—
287#1753—111no—
288C8×C22⋊C4—111no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11C4×D412yes—
303C23×C11C23×C411yescharacteristic
304C22×D11—21no—
305C22×D11—21no—
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11C4×D412yes—
317C22×D11C4×D412yes—
318D4×C11—44no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11C4×D412yes—
338C2×C4×C11#13112yescomplemented
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×C4×C11C2×#4111yescharacteristic
345C22⋊D11—28no—
346C22⋊D11—28no—
347C22⋊D11—44no—
348C22⋊D11—44no—
349C2×Dic11—21no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—21no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—21no—
359C2×Dic11—21no—
360C2×Dic11—21no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11C4×D412yes—
365C2×Dic11C4×D412yes—
366C2×Dic11#13112yescomplemented
367D44—28no—
368C4×D11—22no—
369C4×D11—22no—
370C4×D11—22no—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—22no—
376Dic22—28no—
377C8×C11—22no—
378C8×C11—22no—
379C8×C11—41no—
380C8×C11—41no—
381C11⋊C8—22no—
382C11⋊C8—41no—
383C11⋊C8—41no—
384C11⋊C8#12014yes—
385C22×#41—111no—
386C2×#131—224no—
387C2×#131—224no—
388C2×#131—224no—
389C22×M16—111no—
390C22×M16—111no—
391C22×M16—111no—
392C22×M16—111no—
393C23×C8—111no—
394C23×C8—111no—
395C23×C8C2×D1111yescharacteristic
396C2×C4×D4—111no—
397C2×C4×D4—111no—
398C2×C4×D4C2×D1111yescharacteristic
399#436—224no—
400#436—224no—
401#435—224no—
402C2×C4⋊C8—111no—
403C2×C4⋊C8—111no—
404C2×C4⋊C8—111no—
405C2×C22⋊C8—111no—
406C2×C22⋊C8—111no—
407C2×C22⋊C8—111no—
408C2×C22⋊C8—111no—
409C2×C22⋊C8—111no—
410C2×C22⋊C8—111no—
411C2×C22⋊C8C2×D1111yescharacteristic
412C2×C22⋊C8C2×D1111yescharacteristic
413C2×C22⋊C8C2×D1111yescharacteristic
414C2×#97—111no—
415C2×C4×C8—111no—
416C2×C4×C8—111no—
417#395—111no—
418#394—111no—
419#394—111no—
420#394—111no—
421#393—111no—
422#392—111no—
423#392—111no—
424#392—111no—
425C4×C22⋊C4—111no—
426C4×C22⋊C4—111no—
427C4×C22⋊C4—111no—
428#336—111no—
429#336—111no—
430#336—111no—
431#336—111no—
432#336C2×D1111yescharacteristic
433#336C2×D1111yescharacteristic
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11C2×C4×D411yescharacteristic
449C22×C11C2×C4×D411yescharacteristic
450C22×C11C2×C4×D411yescharacteristic
451C22×C11C2×#13111yescharacteristic
452C22×C11C2×#13111yescharacteristic
453C22×C11#56811yescharacteristic
454C22×C11#56811yescharacteristic
455C2×D11—22no—
456C2×D11—22no—
457C2×D11—22no—
458C2×D11—22no—
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—41no—
462C2×D11—41no—
463C2×D11—41no—
464C2×D11—41no—
465C2×D11—41no—
466C2×D11—41no—
467C2×D11—41no—
468C2×D11—41no—
469C4×C11—22no—
470C4×C11—22no—
471C4×C11—41no—
472C4×C11—41no—
473C4×C11C2×#12011yescharacteristic
474C4×C11#52511yescharacteristic
475C4×C11#52511yescharacteristic
476C4×C11#52511yescharacteristic
477Dic11—22no—
478Dic11—22no—
479Dic11—22no—
480Dic11—41no—
481Dic11—41no—
482Dic11—41no—
483C2×#41—222no—
484C2×#41—222no—
485C2×#41—222no—
486C2×#41—222no—
487C2×#41—222no—
488C2×#41—222no—
489C22×Q8—111no—
490C22×D4—111no—
491C22×D4—111no—
492C22×D4—111no—
493C22×D4—111no—
494C22×D4—111no—
495C22×D4C4×D1111yescharacteristic
496C23×C4—111no—
497C23×C4—111no—
498C23×C4C22×D1111yescharacteristic
499C23×C4C22×D1111yescharacteristic
500#131—2232no—
501C2×M16—114no—
502C2×M16—114no—
503C2×M16—222no—
504C2×M16—222no—
505C2×M16—222no—
506C2×M16—222no—
507C2×M16—222no—
508C2×M16—222no—
509C2×M16—222no—
510C2×M16—222no—
511C2×M16—222no—
512C2×M16—222no—
513C22×C8—22no—
514C22×C8—22no—
515C22×C8—22no—
516C22×C8—111no—
517C22×C8—111no—
518C22×C8—114no—
519C22×C8—111no—
520C22×C8—111no—
521C22×C8—222no—
522C22×C8—222no—
523C22×C8—222no—
524C22×C8—222no—
525C22×C8—222no—
526C22×C8C22×D1111yescharacteristic
527C22×C8C22×D1111yescharacteristic
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—222no—
533C4×D4—222no—
534C4×D4—222no—
535C4×D4—222no—
536C2×C4⋊C4—111no—
537C2×C4⋊C4—111no—
538C2×C4⋊C4C4×D1111yescharacteristic
539C2×C22⋊C4—111no—
540C2×C22⋊C4—111no—
541C2×C22⋊C4—111no—
542C2×C22⋊C4—111no—
543C2×C22⋊C4—111no—
544C2×C22⋊C4—111no—
545C2×C22⋊C4—111no—
546C2×C22⋊C4—111no—
547C2×C22⋊C4—111no—
548C2×C22⋊C4—111no—
549C2×C22⋊C4C4×D1111yescharacteristic
550C2×C22⋊C4C4×D1111yescharacteristic
551C2×C42—111no—
552C2×C42—111no—
553C2×C42C22×D1111yescharacteristic
554C4⋊C8—222no—
555C4⋊C8—222no—
556C4⋊C8—222no—
557C22⋊C8—22no—
558C22⋊C8—22no—
559C22⋊C8—22no—
560C22⋊C8—222no—
561C22⋊C8—222no—
562C22⋊C8—222no—
563C22⋊C8—222no—
564C22⋊C8—222no—
565C22⋊C8—222no—
566#97—222no—
567C4×C8—222no—
568C4×C8—222no—
569#95—111no—
570#95—111no—
571#95—111no—
572#95—111no—
573#95—111no—
574#95—111no—
575C2×C11—42no—
576C2×C11—81no—
577C2×C11C4×#12011yescharacteristic
578C2×C11#293011yescharacteristic
579C2×C11#293111yescharacteristic
580C2×C11#293311yescharacteristic
581C2×C11#293311yescharacteristic
582C2×C11#293511yescharacteristic
583C2×C11#293511yescharacteristic
584D11—42no—
585D11—42no—
586C24—111no—
587C24—111no—
588C24C2×C4×D1111yescharacteristic
589C24C2×C4×D1111yescharacteristic
590#41—228no—
591#41—228no—
592#41—228no—
593#41—228no—
594C2×Q8—222no—
595C2×Q8—222no—
596C2×Q8—222no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—41no—
600C2×D4—222no—
601C2×D4—222no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4—222no—
605C2×D4—222no—
606C2×D4—222no—
607C2×D4—222no—
608C2×D4—222no—
609C2×D4—222no—
610C2×D4—222no—
611C2×D4—222no—
612C2×D4—441no—
613C2×D4—441no—
614C2×D4—441no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—111no—
626C22×C4—111no—
627C22×C4—111no—
628C22×C4—112no—
629C22×C4—112no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—111no—
633C22×C4—111no—
634C22×C4—111no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4C2×C4×D1111yescharacteristic
644C22×C4C2×C4×D1111yescharacteristic
645C22×C4C2×C4×D1111yescharacteristic
646C22×C4C2×C4×D1111yescharacteristic
647C22×C4D4×D1112yes—
648C22×C4#434112yes—
649C22×C4C23×D1111yescharacteristic
650M16—228no—
651M16—228no—
652M16—228no—
653M16—444no—
654C2×C8—28no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—112no—
666C2×C8—112no—
667C2×C8—112no—
668C2×C8—112no—
669C2×C8—228no—
670C2×C8—228no—
671C2×C8—221no—
672C2×C8—221no—
673C2×C8—221no—
674C2×C8—221no—
675C2×C8—221no—
676C2×C8—221no—
677C2×C8—221no—
678C2×C8—221no—
679C2×C8D4×D1112yes—
680C2×C8D4×D1112yes—
681C4⋊C4—22no—
682C4⋊C4—222no—
683C4⋊C4—222no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—222no—
687C22⋊C4—222no—
688C22⋊C4—222no—
689C22⋊C4—222no—
690C22⋊C4—222no—
691C22⋊C4—222no—
692C22⋊C4—222no—
693C22⋊C4—222no—
694C22⋊C4—441no—
695C22⋊C4—441no—
696C42—21no—
697C42—21no—
698C42—221no—
699C42—221no—
700C42—221no—
701C42—221no—
702C11#2144511yescharacteristic, complemented, Sylow
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—112no—
717C23—112no—
718C23—221no—
719C23—221no—
720C23—221no—
721C23—221no—
722C23—221no—
723C23—221no—
724C23—221no—
725C23—221no—
726C23—221no—
727C23—221no—
728C23—221no—
729C23—221no—
730C23(C22⋊D11)⋊C412yes—
731C23C22×C4×D1111yescharacteristic
732Q8—228no—
733D4—44no—
734D4—228no—
735D4—228no—
736D4—228no—
737D4—444no—
738D4—444no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—112no—
758C2×C4—112no—
759C2×C4—112no—
760C2×C4—221no—
761C2×C4—221no—
762C2×C4—221no—
763C2×C4—221no—
764C2×C4—221no—
765C2×C4—221no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—221no—
775C2×C4—221no—
776C2×C4—221no—
777C2×C4—221no—
778C2×C4—221no—
779C2×C4—221no—
780C2×C4—221no—
781C2×C4—221no—
782C2×C4—221no—
783C2×C4(C22⋊D11)⋊C412yes—
784C2×C4#6695412yescomplemented
785C2×C4C2×D4×D1111yescharacteristic
786C2×C4C2×D4×D1111yescharacteristic
787C2×C4C2×D4×D1111yescharacteristic
788C2×C4C2×#434111yescharacteristic
789C2×C4#41×D1111yescharacteristic
790C2×C4#41×D1111yescharacteristic
791C8—22no—
792C8—22no—
793C8—41no—
794C8—41no—
795C8—114no—
796C8—222no—
797C8—441no—
798C8—441no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—222no—
814C22—222no—
815C22—222no—
816C22—222no—
817C22—222no—
818C22—222no—
819C22—441no—
820C22—441no—
821C22—441no—
822C22—441no—
823C22—441no—
824C22—441no—
825C22—441no—
826C22—441no—
827C22C2×(C22⋊D11)⋊C411yescharacteristic
828C22C4×D4×D1111yescharacteristic
829C22C4×D4×D1111yescharacteristic
830C22C2×#6695411yescharacteristic
831C22#1062327611yescharacteristic
832C22D11×#13111yescharacteristic
833C22#1062328111yescharacteristic
834C4—22no—
835C4—22no—
836C4—41no—
837C4—41no—
838C4—222no—
839C4—222no—
840C4—222no—
841C4—441no—
842C4—441no—
843C4—441no—
844C4D11×#12011yescharacteristic
845C4#1062313711yescharacteristic
846C4#1062313711yescharacteristic
847C4#1062318711yescharacteristic
848C2—42no—
849C2—81no—
850C2—442no—
851C2—442no—
852C2#1307112111yescharacteristic
853C2#1307731411yescharacteristic
854C2#1307732311yescharacteristic
855C2#1307733711yescharacteristic
856C2#1307733911yescharacteristic
857C2#1307735511yescharacteristic
858C2#1307735611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1869C2
prime radical#13071831C2
cosocleC22×C4×C11C24
hypercenter#1869D11
hypocenterC11#21445
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C22×#66954C2semidirect
2. C2×#10622625C2semidirect
3. C2×#10622342C2semidirect
4. C2×#10622341C2semidirect
6. #13068910C2semidirect
7. #13068905C2semidirect
8. #13068800C2semidirect
9. #13068795C2semidirect
10. #13068794C2semidirect
11. #13068527C2semidirect
12. #13068402C2semidirect
13. #13068396C2semidirect
14. #13068386C2semidirect
15. C11×#1869C2semidirect
118. C2×#4318D4semidirect
129. C2×#4313D4semidirect
135. C2×C8×D11D4semidirect
281. #1869D11semidirect
338. C2×C4×C11#131semidirect
366. C2×Dic11#131semidirect
702. C11#21445semidirect
784. C2×C4#66954semidirect

Maximal subgroups

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

subgroupindex
C22×#669542
C2×#106226252
C2×#106223422
C2×#106223412
#130718312
#130689102
#130689052
#130688002
#130687952
#130687942
#130685272
#130684022
#130683962
#130683862
C11×#18692
#2144511