Finite Group Databasebeta

← #15622185

Subgroups — #15622185

Order 2816.

2138 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic, complemented
2#13078783C214yesmaximal, complemented
3#13078742C212yesmaximal, complemented
4#13078734C212yesmaximal, complemented
5#13078692C214yesmaximal, complemented
6#13078651C212yesmaximal, complemented
7#13078643C212yesmaximal, complemented
8#13078536C212yesmaximal, complemented
9#13078417C212yesmaximal, complemented
10#13078084C212yesmaximal, complemented
11#13077849C212yesmaximal, complemented
12C4×#67004C214yesmaximal, complemented
13#13077249C211yesmaximal, characteristic, complemented
14C11×#3444C211yesmaximal, characteristic
15C23×Dic22C2211yescharacteristic
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C11×#529—21no—
23C11×#529—21no—
24C11×#529—21no—
25C11×#529—21no—
26C11×#529C2212yes—
27C11×#529C2212yes—
28C11×#525—21no—
29C11×#525—21no—
30C11×#525C2212yes—
31C4×C11×#41—21no—
32C4×C11×#41—21no—
33C4×C11×#41C2212yes—
34C22×C42×C11C2211yescharacteristic
35C2×#67004C2214yes—
36C22×C4⋊Dic11C2211yescharacteristic
37C22×Dic11⋊C4—21no—
38C22×C4×Dic11—21no—
39C2×C4×Dic22—21no—
40C2×C4×Dic22—21no—
41C2×C4×Dic22—21no—
42C2×C4×Dic22—21no—
43C2×C4×Dic22—21no—
44C2×C4×Dic22—21no—
45C2×C4×Dic22C2212yes—
46C2×C4×Dic22C2212yes—
47C2×C4×Dic22C2212yes—
48C2×C4×Dic22C2212yes—
49C2×C4×Dic22C2212yes—
50C2×C4×Dic22C2212yes—
51#10622845C2214yes—
52#10622820C2212yes—
53#10622707C2214yescomplemented
54#10622704C2214yescomplemented
55#10622703C2214yescomplemented
56#10622688C2214yescomplemented
57#10622676C2218yescomplemented
58#10622667C2218yescomplemented
59#10622663C2214yes—
60#10622663C2214yes—
61#10622657C2214yes—
62#10622656C2214yes—
63#10622653C2214yes—
64#10622653C2214yes—
65#10622647C2214yes—
66#10622646C2214yes—
67#10622643C2218yescomplemented
68C4×#4326C2218yescomplemented
69#10622631C2218yescomplemented
70C4×#4324C2218yescomplemented
71#10622617C2214yes—
72#10622608C2214yes—
73#10622539C2212yes—
74#10622539C2212yes—
75#10622538C2212yes—
76#10622538C2212yes—
77#10622537C2212yes—
78C4×#4318C2212yes—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41C2312yes—
82C23×C4×C11D411yescharacteristic
83C23×C4×C11D411yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×Dic11—21no—
86C23×Dic11—21no—
87C22×Dic22—21no—
88C22×Dic22—21no—
89C22×Dic22—21no—
90C22×Dic22—28no—
91C22×Dic22C2312yes—
92C22×Dic22C2312yes—
93C22×Dic22C2312yes—
94C11×C4⋊Q8C2311yescharacteristic
95C11×C4⋊Q8C2311yescharacteristic
96C11×C4⋊Q8C2311yescharacteristic
97C11×#127C2311yescharacteristic
98C11×#126—22no—
99C11×#126—22no—
100C11×#125—21no—
101C11×#125—21no—
102C11×#125C2312yes—
103C11×#124—21no—
104C11×#124—21no—
105C11×#124C2312yes—
106C11×#123—22no—
107C11×#123—22no—
108C11×#123—22no—
109C11×C22⋊Q8—21no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8C2312yes—
114C11×C22⋊Q8C2312yes—
115C11×#121—21no—
116C11×#121—21no—
117C11×#121—21no—
118C11×#121—21no—
119C11×#121C2312yes—
120C11×#121C2312yes—
121C11×#120—22no—
122C4×Q8×C11—21no—
123C4×Q8×C11—21no—
124C4×Q8×C11—21no—
125C4×Q8×C11—21no—
126C4×Q8×C11C2312yes—
127C4×Q8×C11C2312yes—
128C4×D4×C11—22no—
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C4×D4×C11—22no—
132C4×D4×C11—22no—
133C4×D4×C11—22no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11—21no—
138C4×D4×C11C2312yes—
139C4×D4×C11C2312yes—
140C11×#117—21no—
141C11×#117—21no—
142C11×#117—22no—
143C11×#117—22no—
144C11×#117—22no—
145C11×#117C2312yes—
146C2×C42×C11—22no—
147C2×C42×C11D411yescharacteristic
148C2×C42×C11D411yescharacteristic
149C2×C42×C11D411yescharacteristic
150C2×C42×C11D411yescharacteristic
151C2×C42×C11D411yescharacteristic
152C2×C42×C11D411yescharacteristic
153C2×C42×C11C2311yescharacteristic
154C2×C42×C11C2311yescharacteristic
155C2×C42×C11C2311yescharacteristic
156C2×C42×C11C2311yescharacteristic
157C2×C42×C11C2311yescharacteristic
158C2×C42×C11C2311yescharacteristic
159#67004—216no—
160C2×#4326C2318yes—
161C2×#4324C2318yes—
162C2×C4⋊Dic11—21no—
163C2×C4⋊Dic11—21no—
164C2×C4⋊Dic11—21no—
165C2×C4⋊Dic11C2312yes—
166C2×C4⋊Dic11C2312yes—
167C2×C4⋊Dic11C2312yes—
168C2×Dic11⋊C4—22no—
169C2×Dic11⋊C4—22no—
170C2×Dic11⋊C4—22no—
171C2×Dic11⋊C4—22no—
172C2×Dic11⋊C4—22no—
173C2×Dic11⋊C4—22no—
174C2×C4×Dic11—22no—
175C2×C4×Dic11—22no—
176C2×C4×Dic11—22no—
177C2×C4×Dic11—22no—
178C2×C4×Dic11—22no—
179C2×C4×Dic11—22no—
180C2×#4318C2314yes—
181C4×Dic22—22no—
182C4×Dic22—22no—
183C4×Dic22—22no—
184C4×Dic22—22no—
185C4×Dic22—22no—
186C4×Dic22—22no—
187C4×Dic22—22no—
188C4×Dic22—22no—
189C4×Dic22—22no—
190C4×Dic22—22no—
191C4×Dic22—22no—
192C4×Dic22—22no—
193C4×Dic22C2314yes—
194C4×Dic22C2314yes—
195C4×Dic22C2314yes—
196C4×Dic22C2314yes—
197#66899C2318yes—
198#66896C2318yes—
199C22⋊(C11⋊C8)C2314yes—
200C22⋊(C11⋊C8)C2314yes—
201#66874C2318yes—
202#66874C2318yes—
203#66872C2318yes—
204#66871C2318yes—
205C4⋊(C11⋊C8)C2314yes—
206C4⋊(C11⋊C8)C2314yes—
207#66867C2314yes—
208C4×C11⋊C8C2314yes—
209#60560—111nomaximal, Sylow
210C24×C11C2×D411yescharacteristic
211C11×#41—28no—
212C11×#41—44no—
213C11×#41—44no—
214C2×Q8×C11—21no—
215C2×Q8×C11—21no—
216C2×Q8×C11C2412yes—
217C2×D4×C11—22no—
218C2×D4×C11—22no—
219C2×D4×C11—22no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11C2412yes—
223C22×C4×C11—24no—
224C22×C4×C11—24no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—42no—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2411yescharacteristic
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C22×Dic11—28no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—44no—
255C2×Dic22—28no—
256C2×Dic22—28no—
257C2×Dic22—28no—
258C2×Dic22—28no—
259C2×Dic22—28no—
260C2×Dic22—22no—
261C2×Dic22—22no—
262C2×Dic22—22no—
263C2×Dic22—24no—
264C2×Dic22#4118yescomplemented
265C2×Dic22C2414yes—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4C2412yes—
277C11×C4⋊C4C2412yes—
278C11×C22⋊C4—22no—
279C11×C22⋊C4—22no—
280C11×C22⋊C4—22no—
281C11×C22⋊C4—22no—
282C11×C22⋊C4—22no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—22no—
285C11×C22⋊C4—22no—
286C11×C22⋊C4—22no—
287C42×C11—22no—
288C42×C11—22no—
289C42×C11—22no—
290C42×C11C2×D411yescharacteristic
291C42×C11C2×D411yescharacteristic
292C42×C11C2×D411yescharacteristic
293C42×C11C2×D411yescharacteristic
294C42×C11C2×D411yescharacteristic
295C42×C11C2×D411yescharacteristic
296C42×C11C2×D411yescharacteristic
297C42×C11C2×D411yescharacteristic
298C42×C11C2×D411yescharacteristic
299C42×C11C2×D411yescharacteristic
300C42×C11C2×D411yescharacteristic
301C42×C11C2×D411yescharacteristic
302C42×C11C2411yescharacteristic
303C42×C11C2411yescharacteristic
304C42×C11C2411yescharacteristic
305C42×C11C2411yescharacteristic
306#4326—216no—
307#4324—216no—
308C4⋊Dic11—22no—
309C4⋊Dic11—22no—
310C4⋊Dic11—22no—
311C4⋊Dic11C2414yes—
312Dic11⋊C4—24no—
313Dic11⋊C4—24no—
314Dic11⋊C4—24no—
315Dic11⋊C4—24no—
316C4×Dic11—24no—
317C4×Dic11—24no—
318C4×Dic11—24no—
319C4×Dic11—24no—
320#4318—28no—
321C2×C11⋊C8C2418yes—
322#3444D1111yescharacteristic
323C22×C4×Q8—111no—
324#3117—114no—
325#3113—112no—
326#3112—112no—
327#3108—114no—
328#3104—112no—
329#3103—112no—
330#3092—112no—
331#3078—112no—
332#3037—112no—
333#3004—112no—
334C4×#137—114no—
335#2920—111no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11C22×D411yescharacteristic
341C23×C11C22×D411yescharacteristic
342C23×C11C22×D411yescharacteristic
343Q8×C11—24no—
344Q8×C11—42no—
345Q8×C11—42no—
346D4×C11—24no—
347D4×C11—42no—
348D4×C11—44no—
349D4×C11—44no—
350D4×C11—44no—
351D4×C11—42no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11—44no—
374C2×C4×C11#13714yescomplemented
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C2×#4114yes—
387C2×C4×C11C2511yescharacteristic
388C2×Dic11—28no—
389C2×Dic11—28no—
390C2×Dic11—28no—
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—44no—
394C2×Dic11—44no—
395C2×Dic11—44no—
396Dic22—28no—
397Dic22—28no—
398Dic22—28no—
399Dic22—24no—
400Dic22C2×#4118yes—
401C11⋊C8—28no—
402C23×Q8—111no—
403C2×#137—114no—
404#533C2×D1111yescharacteristic
405#533C2×D1111yescharacteristic
406#533C2×D1111yescharacteristic
407#532C2×D1111yescharacteristic
408#532C2×D1111yescharacteristic
409#532C2×D1111yescharacteristic
410#529—21no—
411#529—21no—
412#529—21no—
413#529—21no—
414#529C2×D1112yes—
415#529C2×D1112yes—
416#525—21no—
417#525—21no—
418#525C2×D1112yes—
419C4×#41—21no—
420C4×#41—21no—
421C4×#41C2×D1112yes—
422C2×C4×Q8—112no—
423C2×C4×Q8—112no—
424C2×C4×Q8—112no—
425C2×C4×Q8—112no—
426C2×C4×Q8—112no—
427C2×C4×Q8—112no—
428C2×C4×Q8—221no—
429C2×C4×Q8—221no—
430C2×C4×Q8—221no—
431C2×C4×Q8—221no—
432C2×C4×Q8—221no—
433C2×C4×Q8—221no—
434C22×C4⋊C4—111no—
435C22×C4⋊C4—221no—
436C22×C42—221no—
437C22×C42C2×D1111yescharacteristic
438#484—114no—
439#483—114no—
440#481—114no—
441#480—114no—
442#479—118no—
443#477—114no—
444#475—114no—
445#464—118no—
446#462—114no—
447#460—114no—
448#451—114no—
449#451—114no—
450#448—114no—
451#448—114no—
452#441—118no—
453#440—118no—
454C4×Q16—118no—
455C4×SD16—118no—
456#432—112no—
457#432—112no—
458#431—112no—
459#431—112no—
460#428—114no—
461#423—112no—
462#419—114no—
463#417—114no—
464#407—112no—
465C4×M16—112no—
466C22×C11—28no—
467C22×C11—21no—
468C22×C11—21no—
469C22×C11—21no—
470C22×C11—21no—
471C22×C11—21no—
472C22×C11—21no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11#52512yes—
477C22×C11C2×#13712yes—
478C22×C11#57512yes—
479C22×C11C23×D411yescharacteristic
480C4×C11—21no—
481C4×C11—21no—
482C4×C11—21no—
483C4×C11—21no—
484C4×C11—21no—
485C4×C11—21no—
486C4×C11—21no—
487C4×C11—21no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11#52512yes—
492C4×C11C2×#13712yes—
493C4×C11C2×#13712yes—
494C4×C11C22×#4112yes—
495Dic11—28no—
496Dic11—44no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41C22×D1112yes—
500C22×Q8—112no—
501C22×Q8—112no—
502C22×Q8—112no—
503C22×Q8—228no—
504C22×Q8—221no—
505C22×Q8—221no—
506C22×Q8—221no—
507C23×C4—221no—
508C23×C4—221no—
509C23×C4C22⋊D1111yescharacteristic
510C23×C4C22⋊D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512#137—2216no—
513C2×Q16—118no—
514C2×SD16—118no—
515C2×M16—114no—
516C4⋊Q8C22×D1111yescharacteristic
517C4⋊Q8C22×D1111yescharacteristic
518C4⋊Q8C22×D1111yescharacteristic
519#127C22×D1111yescharacteristic
520#126—22no—
521#126—22no—
522#125—21no—
523#125—21no—
524#125C22×D1112yes—
525#124—21no—
526#124—21no—
527#124C22×D1112yes—
528#123—22no—
529#123—22no—
530#123—22no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8C22×D1112yes—
536C22⋊Q8C22×D1112yes—
537#121—21no—
538#121—21no—
539#121—21no—
540#121—21no—
541#121C22×D1112yes—
542#121C22×D1112yes—
543#120—22no—
544C4×Q8—21no—
545C4×Q8—21no—
546C4×Q8—21no—
547C4×Q8—21no—
548C4×Q8—114no—
549C4×Q8—114no—
550C4×Q8—114no—
551C4×Q8—114no—
552C4×Q8—222no—
553C4×Q8—222no—
554C4×Q8—222no—
555C4×Q8—222no—
556C4×Q8—222no—
557C4×Q8—222no—
558C4×Q8—222no—
559C4×Q8—222no—
560C4×Q8—222no—
561C4×Q8—222no—
562C4×Q8—222no—
563C4×Q8—222no—
564C4×Q8C22×D1112yes—
565C4×Q8C22×D1112yes—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4—21no—
575C4×D4—21no—
576C4×D4C22×D1112yes—
577C4×D4C22×D1112yes—
578#117—21no—
579#117—21no—
580#117—22no—
581#117—22no—
582#117—22no—
583#117C22×D1112yes—
584C2×C4⋊C4—112no—
585C2×C4⋊C4—112no—
586C2×C4⋊C4—112no—
587C2×C4⋊C4—221no—
588C2×C4⋊C4—221no—
589C2×C4⋊C4—221no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—222no—
596C2×C42—22no—
597C2×C42—222no—
598C2×C42—222no—
599C2×C42—222no—
600C2×C42—222no—
601C2×C42—222no—
602C2×C42—222no—
603C2×C42C22⋊D1111yescharacteristic
604C2×C42C22⋊D1111yescharacteristic
605C2×C42C22⋊D1111yescharacteristic
606C2×C42C22⋊D1111yescharacteristic
607C2×C42C22⋊D1111yescharacteristic
608C2×C42C22⋊D1111yescharacteristic
609C2×C42C22×D1111yescharacteristic
610C2×C42C22×D1111yescharacteristic
611C2×C42C22×D1111yescharacteristic
612C2×C42C22×D1111yescharacteristic
613C2×C42C22×D1111yescharacteristic
614C2×C42C22×D1111yescharacteristic
615#107—118no—
616#106—118no—
617C4⋊C8—114no—
618C4⋊C8—114no—
619#103—118no—
620#103—118no—
621#103—118no—
622#102—118no—
623C22⋊C8—114no—
624C22⋊C8—114no—
625#97—114no—
626C4×C8—114no—
627C2×C11—22no—
628C2×C11—22no—
629C2×C11—22no—
630C2×C11—82no—
631C2×C11C2×#52511yescharacteristic
632C2×C11C22×#13711yescharacteristic
633C2×C11C2×#57511yescharacteristic
634C24C2×C22⋊D1111yescharacteristic
635#41—28no—
636#41—44no—
637#41—44no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—118no—
641C2×Q8—114no—
642C2×Q8—228no—
643C2×Q8—228no—
644C2×Q8—228no—
645C2×Q8—228no—
646C2×Q8—228no—
647C2×Q8—224no—
648C2×Q8—222no—
649C2×Q8—222no—
650C2×Q8—222no—
651C2×Q8C23×D1112yes—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4C23×D1112yes—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—42no—
664C22×C4—228no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—444no—
672C22×C4C2×C22⋊D1111yescharacteristic
673C22×C4C2×C22⋊D1111yescharacteristic
674C22×C4C2×C22⋊D1111yescharacteristic
675C22×C4C2×C22⋊D1111yescharacteristic
676C22×C4C2×C22⋊D1111yescharacteristic
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C2×C22⋊D1111yescharacteristic
683C22×C4C2×C22⋊D1111yescharacteristic
684C22×C4C2×C22⋊D1111yescharacteristic
685C22×C4C2×C22⋊D1111yescharacteristic
686C22×C4C2×C22⋊D1111yescharacteristic
687C22×C4C23×D1111yescharacteristic
688C22×C4C23×D1111yescharacteristic
689C22×C4C23×D1111yescharacteristic
690Q16—2216no—
691SD16—2216no—
692M16—228no—
693C2×C8—118no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—114no—
705C4⋊C4—222no—
706C4⋊C4—222no—
707C4⋊C4—222no—
708C4⋊C4—224no—
709C4⋊C4—224no—
710C4⋊C4—224no—
711C4⋊C4—224no—
712C4⋊C4C23×D1112yes—
713C4⋊C4C23×D1112yes—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—224no—
727C42—224no—
728C42—224no—
729C42—224no—
730C42C2×C22⋊D1111yescharacteristic
731C42C2×C22⋊D1111yescharacteristic
732C42C2×C22⋊D1111yescharacteristic
733C42C2×C22⋊D1111yescharacteristic
734C42C2×C22⋊D1111yescharacteristic
735C42C2×C22⋊D1111yescharacteristic
736C42C2×C22⋊D1111yescharacteristic
737C42C2×C22⋊D1111yescharacteristic
738C42C2×C22⋊D1111yescharacteristic
739C42C2×C22⋊D1111yescharacteristic
740C42C2×C22⋊D1111yescharacteristic
741C42C2×C22⋊D1111yescharacteristic
742C42C23×D1111yescharacteristic
743C42C23×D1111yescharacteristic
744C42C23×D1111yescharacteristic
745C42C23×D1111yescharacteristic
746C11#6056011yescharacteristic, complemented, Sylow
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23C22×C22⋊D1111yescharacteristic
752C23C22×C22⋊D1111yescharacteristic
753C23C22×C22⋊D1111yescharacteristic
754Q8—24no—
755Q8—42no—
756Q8—42no—
757Q8—118no—
758Q8—228no—
759Q8—228no—
760Q8—228no—
761Q8—224no—
762D4—24no—
763D4—42no—
764D4—44no—
765D4—44no—
766D4—44no—
767D4—42no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—228no—
791C2×C4—228no—
792C2×C4—228no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—444no—
796C2×C4—444no—
797C2×C4—444no—
798C2×C4#6700414yescomplemented
799C2×C4#41×D1114yes—
800C2×C4C22×C22⋊D1111yescharacteristic
801C2×C4C22×C22⋊D1111yescharacteristic
802C2×C4C22×C22⋊D1111yescharacteristic
803C2×C4C22×C22⋊D1111yescharacteristic
804C2×C4C22×C22⋊D1111yescharacteristic
805C2×C4C22×C22⋊D1111yescharacteristic
806C2×C4C22×C22⋊D1111yescharacteristic
807C2×C4C22×C22⋊D1111yescharacteristic
808C2×C4C22×C22⋊D1111yescharacteristic
809C2×C4C22×C22⋊D1111yescharacteristic
810C2×C4C22×C22⋊D1111yescharacteristic
811C2×C4C24×D1111yescharacteristic
812C8—228no—
813C22—28no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22#1062335312yes—
824C22C2×#6700412yes—
825C22#1062335912yes—
826C22C23×C22⋊D1111yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—228no—
839C4—444no—
840C4C2×#6700412yes—
841C4C2×#6700412yes—
842C4#1062335912yes—
843C4C2×#41×D1112yes—
844C2—22no—
845C2—22no—
846C2—22no—
847C2—82no—
848C2C2×#1062335911yescharacteristic
849C2C22×#6700411yescharacteristic
850C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3444C2
socleC22×C11C23×D4
hypercenter#3444D11
hypocenterC11#60560
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic22C2semidirect
2. #13078783C2semidirect
3. #13078742C2semidirect
4. #13078734C2semidirect
5. #13078692C2semidirect
6. #13078651C2semidirect
7. #13078643C2semidirect
8. #13078536C2semidirect
9. #13078417C2semidirect
10. #13078084C2semidirect
11. #13077849C2semidirect
12. C4×#67004C2semidirect
13. #13077249C2semidirect
53. #10622707C22semidirect
54. #10622704C22semidirect
55. #10622703C22semidirect
56. #10622688C22semidirect
57. #10622676C22semidirect
58. #10622667C22semidirect
67. #10622643C22semidirect
68. C4×#4326C22semidirect
69. #10622631C22semidirect
70. C4×#4324C22semidirect
264. C2×Dic22#41semidirect
374. C2×C4×C11#137semidirect
746. C11#60560semidirect
798. C2×C4#67004semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
#130787832
#130787422
#130787342
#130786922
#130786512
#130786432
#130785362
#130784172
#130780842
#130778492
C4×#670042
#130772492
C11×#34442
#6056011