Finite Group Databasebeta

← #14800955

Subgroups — #14800955

Order 2816.

1124 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622665C211yesmaximal, characteristic, complemented
2C2×#10622852C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4C2×#10622845C211yesmaximal, characteristic, complemented
5#13072067C211yesmaximal, characteristic, complemented
6#13069990C211yesmaximal, characteristic, complemented
7#13069938C211yesmaximal, characteristic, complemented
8#13069809C211yesmaximal, characteristic, complemented
9#13069619C211yesmaximal, characteristic, complemented
10#13069469C211yesmaximal, characteristic, complemented
11#13069295C211yesmaximal, characteristic, complemented
12#13069055C211yesmaximal, characteristic, complemented
13#13069047C211yesmaximal, characteristic, complemented
14#13068808C211yesmaximal, characteristic, complemented
15C11×#2407C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C11×#394—21no—
28C11×#392—21no—
29C11×#391C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#386—21no—
32C11×#385—21no—
33C11×#380C2211yescharacteristic
34#10622852—24no—
35#10622845—24no—
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622833—21no—
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622665—24no—
47#10622625—24no—
48#10622597—21no—
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53#10622561—21no—
54#10622555—21no—
55#10622542C2211yescharacteristic
56#10622541C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11—21no—
71C22×D4×C11—21no—
72C22×D4×C11D411yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×Dic11—21no—
78C22×Dic22C2311yescharacteristic
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—41no—
81C11×#121—22no—
82C11×#121—41no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—21no—
100C2×#4326—22no—
101C2×#4326—22no—
102C2×#4326—41no—
103C2×#4324—22no—
104C2×#4324—22no—
105C2×#4324—41no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—41no—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112#66977—22no—
113#66977—22no—
114#66977—22no—
115#66977—41no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×#4318—22no—
120C2×#4318—22no—
121C2×#4318—22no—
122C2×#4318—22no—
123C2×#4318—41no—
124C2×#4318—41no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132#66899—22no—
133#66899—22no—
134#66899D414yescomplemented
135#66896—22no—
136#66896—22no—
137#66896—22no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C22⋊(C11⋊C8)—22no—
143C22⋊(C11⋊C8)D414yescomplemented
144#66874—22no—
145#66874—41no—
146#66872—22no—
147#66872—41no—
148C4⋊(C11⋊C8)—22no—
149C4×C11⋊C8—22no—
150#25135—111nomaximal, Sylow
151C24×C11—21no—
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C11×#41—28no—
155C11×#41—44no—
156C11×#41—44no—
157C11×#41—44no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11C2×D412yes—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—41no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—42no—
175C2×D4×C11—42no—
176C2×D4×C11—42no—
177C2×D4×C11—81no—
178C2×D4×C11#4112yes—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11#4112yes—
201C22×C4×C11C2411yescharacteristic
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—42no—
207C22×Dic11—42no—
208C22×Dic11—81no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—21no—
212C2×Dic22—21no—
213C2×Dic22—21no—
214C2×Dic22—21no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—42no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—81no—
227C11×C22⋊C4—81no—
228C42×C11—21no—
229C42×C11—21no—
230C22⋊Dic11—42no—
231C22⋊Dic11—42no—
232C22⋊Dic11—81no—
233#4326—44no—
234#4324—44no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—42no—
241C4⋊Dic11C2×D412yes—
242Dic11⋊C4—42no—
243Dic11⋊C4—42no—
244Dic11⋊C4—81no—
245#4318—44no—
246#4318—44no—
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—21no—
256C2×C11⋊C8C2×D412yes—
257C2×C11⋊C8C2×D412yes—
258C2×C11⋊C8C2×D412yes—
259C2×#470—111no—
260C2×#452—111no—
261C2×#436—111no—
262C2×#417—111no—
263#2417—111no—
264#2407D1111yescharacteristic
265#2065—111no—
266#2056—111no—
267#2035—111no—
268#2000—111no—
269#1968—111no—
270#1933—111no—
271#1895—111no—
272#1894—111no—
273#1853—111no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—22no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11#12112yes—
295C23×C11C22×D411yescharacteristic
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11—41no—
299Q8×C11—41no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—44no—
303D4×C11—48no—
304D4×C11—41no—
305D4×C11—41no—
306D4×C11—84no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—48no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11#12112yes—
336C2×C4×C11#13712yes—
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C2×#4111yescharacteristic
340C2×C4×C11C2×#4111yescharacteristic
341C2×C4×C11H(5,𝔽2)11yescharacteristic
342C2×C4×C11H(5,𝔽2)11yescharacteristic
343C2×Dic11—22no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—84no—
356Dic22—41no—
357Dic22—41no—
358Dic22—41no—
359Dic22—41no—
360C11⋊C8—22no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C11⋊C8—41no—
364C22×#41C2×D1111yescharacteristic
365C22×Q16—111no—
366C22×SD16—111no—
367C22×M16—111no—
368C22×M16—111no—
369C2×C22⋊Q8—111no—
370C2×C22⋊Q8—111no—
371C2×C22⋊Q8C2×D1111yescharacteristic
372C2×#121C2×D1111yescharacteristic
373C2×C4×D4C2×D1111yescharacteristic
374C22×C4⋊C4—111no—
375#470—224no—
376#452—224no—
377#436—224no—
378C2×#106—111no—
379C2×#106—111no—
380C2×C4⋊C8—111no—
381#417—224no—
382C2×#103—111no—
383C2×#103—111no—
384C2×#103—111no—
385C2×#103—111no—
386C2×#103—111no—
387C2×#102—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—111no—
392C2×C4×C8—111no—
393#398—221no—
394#396—221no—
395#394—21no—
396#392—21no—
397#391—111no—
398#391C2×D1111yescharacteristic
399#390C2×D1111yescharacteristic
400#389—111no—
401#386—21no—
402#386—221no—
403#385—21no—
404#380—111no—
405#380—221no—
406#380C2×D1111yescharacteristic
407#340—111no—
408#340—111no—
409#340—111no—
410#340—111no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—42no—
428C22×C11—81no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11—81no—
432C22×C11C2×#12111yescharacteristic
433C22×C11D4211yescharacteristic
434C22×C11#54611yescharacteristic
435C22×C11C2×#13711yescharacteristic
436C22×C11#57511yescharacteristic
437C22×C11#57711yescharacteristic
438C22×C11#57711yescharacteristic
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—41no—
442C4×C11—42no—
443C4×C11—41no—
444C4×C11—81no—
445C4×C11—81no—
446C4×C11#52511yescharacteristic
447C4×C11#53811yescharacteristic
448C4×C11D4211yescharacteristic
449C4×C11#54611yescharacteristic
450Dic11—42no—
451Dic11—81no—
452Dic11—81no—
453Dic11—81no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41—41no—
459C2×#41—41no—
460C22×Q8—111no—
461C22×Q8C22×D1111yescharacteristic
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C22⋊D1111yescharacteristic
465C22×D4C22×D1111yescharacteristic
466C23×C4—21no—
467C23×C4—221no—
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470C2×Q16—222no—
471C2×Q16—222no—
472C2×Q16—441no—
473C2×SD16—222no—
474C2×SD16—222no—
475C2×SD16—441no—
476C2×M16—222no—
477C2×M16—222no—
478C2×M16—222no—
479C2×M16—222no—
480C2×M16—441no—
481C2×M16—441no—
482C22×C8—111no—
483C22×C8—111no—
484C22×C8—111no—
485C22×C8—111no—
486C22⋊Q8—22no—
487C22⋊Q8—41no—
488C22⋊Q8—222no—
489C22⋊Q8—222no—
490C22⋊Q8—222no—
491C22⋊Q8—441no—
492#121—22no—
493#121—41no—
494C4×D4—22no—
495C4×D4—22no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—222no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—441no—
506C2×C4⋊C4C22⋊D1111yescharacteristic
507C2×C4⋊C4C22×D1111yescharacteristic
508C2×C4⋊C4C22×D1111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4C22⋊D1111yescharacteristic
518C2×C22⋊C4C22⋊D1111yescharacteristic
519C2×C42C22×D1111yescharacteristic
520#106—222no—
521#106—441no—
522C4⋊C8—222no—
523#103—114no—
524#103—222no—
525#103—222no—
526#103—222no—
527#103—441no—
528#102—222no—
529#102—222no—
530#102—222no—
531C22⋊C8—114no—
532C22⋊C8—222no—
533C4×C8—222no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—221no—
538#95—221no—
539#95—221no—
540#95—221no—
541C2×C11—42no—
542C2×C11—81no—
543C2×C11—82no—
544C2×C11#242411yescharacteristic
545C2×C11#305611yescharacteristic
546C2×C11#306011yescharacteristic
547C2×C11#327511yescharacteristic
548C2×C11#327811yescharacteristic
549C2×C11#332311yescharacteristic
550C2×C11#333111yescharacteristic
551C24—21no—
552C24C2×C22⋊D1111yescharacteristic
553C24C2×C22⋊D1111yescharacteristic
554#41—28no—
555#41—44no—
556#41—44no—
557#41—44no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—221no—
564C2×Q8—221no—
565C2×Q8—221no—
566C2×Q8—221no—
567C2×Q8—221no—
568C2×Q8—221no—
569C2×Q8D4×D1112yes—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—41no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—81no—
584C2×D4#434112yes—
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—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—442no—
606C22×C4—442no—
607C22×C4—881no—
608C22×C4D4×D1112yes—
609C22×C4#434112yes—
610C22×C4C2×C22⋊D1111yescharacteristic
611C22×C4C2×C22⋊D1111yescharacteristic
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C23×D1111yescharacteristic
615Q16—444no—
616SD16—444no—
617M16—444no—
618M16—444no—
619C2×C8—112no—
620C2×C8—112no—
621C2×C8—112no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—221no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—42no—
637C4⋊C4—112no—
638C4⋊C4—221no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—442no—
644C4⋊C4—442no—
645C4⋊C4—442no—
646C4⋊C4—881no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—81no—
653C22⋊C4—81no—
654C22⋊C4—442no—
655C22⋊C4—442no—
656C22⋊C4—881no—
657C42—21no—
658C42—21no—
659C11#2513511yescharacteristic, complemented, Sylow
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23#6699212yes—
681C23C22×C22⋊D1111yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686Q8—441no—
687Q8—441no—
688Q8—441no—
689Q8—441no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—48no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
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—222no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—884no—
738C2×C4#6699212yes—
739C2×C4#6700412yes—
740C2×C4C2×D4×D1111yescharacteristic
741C2×C4C2×D4×D1111yescharacteristic
742C2×C4C2×#434111yescharacteristic
743C2×C4C2×#434111yescharacteristic
744C2×C4#6703711yescharacteristic
745C2×C4#6703711yescharacteristic
746C8—222no—
747C8—222no—
748C8—222no—
749C8—441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22D4×C22⋊D1111yescharacteristic
772C22C2×#6699211yescharacteristic
773C22#1062333711yescharacteristic
774C22#1062335311yescharacteristic
775C22C2×#6700411yescharacteristic
776C22#1062336711yescharacteristic
777C22#1062336811yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—42no—
783C4—81no—
784C4—81no—
785C4—442no—
786C4—881no—
787C4—881no—
788C4—881no—
789C4#1062311711yescharacteristic
790C4#1062312111yescharacteristic
791C4#1062312211yescharacteristic
792C4#1062312411yescharacteristic
793C2—42no—
794C2—81no—
795C2—82no—
796C2#1307215611yescharacteristic
797C2#1307824811yescharacteristic
798C2#1307827511yescharacteristic
799C2#1308024811yescharacteristic
800C2#1308028211yescharacteristic
801C2#1308083211yescharacteristic
802C2#1308093211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2407C2
socleC23×C11C22×D4
hypercenter#2407D11
hypocenterC11#25135
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#10622665C2semidirect
2. C2×#10622852C2semidirect
3. C2×#10622625C2semidirect
4. C2×#10622845C2semidirect
5. #13072067C2semidirect
6. #13069990C2semidirect
7. #13069938C2semidirect
8. #13069809C2semidirect
9. #13069619C2semidirect
10. #13069469C2semidirect
11. #13069295C2semidirect
12. #13069055C2semidirect
13. #13069047C2semidirect
14. #13068808C2semidirect
134. #66899D4semidirect
143. C22⋊(C11⋊C8)D4semidirect
659. C11#25135semidirect

Maximal subgroups

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

subgroupindex
C2×#106226652
C2×#106228522
C2×#106226252
C2×#106228452
#130720672
#130699902
#130699382
#130698092
#130696192
#130694692
#130692952
#130690552
#130690472
#130688082
C11×#24072
#2513511