Finite Group Databasebeta

← #14765200

Subgroups — #14765200

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077320C211yesmaximal, characteristic, complemented
2#13077061C211yesmaximal, characteristic, complemented
3#13069510C211yesmaximal, characteristic, complemented
4#13069505C211yesmaximal, characteristic, complemented
5#13069329C211yesmaximal, characteristic, complemented
6#13069322C211yesmaximal, characteristic, complemented
7#13069266C211yesmaximal, characteristic, complemented
8#13069266C211yesmaximal, characteristic, complemented
9#13068945C211yesmaximal, characteristic, complemented
10#13068945C211yesmaximal, characteristic, complemented
11#13068919C211yesmaximal, characteristic, complemented
12#13068823C211yesmaximal, characteristic, complemented
13#13068560C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#3002C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×C11×#135C2211yescharacteristic
18C2×C11×#135C2211yescharacteristic
19C11×#525C2211yescharacteristic
20C2×#67001C2211yescharacteristic, complemented
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C11×#452C411yescharacteristic, complemented
24C11×#452C411yescharacteristic, complemented
25C11×#451C411yescharacteristic, complemented
26C11×#450C411yescharacteristic, complemented
27C11×#449C411yescharacteristic, complemented
28C11×#449C411yescharacteristic, complemented
29C11×#448C411yescharacteristic, complemented
30C11×#447C411yescharacteristic, complemented
31C11×#416C2211yescharacteristic
32C11×#416C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×#66901C2211yescharacteristic
35C2×#66901C2211yescharacteristic
36C2×#66901C2211yescharacteristic
37C2×#66901C2211yescharacteristic
38C2×#66901C2211yescharacteristic, complemented
39C2×#66901C2211yescharacteristic, complemented
40#10622847—21no—
41#10622847—21no—
42#10622847C2211yescharacteristic
43#10622847C2211yescharacteristic
44#10622847C2211yescharacteristic
45#10622847C2211yescharacteristic
46#10622847C2211yescharacteristic, complemented
47C4×C22⋊Dic11C2211yescharacteristic
48#10622820—21no—
49#10622820—21no—
50#10622820C2211yescharacteristic
51C2×#66883C2211yescharacteristic, complemented
52C2×#66883C2211yescharacteristic, complemented
53C2×#66879C2211yescharacteristic, complemented
54C2×C8×Dic11C2211yescharacteristic, complemented
55#10622625—21no—
56#10622625—21no—
57#10622624—21no—
58#10622624—21no—
59#10622612C2211yescharacteristic, complemented
60#10622610C2211yescharacteristic, complemented
61#10622190C2211yescharacteristic, complemented
62#10622190C2211yescharacteristic, complemented
63#10622188C2211yescharacteristic, complemented
64#10622188C2211yescharacteristic, complemented
65#10622170C2211yescharacteristic, complemented
66#10622170C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C2×C11×#41—41no—
73C2×C11×#41C2×C411yescharacteristic
74C2×C11×#41C2×C411yescharacteristic
75C2×C11×#41C2311yescharacteristic
76C2×C11×#41C2311yescharacteristic
77C2×C11×#41C2311yescharacteristic
78C22×Q8×C11C2×C411yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11C2×C411yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11C2311yescharacteristic
83C11×#135—41no—
84C11×#135—41no—
85C11×#135—41no—
86C11×#135—41no—
87C2×C11×Q16C2×C411yescharacteristic
88C2×C11×Q16C2×C411yescharacteristic
89C2×C11×SD16C2×C411yescharacteristic
90C2×C11×SD16C2×C411yescharacteristic
91C2×C11×SD16C2×C411yescharacteristic
92C2×C11×SD16C2×C411yescharacteristic
93C2×C11×D8C2×C411yescharacteristic
94C2×C11×D8C2×C411yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C11×#123—21no—
98C11×C22⋊Q8C2×C411yescharacteristic
99C11×C22⋊Q8C2×C411yescharacteristic
100C11×#121C2×C411yescharacteristic
101C11×#121C2×C411yescharacteristic
102C11×#120—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C11×#117C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107#67001—41no—
108#67001—41no—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C2×#4318—21no—
112C2×#4318—21no—
113C2×#4318—41no—
114C2×#4318—41no—
115C2×#4318—41no—
116C2×#4318—41no—
117C2×#4318D411yescharacteristic
118C2×#4318D411yescharacteristic
119C2×#4318D411yescharacteristic
120C2×#4318D411yescharacteristic
121C2×#4318C2311yescharacteristic
122C2×#4318C2311yescharacteristic
123C2×#4318C2311yescharacteristic
124C2×#4318C2311yescharacteristic
125C22×C11⋊C8—21no—
126C22×C11⋊C8—21no—
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C11×#103C2×C411yescharacteristic
130C11×#103C2×C411yescharacteristic
131C11×#103C2×C411yescharacteristic
132C11×#103C2×C411yescharacteristic
133C11×#102C2×C411yescharacteristic
134C11×#102C2×C411yescharacteristic
135C11×#102C2×C411yescharacteristic
136C11×#102C2×C411yescharacteristic
137C11×C22⋊C8C2×C411yescharacteristic
138C11×C22⋊C8C2×C411yescharacteristic
139C11×C22⋊C8C2×C411yescharacteristic
140C11×C22⋊C8C2×C411yescharacteristic
141#66901—41no—
142#66901—41no—
143#66901—41no—
144#66901—41no—
145#66901—41no—
146#66901—41no—
147C11⋊#95—21no—
148C22⋊(C11⋊C8)—21no—
149C22⋊(C11⋊C8)—21no—
150C22⋊(C11⋊C8)—21no—
151C22⋊(C11⋊C8)—21no—
152C22⋊(C11⋊C8)—21no—
153C22⋊(C11⋊C8)—21no—
154C22⋊(C11⋊C8)—21no—
155C22⋊(C11⋊C8)—21no—
156C22⋊(C11⋊C8)—21no—
157C22⋊(C11⋊C8)—21no—
158C22⋊(C11⋊C8)—21no—
159C22⋊(C11⋊C8)—21no—
160#66883—41no—
161#66883—41no—
162#66879—41no—
163C8×Dic11—41no—
164C4⋊(C11⋊C8)—21no—
165C4⋊(C11⋊C8)—21no—
166#66867—21no—
167C4×C11⋊C8—21no—
168#22062—111nomaximal, Sylow
169C24×C11—21no—
170C24×C11#4111yescharacteristic
171C11×#41—21no—
172C11×#41—21no—
173C11×#41—21no—
174C11×#41—21no—
175C11×#41—21no—
176C11×#41—21no—
177C11×#41—21no—
178C11×#41—21no—
179C11×#41—21no—
180C11×#41—21no—
181C11×#41—21no—
182C11×#41—21no—
183C11×#41—41no—
184C11×#41—41no—
185C11×#41—41no—
186C11×#41—41no—
187C11×#41—42no—
188C11×#41—42no—
189C11×#41—42no—
190C11×#41—42no—
191C2×Q8×C11—21no—
192C2×Q8×C11—41no—
193C2×Q8×C11—41no—
194C2×Q8×C11C22×C411yescharacteristic
195C2×Q8×C11C22×C411yescharacteristic
196C2×Q8×C11C22×C411yescharacteristic
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—41no—
206C2×D4×C11—41no—
207C2×D4×C11—42no—
208C2×D4×C11—42no—
209C2×D4×C11C22×C411yescharacteristic
210C2×D4×C11C22×C411yescharacteristic
211C2×D4×C11C22×C411yescharacteristic
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—42no—
223C22×C4×C11—42no—
224C22×C4×C11C22×C411yescharacteristic
225C22×C4×C11C22×C411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11#4111yescharacteristic
229C22×C4×C11C2411yescharacteristic
230C22×Dic11—21no—
231C22×Dic11—21no—
232C11×Q16—41no—
233C11×Q16—41no—
234C11×SD16—41no—
235C11×SD16—41no—
236C11×SD16—41no—
237C11×SD16—41no—
238C11×D8—41no—
239C11×D8—41no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11C22×C411yescharacteristic
245C2×C8×C11C22×C411yescharacteristic
246C2×C8×C11C22×C411yescharacteristic
247C2×C8×C11C22×C411yescharacteristic
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4C22×C411yescharacteristic
251C11×C4⋊C4C22×C411yescharacteristic
252C11×C22⋊C4—21no—
253C11×C22⋊C4—21no—
254C11×C22⋊C4—21no—
255C11×C22⋊C4—21no—
256C11×C22⋊C4—21no—
257C42×C11—21no—
258C22⋊Dic11—42no—
259C4×Dic11—21no—
260C4×Dic11—21no—
261C4×Dic11—21no—
262C4×Dic11—21no—
263#4318—21no—
264#4318—21no—
265#4318—21no—
266#4318—21no—
267#4318—21no—
268#4318—21no—
269#4318—21no—
270#4318—21no—
271#4318—41no—
272#4318—41no—
273#4318—41no—
274#4318—41no—
275#4318—42no—
276#4318—42no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—42no—
286C2×C11⋊C8—42no—
287C2×C11⋊C8C2×D411yescharacteristic
288C2×C11⋊C8C2×D411yescharacteristic
289C2×C11⋊C8C2×D411yescharacteristic
290C2×C11⋊C8C2×D411yescharacteristic
291#3002D1111yescharacteristic
292#2930—111no—
293#2879—111no—
294#1975—111no—
295#1974—111no—
296#1938—111no—
297#1937—111no—
298#1929—111no—
299#1929—111no—
300#1876—111no—
301#1876—111no—
302#1871—111no—
303#1855—111no—
304#1789—111no—
305#1753—111no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—42no—
314C23×C11—81no—
315C23×C11—81no—
316C23×C11C4×D411yescharacteristic
317C23×C11C4×D411yescharacteristic
318C23×C11C2×#4111yescharacteristic
319Q8×C11—21no—
320Q8×C11—21no—
321Q8×C11—21no—
322Q8×C11—21no—
323Q8×C11—21no—
324Q8×C11—21no—
325Q8×C11—42no—
326D4×C11—21no—
327D4×C11—21no—
328D4×C11—21no—
329D4×C11—21no—
330D4×C11—21no—
331D4×C11—21no—
332D4×C11—42no—
333D4×C11—42no—
334D4×C11—42no—
335D4×C11—41no—
336D4×C11—41no—
337D4×C11—41no—
338D4×C11—41no—
339D4×C11—41no—
340D4×C11—41no—
341D4×C11—81no—
342D4×C11—81no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—42no—
359C2×C4×C11—42no—
360C2×C4×C11—42no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11C4×D411yescharacteristic
368C2×C4×C11C4×D411yescharacteristic
369C2×C4×C11C23×C411yescharacteristic
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11H(5,𝔽2)11yescharacteristic
372C2×C4×C11H(5,𝔽2)11yescharacteristic
373C2×C4×C11H(5,𝔽2)11yescharacteristic
374C2×C4×C11H(5,𝔽2)11yescharacteristic
375C2×Dic11—22no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C8×C11—21no—
382C8×C11—21no—
383C8×C11—21no—
384C8×C11—21no—
385C11⋊C8—21no—
386C11⋊C8—21no—
387C11⋊C8—21no—
388C11⋊C8—21no—
389C11⋊C8—41no—
390C11⋊C8—41no—
391C11⋊C8—41no—
392C11⋊C8—41no—
393C22×#41C2×D1111yescharacteristic
394C2×#135C2×D1111yescharacteristic
395C2×#135C2×D1111yescharacteristic
396C2×#131—111no—
397C22×M16—111no—
398C22×M16—111no—
399#525C2×D1111yescharacteristic
400#452Dic1111yescharacteristic, complemented
401#452Dic1111yescharacteristic, complemented
402#451Dic1111yescharacteristic, complemented
403#450Dic1111yescharacteristic, complemented
404#449Dic1111yescharacteristic, complemented
405#449Dic1111yescharacteristic, complemented
406#448Dic1111yescharacteristic, complemented
407#447Dic1111yescharacteristic, complemented
408#436—221no—
409#436—221no—
410#435—221no—
411#435—221no—
412C2×#108—111no—
413C2×#108—111no—
414#424—111no—
415C2×#104—111no—
416C2×#104—111no—
417C2×#104—111no—
418C2×#104—111no—
419C2×#104—111no—
420C2×#104—111no—
421#416C2×D1111yescharacteristic
422#416C2×D1111yescharacteristic
423#408—111no—
424#408—111no—
425#408—111no—
426#408—111no—
427#408—111no—
428#408—221no—
429#408—221no—
430#407—111no—
431#407—221no—
432#407—221no—
433C2×C22⋊C8C2×D1111yescharacteristic
434#405—111no—
435C2×#97—111no—
436C2×C4×C8—111no—
437C4×C22⋊C4—111no—
438#341—111no—
439#341—111no—
440#339—111no—
441#339—111no—
442#336—111no—
443#336—111no—
444C22×C11—21no—
445C22×C11—21no—
446C22×C11—21no—
447C22×C11—21no—
448C22×C11—21no—
449C22×C11—21no—
450C22×C11—21no—
451C22×C11—21no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—81no—
462C22×C11—81no—
463C22×C11—84no—
464C22×C11C2×C4×D411yescharacteristic
465C22×C11#53811yescharacteristic
466C22×C11#53811yescharacteristic
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—41no—
470C4×C11—41no—
471C4×C11—41no—
472C4×C11—41no—
473C4×C11—41no—
474C4×C11#51811yescharacteristic
475C4×C11#51811yescharacteristic
476C4×C11#53411yescharacteristic
477C4×C11#53511yescharacteristic
478Dic11—42no—
479Dic11—81no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—41no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41C2×Dic1111yescharacteristic
487C2×#41C2×Dic1111yescharacteristic
488C2×#41C22×D1111yescharacteristic
489C2×#41C22×D1111yescharacteristic
490C2×#41C22×D1111yescharacteristic
491C22×Q8C2×Dic1111yescharacteristic
492C22×D4—21no—
493C22×D4C2×Dic1111yescharacteristic
494C23×C4—21no—
495C23×C4C22×D1111yescharacteristic
496#135—41no—
497#135—41no—
498#135—41no—
499#135—41no—
500C2×Q16C2×Dic1111yescharacteristic
501C2×Q16C2×Dic1111yescharacteristic
502C2×SD16C2×Dic1111yescharacteristic
503C2×SD16C2×Dic1111yescharacteristic
504C2×SD16C2×Dic1111yescharacteristic
505C2×SD16C2×Dic1111yescharacteristic
506C2×D8C2×Dic1111yescharacteristic
507C2×D8C2×Dic1111yescharacteristic
508#131—441no—
509#131—441no—
510C2×M16—111no—
511C2×M16—111no—
512C2×M16—111no—
513C2×M16—111no—
514C2×M16—111no—
515C2×M16—111no—
516C2×M16—111no—
517C2×M16—111no—
518C2×M16—221no—
519C2×M16—221no—
520C2×M16—441no—
521C2×M16—441no—
522C2×M16—441no—
523C2×M16—441no—
524C22×C8—111no—
525C22×C8—111no—
526C22×C8—221no—
527C22×C8—221no—
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530#123—21no—
531C22⋊Q8C2×Dic1111yescharacteristic
532C22⋊Q8C2×Dic1111yescharacteristic
533#121C2×Dic1111yescharacteristic
534#121C2×Dic1111yescharacteristic
535#120—21no—
536C4×D4—21no—
537C4×D4—21no—
538#117C22×D1111yescharacteristic
539C2×C22⋊C4—221no—
540C2×C42—111no—
541C2×C42—111no—
542#108—441no—
543#108—441no—
544C4⋊C8—221no—
545C4⋊C8—221no—
546#104—441no—
547#104—441no—
548#104—441no—
549#104—441no—
550#104—441no—
551#104—441no—
552#103C2×Dic1111yescharacteristic
553#103C2×Dic1111yescharacteristic
554#103C2×Dic1111yescharacteristic
555#103C2×Dic1111yescharacteristic
556#102C2×Dic1111yescharacteristic
557#102C2×Dic1111yescharacteristic
558#102C2×Dic1111yescharacteristic
559#102C2×Dic1111yescharacteristic
560C22⋊C8—221no—
561C22⋊C8—221no—
562C22⋊C8—221no—
563C22⋊C8—221no—
564C22⋊C8—221no—
565C22⋊C8—221no—
566C22⋊C8—221no—
567C22⋊C8—221no—
568C22⋊C8—221no—
569C22⋊C8—221no—
570C22⋊C8—221no—
571C22⋊C8—221no—
572C22⋊C8C2×Dic1111yescharacteristic
573C22⋊C8C2×Dic1111yescharacteristic
574C22⋊C8C2×Dic1111yescharacteristic
575C22⋊C8C2×Dic1111yescharacteristic
576#97—221no—
577#97—441no—
578C4×C8—221no—
579C4×C8—441no—
580#95—221no—
581C2×C11—21no—
582C2×C11—21no—
583C2×C11—41no—
584C2×C11—41no—
585C2×C11—81no—
586C2×C11—81no—
587C2×C11—81no—
588C2×C11#232111yescharacteristic
589C2×C11#295611yescharacteristic
590C2×C11#295711yescharacteristic
591C24—21no—
592C24#434111yescharacteristic
593#41—21no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—41no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—42no—
610#41—42no—
611#41—42no—
612#41—42no—
613C2×Q8—21no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22×Dic1111yescharacteristic
617C2×Q8C22×Dic1111yescharacteristic
618C2×Q8C22×Dic1111yescharacteristic
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4C22×Dic1111yescharacteristic
632C2×D4C22×Dic1111yescharacteristic
633C2×D4C22×Dic1111yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4D4×D1111yescharacteristic
649C22×C4D4×D1111yescharacteristic
650C22×C4#434111yescharacteristic
651C22×C4C22×Dic1111yescharacteristic
652C22×C4C22×Dic1111yescharacteristic
653C22×C4C23×D1111yescharacteristic
654Q16—41no—
655Q16—41no—
656SD16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660D8—41no—
661D8—41no—
662M16—221no—
663M16—221no—
664M16—221no—
665M16—221no—
666M16—221no—
667M16—221no—
668M16—221no—
669M16—221no—
670M16—441no—
671M16—441no—
672M16—441no—
673M16—441no—
674M16—442no—
675M16—442no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—111no—
681C2×C8—111no—
682C2×C8—111no—
683C2×C8—111no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—442no—
693C2×C8—442no—
694C2×C8C22×Dic1111yescharacteristic
695C2×C8C22×Dic1111yescharacteristic
696C2×C8C22×Dic1111yescharacteristic
697C2×C8C22×Dic1111yescharacteristic
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4C22×Dic1111yescharacteristic
701C4⋊C4C22×Dic1111yescharacteristic
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—442no—
708C42—21no—
709C42—221no—
710C42—221no—
711C42—221no—
712C42—221no—
713C11#2206211yescharacteristic, complemented, Sylow
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23D4×Dic1111yescharacteristic
725C23D4×Dic1111yescharacteristic
726C23C2×#434111yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—222no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4D4×Dic1111yescharacteristic
782C2×C4D4×Dic1111yescharacteristic
783C2×C4C2×D4×D1111yescharacteristic
784C2×C4#6703711yescharacteristic
785C2×C4#6703711yescharacteristic
786C2×C4#6703711yescharacteristic
787C2×C4#6703711yescharacteristic
788C2×C4C23×Dic1111yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—221no—
794C8—221no—
795C8—221no—
796C8—221no—
797C8—441no—
798C8—441no—
799C8—441no—
800C8—441no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22#1062312411yescharacteristic
822C22#1062312411yescharacteristic
823C22C2×D4×Dic1111yescharacteristic
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—442no—
832C4—881no—
833C4#1062312011yescharacteristic
834C4#1062312311yescharacteristic
835C4#1062332911yescharacteristic
836C4#1062332911yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2#1307127711yescharacteristic
845C2#1307752611yescharacteristic
846C2#1307753311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3002C2
socleC22×C11C2×C4×D4
cosocleC22×C4×C11C24
hypercenter#3002D11
hypocenterC11#22062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. #13077320C2semidirect
2. #13077061C2semidirect
3. #13069510C2semidirect
4. #13069505C2semidirect
5. #13069329C2semidirect
6. #13069322C2semidirect
7. #13069266C2semidirect
8. #13069266C2semidirect
9. #13068945C2semidirect
10. #13068945C2semidirect
11. #13068919C2semidirect
12. #13068823C2semidirect
13. #13068560C2semidirect
14. #13068402C2semidirect
20. C2×#67001C22semidirect
23. C11×#452C4semidirect
24. C11×#452C4semidirect
25. C11×#451C4semidirect
26. C11×#450C4semidirect
27. C11×#449C4semidirect
28. C11×#449C4semidirect
29. C11×#448C4semidirect
30. C11×#447C4semidirect
38. C2×#66901C22semidirect
39. C2×#66901C22semidirect
46. #10622847C22semidirect
51. C2×#66883C22semidirect
52. C2×#66883C22semidirect
53. C2×#66879C22semidirect
54. C2×C8×Dic11C22semidirect
59. #10622612C22semidirect
60. #10622610C22semidirect
61. #10622190C22semidirect
62. #10622190C22semidirect
63. #10622188C22semidirect
64. #10622188C22semidirect
65. #10622170C22semidirect
66. #10622170C22semidirect
400. #452Dic11semidirect
401. #452Dic11semidirect
402. #451Dic11semidirect
403. #450Dic11semidirect
404. #449Dic11semidirect
405. #449Dic11semidirect
406. #448Dic11semidirect
407. #447Dic11semidirect
713. C11#22062semidirect

Maximal subgroups

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

subgroupindex
#130773202
#130770612
#130695102
#130695052
#130693292
#130693222
#130692662
#130689452
#130689192
#130688232
#130685602
#130684022
C11×#30022
#2206211