Finite Group Databasebeta

← #14913212

Subgroups — #14913212

Order 2816.

3142 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2#13071588C212yesmaximal, complemented
3#13071554C214yesmaximal, complemented
4#13071521C212yesmaximal, complemented
5#13071495C211yesmaximal, characteristic, complemented
6#13071491C211yesmaximal, characteristic, complemented
7#13071467C212yesmaximal, complemented
8#13071461C212yesmaximal, complemented
9D4×C22⋊Dic11C211yesmaximal, characteristic
10#13071078C212yesmaximal, complemented
11#13071056C214yesmaximal, complemented
12#13071011C211yesmaximal, characteristic, complemented
13#13070994C212yesmaximal, complemented
14C4×D4×Dic11C212yesmaximal, complemented
15C4×#66930C211yesmaximal, characteristic, complemented
16C2×C22⋊C4×Dic11C212yesmaximal, complemented
17D4×C11×C22⋊C4C211yesmaximal, characteristic
18C23×D4×C11C2211yescharacteristic
19C24×Dic11C2212yes—
20C2×C4×D4×C11C2212yes—
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C2×D4×Dic11C4116yescomplemented
25C2×D4×Dic11C2212yes—
26C2×D4×Dic11C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C2×D4×Dic11C2212yes—
29C2×D4×Dic11C2212yes—
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2214yescomplemented
35C2×#66930C2211yescharacteristic
36C2×#66930C2211yescharacteristic
37C2×#66930C2214yescomplemented
38C11×#390C2212yes—
39C11×#386C2214yes—
40C11×#380C2211yescharacteristic
41C11×#379C2212yes—
42C4×C11×C22⋊C4C2211yescharacteristic
43#10622860C2212yes—
44#10622834C2212yes—
45#10622833C2214yes—
46#10622825C2211yescharacteristic
47#10622823C2214yescomplemented
48C4×C22⋊Dic11C2211yescharacteristic
49C4×C22⋊Dic11C2214yescomplemented
50C2×C11⋊#95C2214yescomplemented
51#10622590C2212yescomplemented
52C4⋊C4×Dic11C2212yescomplemented
53C4⋊C4×Dic11C2212yescomplemented
54#10622586C2212yescomplemented
55#10622559C2214yescomplemented
56#10622558C2214yescomplemented
57#10622558C2214yescomplemented
58#10622557C2214yescomplemented
59#10622557C2214yescomplemented
60#10622556C2212yes—
61#10622556C2214yescomplemented
62#10622555C2212yes—
63#10622555C2212yes—
64#10622555C2214yescomplemented
65C22⋊C4×Dic11C2211yescharacteristic
66C22⋊C4×Dic11C2212yes—
67C22⋊C4×Dic11C2212yes—
68C22⋊C4×Dic11C2212yes—
69C22⋊C4×Dic11C2211yescharacteristic
70C22⋊C4×Dic11C2214yescomplemented
71C22⋊C4×Dic11C2214yescomplemented
72C22⋊C4×Dic11C2214yescomplemented
73C22⋊C4×Dic11C2214yescomplemented
74C4×C4⋊Dic11C2212yescomplemented
75C4×Dic11⋊C4C2212yescomplemented
76C42×Dic11C2212yescomplemented
77#10622541C2212yescomplemented
78#10622267C2214yescomplemented
79#10622266C2214yescomplemented
80#10622264C2212yescomplemented
81#10622262C2212yescomplemented
82#10622261C2212yescomplemented
83#10622261C2212yescomplemented
84C25×C11C2312yes—
85C22×D4×C11—28no—
86C22×D4×C11C2×C418yes—
87C22×D4×C11C2312yes—
88C22×D4×C11C2311yescharacteristic
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11C2314yes—
91C23×C4×C11C2311yescharacteristic
92C23×Dic11—48no—
93C23×Dic11C2×C4116yescomplemented
94C23×Dic11C2314yes—
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2312yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2312yes—
99C23×Dic11C2312yes—
100C23×Dic11C2312yes—
101C23×Dic11C2312yes—
102C4×D4×C11—28no—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C22⋊C4—28no—
105C2×C11×C22⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4C2312yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2311yescharacteristic
111C2×C42×C11C2312yes—
112C2×C22⋊Dic11—28no—
113C2×C22⋊Dic11C2×C4116yescomplemented
114C2×C22⋊Dic11C2311yescharacteristic
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2311yescharacteristic
124D4×Dic11—28no—
125D4×Dic11C2×C418yes—
126D4×Dic11C2×C418yes—
127D4×Dic11C2×C418yescomplemented
128D4×Dic11C2×C418yescomplemented
129D4×Dic11C2×C4116yescomplemented
130D4×Dic11C2×C4116yescomplemented
131C2×C4⋊Dic11C2×C418yescomplemented
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×C4×Dic11—48no—
141C2×C4×Dic11C2×C418yescomplemented
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2312yes—
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2312yes—
147C2×C4×Dic11C2312yes—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2314yes—
150C2×C4×Dic11C2311yescharacteristic
151C2×C4×Dic11C2311yescharacteristic
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154#66930—24no—
155#66930—24no—
156#66930—48no—
157C11×#95C2312yes—
158C11×#95C2312yes—
159C11⋊#95C2312yes—
160C11⋊#95C2312yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170#34126—111nomaximal, Sylow
171C24×C11—24no—
172C24×C11—24no—
173C24×C11—28no—
174C24×C11—44no—
175C24×C11C22×C418yes—
176C24×C11C2412yes—
177C24×C11C2411yescharacteristic
178C24×C11C2412yes—
179C2×D4×C11—28no—
180C2×D4×C11—232no—
181C2×D4×C11—24no—
182C2×D4×C11C22×C418yes—
183C2×D4×C11C22×C414yes—
184C2×D4×C11C22×C414yes—
185C2×D4×C11#4118yes—
186C22×C4×C11—24no—
187C22×C4×C11—28no—
188C22×C4×C11—28no—
189C22×C4×C11—44no—
190C22×C4×C11C22×C414yes—
191C22×C4×C11C2414yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2411yescharacteristic
194C22×C4×C11C2412yes—
195C22×C4×C11C2411yescharacteristic
196C22×Dic11—28no—
197C22×Dic11—28no—
198C22×Dic11—24no—
199C22×Dic11—28no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—28no—
203C22×Dic11—44no—
204C22×Dic11—44no—
205C22×Dic11—44no—
206C22×Dic11—44no—
207C22×Dic11—432no—
208C22×Dic11C22×C414yes—
209C22×Dic11C22×C414yes—
210C22×Dic11C22×C418yes—
211C22×Dic11C22×C418yes—
212C22×Dic11C22×C418yes—
213C22×Dic11C22×C418yes—
214C22×Dic11C22×C418yes—
215C22×Dic11C2414yes—
216C22×Dic11C2412yes—
217C22×Dic11C2411yescharacteristic
218C22×Dic11C2411yescharacteristic
219C22×Dic11C2412yes—
220C22×Dic11C2411yescharacteristic
221C22×Dic11C2412yes—
222C22×Dic11C2412yes—
223C22×Dic11C2411yescharacteristic
224C11×C4⋊C4—24no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—28no—
228C11×C22⋊C4—28no—
229C11×C22⋊C4—44no—
230C11×C22⋊C4#4114yes—
231C42×C11—24no—
232C22⋊Dic11—28no—
233C22⋊Dic11—22no—
234C22⋊Dic11—28no—
235C22⋊Dic11—24no—
236C22⋊Dic11—44no—
237C22⋊Dic11C22×C418yes—
238C22⋊Dic11C22×C418yes—
239C22⋊Dic11C22×C418yes—
240C22⋊Dic11C22×C418yes—
241C22⋊Dic11#4114yes—
242C4⋊Dic11—24no—
243C4⋊Dic11C22×C414yes—
244C4⋊Dic11C22×C414yes—
245C4⋊Dic11C22×C418yes—
246Dic11⋊C4—24no—
247Dic11⋊C4—24no—
248Dic11⋊C4—44no—
249Dic11⋊C4—44no—
250C4×Dic11—24no—
251C4×Dic11—24no—
252C4×Dic11—28no—
253C4×Dic11—24no—
254C4×Dic11—24no—
255C4×Dic11—24no—
256C4×Dic11—44no—
257C4×Dic11—44no—
258C4×Dic11C22×C414yes—
259C4×Dic11C22×C414yes—
260C4×Dic11C22×C414yes—
261C4×Dic11C22×C414yes—
262C22×C4×D4—111no—
263#2357—112no—
264#2353—114no—
265#2349—112no—
266#2345—111no—
267#2345—111no—
268#2342—112no—
269#2342—112no—
270D4×C22⋊C4—111no—
271D4×C22⋊C4D1111yescharacteristic
272#2293—112no—
273#2290—114no—
274#2283—111no—
275#2280—112no—
276C42×D4—112no—
277C4×#117—111no—
278C2×C4×C22⋊C4—112no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—24no—
283C23×C11—22no—
284C23×C11—216no—
285C23×C11—216no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—24no—
289C23×C11—24no—
290C23×C11—48no—
291C23×C11—416no—
292C23×C11—416no—
293C23×C11C23×C414yes—
294C23×C11C23×C414yes—
295C23×C11C23×C412yes—
296C23×C11C2×#4118yes—
297C23×C11C2×#4112yes—
298C23×C11C2×#4112yes—
299C23×C11C2511yescharacteristic
300D4×C11—216no—
301D4×C11—28no—
302D4×C11#117116yescomplemented
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—28no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—24no—
311C2×C4×C11—24no—
312C2×C4×C11—22no—
313C2×C4×C11—416no—
314C2×C4×C11C23×C412yes—
315C2×C4×C11C23×C412yes—
316C2×C4×C11C2×#4114yes—
317C2×C4×C11C2×#4114yes—
318C2×Dic11—28no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—22no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—22no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—28no—
329C2×Dic11—216no—
330C2×Dic11—216no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—22no—
337C2×Dic11—48no—
338C2×Dic11—48no—
339C2×Dic11—48no—
340C2×Dic11—416no—
341C2×Dic11C23×C412yes—
342C2×Dic11C23×C412yes—
343C2×Dic11C23×C412yes—
344C2×Dic11C23×C414yes—
345C2×Dic11C23×C414yes—
346C2×Dic11C23×C412yes—
347C2×Dic11C2×#4114yes—
348C2×Dic11H(5,𝔽2)14yes—
349C23×D4C2×D1111yescharacteristic
350C24×C4—112no—
351C2×C4×D4—111no—
352C2×C4×D4—112no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C2×C4×D4—112no—
356C2×C4×D4—111no—
357C2×C4×D4—1116no—
358C2×C4×D4—112no—
359C2×C4×D4C2×D1112yes—
360C2×#117—111no—
361C2×#117—111no—
362C2×#117—114no—
363C22×C4⋊C4—111no—
364C22×C22⋊C4—112no—
365C22×C22⋊C4—112no—
366C22×C22⋊C4C2×D1112yes—
367C22×C42—111no—
368C22×C42—114no—
369#390—112no—
370#390C2×D1112yes—
371#389—112no—
372#389—112no—
373#388—114no—
374#388—114no—
375#388—114no—
376#388—114no—
377#387—114no—
378#387—114no—
379#386—114no—
380#386C2×D1114yes—
381#385—114no—
382#385—114no—
383#383—112no—
384#382—112no—
385#381—112no—
386#381—114no—
387#380—111no—
388#380—112no—
389#380—112no—
390#380—114no—
391#380C2×D1111yescharacteristic
392#379—112no—
393#379C2×D1112yes—
394C4×C4⋊C4—112no—
395C4×C4⋊C4—112no—
396C4×C4⋊C4—112no—
397C4×C4⋊C4—112no—
398C4×C4⋊C4—112no—
399C4×C22⋊C4—111no—
400C4×C22⋊C4—114no—
401C4×C22⋊C4—112no—
402C4×C22⋊C4—112no—
403C4×C22⋊C4—114no—
404C4×C22⋊C4—114no—
405C4×C22⋊C4—111no—
406C4×C22⋊C4—112no—
407C4×C22⋊C4—111no—
408C4×C22⋊C4—114no—
409C4×C22⋊C4—114no—
410C4×C22⋊C4C2×D1111yescharacteristic
411#376—112no—
412#376—112no—
413C2×#95—114no—
414C43—112no—
415C22×C11—22no—
416C22×C11—24no—
417C22×C11—22no—
418C22×C11—24no—
419C22×C11—28no—
420C22×C11—24no—
421C22×C11—24no—
422C22×C11—28no—
423C22×C11—24no—
424C22×C11—24no—
425C22×C11—24no—
426C22×C11—432no—
427C22×C11—44no—
428C22×C11—44no—
429C22×C11C2×#11718yes—
430C22×C11C4×#4114yes—
431C22×C11C24×C411yescharacteristic
432C22×C11C22×#4112yes—
433C22×C11C22×#4111yescharacteristic
434C22×C11C22×#4111yescharacteristic
435C22×C11C2×H(5,𝔽2)12yes—
436C4×C11—22no—
437C4×C11—24no—
438C4×C11—42no—
439C4×C11—44no—
440C4×C11C2×#11714yes—
441Dic11—22no—
442Dic11—22no—
443Dic11—22no—
444Dic11—24no—
445Dic11—24no—
446Dic11—24no—
447Dic11—42no—
448Dic11—44no—
449Dic11#51814yes—
450C25C22×D1112yes—
451C22×D4—28no—
452C22×D4C4×D1118yes—
453C22×D4C22×D1112yes—
454C22×D4C22×D1111yescharacteristic
455C22×D4C22×D1111yescharacteristic
456C23×C4—111no—
457C23×C4—112no—
458C23×C4—112no—
459C23×C4—111no—
460C23×C4—1116no—
461C23×C4—112no—
462C23×C4—112no—
463C23×C4—112no—
464C23×C4—114no—
465C23×C4—448no—
466C23×C4C22×D1114yes—
467C23×C4C22×D1111yescharacteristic
468C4×D4—28no—
469C4×D4—118no—
470C4×D4—118no—
471C4×D4—1116no—
472C4×D4—118no—
473C4×D4—1116no—
474C4×D4—118no—
475C4×D4—228no—
476#117—224no—
477#117—224no—
478#117—448no—
479C2×C4⋊C4—118no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—112no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—112no—
484C2×C4⋊C4—112no—
485C2×C4⋊C4—112no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4C22×D1112yes—
489C2×C22⋊C4—28no—
490C2×C22⋊C4—1116no—
491C2×C22⋊C4—111no—
492C2×C22⋊C4—112no—
493C2×C22⋊C4—112no—
494C2×C22⋊C4—112no—
495C2×C22⋊C4—112no—
496C2×C22⋊C4—112no—
497C2×C22⋊C4—114no—
498C2×C22⋊C4—111no—
499C2×C22⋊C4—114no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—228no—
502C2×C22⋊C4C22×D1112yes—
503C2×C22⋊C4C22×D1114yes—
504C2×C22⋊C4C22×D1111yescharacteristic
505C2×C22⋊C4C22×D1114yes—
506C2×C22⋊C4C22×D1114yes—
507C2×C22⋊C4C22×D1111yescharacteristic
508C2×C42—118no—
509C2×C42—111no—
510C2×C42—111no—
511C2×C42—111no—
512C2×C42—111no—
513C2×C42—112no—
514C2×C42—112no—
515C2×C42—112no—
516C2×C42—114no—
517C2×C42—112no—
518C2×C42—112no—
519C2×C42—114no—
520C2×C42—114no—
521C2×C42—448no—
522C2×C42C22×D1112yes—
523#95—112no—
524#95—114no—
525#95—114no—
526#95—114no—
527#95—112no—
528#95—112no—
529#95—112no—
530#95—114no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95C22×D1112yes—
535#95C22×D1112yes—
536C2×C11—24no—
537C2×C11—28no—
538C2×C11—44no—
539C2×C11C22×#11711yescharacteristic
540C2×C11C2×C4×#4111yescharacteristic
541C2×C11C2×#51811yescharacteristic
542C2×C11#348112yes—
543C2×C11#348112yes—
544C24—24no—
545C24—28no—
546C24—24no—
547C24—44no—
548C24C2×C4×D1118yes—
549C24C23×D1112yes—
550C24C23×D1112yes—
551C24C23×D1111yescharacteristic
552C2×D4—28no—
553C2×D4—232no—
554C2×D4—24no—
555C2×D4C2×C4×D1118yes—
556C2×D4C2×C4×D1114yes—
557C2×D4C2×C4×D1114yes—
558C2×D4#434118yes—
559C22×C4—24no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—44no—
563C22×C4—111no—
564C22×C4—114no—
565C22×C4—114no—
566C22×C4—118no—
567C22×C4—118no—
568C22×C4—111no—
569C22×C4—111no—
570C22×C4—112no—
571C22×C4—112no—
572C22×C4—111no—
573C22×C4—112no—
574C22×C4—118no—
575C22×C4—118no—
576C22×C4—118no—
577C22×C4—114no—
578C22×C4—112no—
579C22×C4—228no—
580C22×C4—228no—
581C22×C4—224no—
582C22×C4—228no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—228no—
586C22×C4—4432no—
587C22×C4—444no—
588C22×C4—444no—
589C22×C4—444no—
590C22×C4—444no—
591C22×C4C2×C4×D1114yes—
592C22×C4C23×D1114yes—
593C22×C4C23×D1112yes—
594C22×C4C23×D1111yescharacteristic
595C22×C4C23×D1112yes—
596C22×C4C23×D1111yescharacteristic
597C4⋊C4—24no—
598C4⋊C4—118no—
599C4⋊C4—114no—
600C4⋊C4—114no—
601C4⋊C4—224no—
602C4⋊C4—224no—
603C4⋊C4—224no—
604C4⋊C4—444no—
605C4⋊C4—444no—
606C22⋊C4—24no—
607C22⋊C4—28no—
608C22⋊C4—22no—
609C22⋊C4—28no—
610C22⋊C4—44no—
611C22⋊C4—118no—
612C22⋊C4—118no—
613C22⋊C4—118no—
614C22⋊C4—118no—
615C22⋊C4—114no—
616C22⋊C4—228no—
617C22⋊C4—222no—
618C22⋊C4—228no—
619C22⋊C4—224no—
620C22⋊C4—444no—
621C22⋊C4#434114yes—
622C42—24no—
623C42—114no—
624C42—114no—
625C42—114no—
626C42—114no—
627C42—224no—
628C42—228no—
629C42—224no—
630C42—224no—
631C42—224no—
632C42—224no—
633C42—444no—
634C42—444no—
635C11#3412611yescharacteristic, complemented, Sylow
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—22no—
641C23—216no—
642C23—216no—
643C23—22no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—48no—
648C23—416no—
649C23—416no—
650C23C22×C4×D1114yes—
651C23C22×C4×D1114yes—
652C23C22×C4×D1112yes—
653C23C2×#434118yes—
654C23C2×#434112yes—
655C23#41×D1112yes—
656C23C24×D1111yescharacteristic
657D4—216no—
658D4—28no—
659D4#66930116yescomplemented
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—28no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—416no—
671C2×C4—112no—
672C2×C4—114no—
673C2×C4—112no—
674C2×C4—112no—
675C2×C4—112no—
676C2×C4—114no—
677C2×C4—114no—
678C2×C4—114no—
679C2×C4—228no—
680C2×C4—2216no—
681C2×C4—2216no—
682C2×C4—228no—
683C2×C4—221no—
684C2×C4—222no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—222no—
689C2×C4—224no—
690C2×C4—224no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—224no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—222no—
698C2×C4—448no—
699C2×C4—448no—
700C2×C4—448no—
701C2×C4—4416no—
702C2×C4C22×C4×D1112yes—
703C2×C4C22×C4×D1112yes—
704C2×C4C2×#434114yes—
705C2×C4C2×#434114yes—
706C22—28no—
707C22—24no—
708C22—28no—
709C22—24no—
710C22—22no—
711C22—24no—
712C22—22no—
713C22—24no—
714C22—24no—
715C22—24no—
716C22—24no—
717C22—432no—
718C22—44no—
719C22—44no—
720C22C2×#6693018yes—
721C22C4×#434114yes—
722C22C23×C4×D1111yescharacteristic
723C22C22×#434111yescharacteristic
724C22C22×#434112yes—
725C22C2×#41×D1111yescharacteristic
726C22D11×H(5,𝔽2)12yes—
727C4—24no—
728C4—22no—
729C4—44no—
730C4—42no—
731C4—114no—
732C4—224no—
733C4—222no—
734C4—222no—
735C4—222no—
736C4—224no—
737C4—224no—
738C4—442no—
739C4—444no—
740C4C2×#6693014yes—
741C2—24no—
742C2—28no—
743C2—44no—
744C2C22×#6693011yescharacteristic
745C2C2×C4×#434111yescharacteristic
746C2D11×#51811yescharacteristic
747C2#1308221712yes—
748C2#1308222112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC23×D4×C11C22
hypercenterD4×C22⋊C4D11
hypocenterC11#34126
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071588C2semidirect
3. #13071554C2semidirect
4. #13071521C2semidirect
5. #13071495C2semidirect
6. #13071491C2semidirect
7. #13071467C2semidirect
8. #13071461C2semidirect
10. #13071078C2semidirect
11. #13071056C2semidirect
12. #13071011C2semidirect
13. #13070994C2semidirect
14. C4×D4×Dic11C2semidirect
15. C4×#66930C2semidirect
16. C2×C22⋊C4×Dic11C2semidirect
24. C2×D4×Dic11C4semidirect
34. C22×C4×Dic11C22semidirect
37. C2×#66930C22semidirect
47. #10622823C22semidirect
49. C4×C22⋊Dic11C22semidirect
50. C2×C11⋊#95C22semidirect
51. #10622590C22semidirect
52. C4⋊C4×Dic11C22semidirect
53. C4⋊C4×Dic11C22semidirect
54. #10622586C22semidirect
55. #10622559C22semidirect
56. #10622558C22semidirect
57. #10622558C22semidirect
58. #10622557C22semidirect
59. #10622557C22semidirect
61. #10622556C22semidirect
64. #10622555C22semidirect
70. C22⋊C4×Dic11C22semidirect
71. C22⋊C4×Dic11C22semidirect
72. C22⋊C4×Dic11C22semidirect
73. C22⋊C4×Dic11C22semidirect
74. C4×C4⋊Dic11C22semidirect
75. C4×Dic11⋊C4C22semidirect
76. C42×Dic11C22semidirect
77. #10622541C22semidirect
78. #10622267C22semidirect
79. #10622266C22semidirect
80. #10622264C22semidirect
81. #10622262C22semidirect
82. #10622261C22semidirect
83. #10622261C22semidirect
93. C23×Dic11C2×C4semidirect
113. C2×C22⋊Dic11C2×C4semidirect
127. D4×Dic11C2×C4semidirect
128. D4×Dic11C2×C4semidirect
129. D4×Dic11C2×C4semidirect
130. D4×Dic11C2×C4semidirect
131. C2×C4⋊Dic11C2×C4semidirect
141. C2×C4×Dic11C2×C4semidirect
302. D4×C11#117semidirect
635. C11#34126semidirect
659. D4#66930semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
#130715882
#130715542
#130715212
#130714952
#130714912
#130714672
#130714612
D4×C22⋊Dic112
#130710782
#130710562
#130710112
#130709942
C4×D4×Dic112
C4×#669302
C2×C22⋊C4×Dic112
D4×C11×C22⋊C42
#3412611