Finite Group Databasebeta

← C113×#13876 #43281896

Subgroups — C113×#13876 #43281896

Order 28928.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C113C212yesmaximal
2C2×#384×C113C211yesmaximal, characteristic, complemented
3C2×#380×C113C211yesmaximal, characteristic
4C2×#380×C113C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C113C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C113C211yesmaximal, characteristic
7C113×#1442C212yesmaximal, complemented
8C113×#1439C212yesmaximal
9C113×#1436C212yesmaximal, complemented
10C113×C4⋊#95C211yesmaximal, characteristic, complemented
11C113×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C113C2211yescharacteristic
13C22×C4⋊C4×C113C2211yescharacteristic
14C22×C4⋊C4×C113C2211yescharacteristic
15C22×C4⋊C4×C113C2212yes—
16C22×C4⋊C4×C113C2212yes—
17C22×C4⋊C4×C113C2211yescharacteristic
18C22×C4⋊C4×C113C2211yescharacteristic
19C22×C22⋊C4×C113C2212yes—
20C22×C22⋊C4×C113C2212yes—
21C22×C22⋊C4×C113C2211yescharacteristic
22C22×C22⋊C4×C113C2211yescharacteristic
23C22×C42×C113C2212yes—
24C22×C42×C113C2211yescharacteristic
25C22×C42×C113C2211yescharacteristic
26#388×C113—28no—
27#384×C113—24no—
28#380×C113—24no—
29#380×C113—24no—
30C4×C4⋊C4×C113—24no—
31C4×C22⋊C4×C113C418yescomplemented
32C2×#95×C113C2212yes—
33C2×#95×C113C2212yes—
34C2×#95×C113C2212yes—
35C2×#95×C113C2212yes—
36C2×#95×C113C2212yes—
37C2×#95×C113C2212yes—
38C2×#95×C113C2212yes—
39C2×#95×C113C2211yescharacteristic
40C2×#95×C113C2211yescharacteristic
41C25×C113C2311yescharacteristic
42C23×C4×C113—22no—
43C23×C4×C113—22no—
44C23×C4×C113—22no—
45C23×C4×C113—22no—
46C23×C4×C113—22no—
47C23×C4×C113—22no—
48C23×C4×C113C2×C414yes—
49C23×C4×C113C2312yes—
50C23×C4×C113C2312yes—
51C23×C4×C113C2311yescharacteristic
52C23×C4×C113C2311yescharacteristic
53C23×C4×C113C2312yes—
54C23×C4×C113C2312yes—
55C23×C4×C113C2311yescharacteristic
56C23×C4×C113C2311yescharacteristic
57C23×C4×C113C2311yescharacteristic
58C23×C4×C113C2311yescharacteristic
59C2×C4⋊C4×C113—22no—
60C2×C4⋊C4×C113—22no—
61C2×C4⋊C4×C113—22no—
62C2×C4⋊C4×C113—22no—
63C2×C4⋊C4×C113—22no—
64C2×C4⋊C4×C113—22no—
65C2×C4⋊C4×C113—24no—
66C2×C4⋊C4×C113—24no—
67C2×C4⋊C4×C113—22no—
68C2×C4⋊C4×C113—24no—
69C2×C4⋊C4×C113—24no—
70C2×C4⋊C4×C113—22no—
71C2×C4⋊C4×C113—22no—
72C2×C4⋊C4×C113—22no—
73C2×C4⋊C4×C113—42no—
74C2×C4⋊C4×C113—42no—
75C2×C4⋊C4×C113D414yes—
76C2×C4⋊C4×C113D414yes—
77C2×C22⋊C4×C113—22no—
78C2×C22⋊C4×C113—22no—
79C2×C22⋊C4×C113—24no—
80C2×C22⋊C4×C113—24no—
81C2×C22⋊C4×C113—24no—
82C2×C22⋊C4×C113—24no—
83C2×C22⋊C4×C113—42no—
84C2×C22⋊C4×C113—42no—
85C2×C22⋊C4×C113C2×C414yes—
86C2×C22⋊C4×C113C2×C414yes—
87C2×C22⋊C4×C113D414yes—
88C2×C22⋊C4×C113Q814yes—
89C2×C42×C113—22no—
90C2×C42×C113—22no—
91C2×C42×C113—22no—
92C2×C42×C113—22no—
93C2×C42×C113—24no—
94C2×C42×C113—24no—
95C2×C42×C113—42no—
96C2×C42×C113C2×C414yes—
97C2×C42×C113C2×C414yes—
98#95×C113—24no—
99#95×C113—24no—
100#95×C113—24no—
101#95×C113—24no—
102#95×C113—24no—
103#95×C113—24no—
104#95×C113—42no—
105#95×C113C2×C414yes—
106#95×C113C2×C414yes—
107C24×C113—21no—
108C24×C113—21no—
109C24×C113—21no—
110C24×C113—21no—
111C24×C113—21no—
112C24×C113—21no—
113C24×C113—21no—
114C24×C113—21no—
115C24×C113—21no—
116C24×C113—21no—
117C24×C113—21no—
118C24×C113—21no—
119C24×C113C22×C412yes—
120C24×C113C2×D412yes—
121C24×C113C2×Q812yes—
122C24×C113C2411yescharacteristic
123C22×C4×C113—21no—
124C22×C4×C113—21no—
125C22×C4×C113—21no—
126C22×C4×C113—21no—
127C22×C4×C113—21no—
128C22×C4×C113—21no—
129C22×C4×C113—21no—
130C22×C4×C113—21no—
131C22×C4×C113—21no—
132C22×C4×C113—21no—
133C22×C4×C113—21no—
134C22×C4×C113—21no—
135C22×C4×C113—21no—
136C22×C4×C113—21no—
137C22×C4×C113—21no—
138C22×C4×C113—22no—
139C22×C4×C113—22no—
140C22×C4×C113—22no—
141C22×C4×C113—22no—
142C22×C4×C113—21no—
143C22×C4×C113—21no—
144C22×C4×C113—21no—
145C22×C4×C113—22no—
146C22×C4×C113—22no—
147C22×C4×C113—22no—
148C22×C4×C113—22no—
149C22×C4×C113—21no—
150C22×C4×C113—21no—
151C22×C4×C113—21no—
152C22×C4×C113—21no—
153C22×C4×C113—21no—
154C22×C4×C113—22no—
155C22×C4×C113—22no—
156C22×C4×C113—22no—
157C22×C4×C113—21no—
158C22×C4×C113—22no—
159C22×C4×C113—28no—
160C22×C4×C113—28no—
161C22×C4×C113—28no—
162C22×C4×C113—22no—
163C22×C4×C113—22no—
164C22×C4×C113—22no—
165C22×C4×C113—22no—
166C22×C4×C113—22no—
167C22×C4×C113—22no—
168C22×C4×C113—22no—
169C22×C4×C113—22no—
170C22×C4×C113—22no—
171C22×C4×C113—22no—
172C22×C4×C113—22no—
173C22×C4×C113—22no—
174C22×C4×C113—22no—
175C22×C4×C113—22no—
176C22×C4×C113—44no—
177C22×C4×C113—44no—
178C22×C4×C113—44no—
179C22×C4×C113—44no—
180C22×C4×C113C22×C412yes—
181C22×C4×C113C22×C412yes—
182C22×C4×C113C22×C412yes—
183C22×C4×C113C22×C412yes—
184C22×C4×C113C22×C412yes—
185C22×C4×C113C22×C412yes—
186C22×C4×C113C2×D414yes—
187C22×C4×C113C2×D414yes—
188C22×C4×C113C2×D412yes—
189C22×C4×C113C2×D412yes—
190C22×C4×C113C2×D412yes—
191C22×C4×C113C2×D412yes—
192C22×C4×C113C2×Q812yes—
193C22×C4×C113C2×Q812yes—
194C22×C4×C113#4112yes—
195C22×C4×C113#4112yes—
196C22×C4×C113#4112yes—
197C22×C4×C113#4112yes—
198C22×C4×C113#4112yes—
199C22×C4×C113#4112yes—
200C4⋊C4×C113—28no—
201C4⋊C4×C113—28no—
202C4⋊C4×C113—48no—
203C4⋊C4×C113—48no—
204C4⋊C4×C113—44no—
205C4⋊C4×C113—44no—
206C22⋊C4×C113—28no—
207C22⋊C4×C113—48no—
208C22⋊C4×C113—48no—
209C22⋊C4×C113C4⋊C4116yescomplemented
210C42×C113—28no—
211C42×C113—28no—
212C42×C113—48no—
213C23×C113—22no—
214C23×C113—22no—
215C23×C113—22no—
216C23×C113—22no—
217C23×C113—22no—
218C23×C113—22no—
219C23×C113—22no—
220C23×C113—22no—
221C23×C113—22no—
222C23×C113—22no—
223C23×C113—22no—
224C23×C113—22no—
225C23×C113—22no—
226C23×C113—22no—
227C23×C113—22no—
228C23×C113—22no—
229C23×C113—22no—
230C23×C113—22no—
231C23×C113—41no—
232C23×C113—41no—
233C23×C113—41no—
234C23×C113—41no—
235C23×C113—41no—
236C23×C113—41no—
237C23×C113—41no—
238C23×C113—41no—
239C23×C113—41no—
240C23×C113—41no—
241C23×C113—41no—
242C23×C113—41no—
243C23×C113—41no—
244C23×C113—41no—
245C23×C113—41no—
246C23×C113—41no—
247C23×C113C2×C4⋊C414yes—
248C23×C113C23×C411yescharacteristic
249C23×C113C22×D411yescharacteristic
250C23×C113C22×D411yescharacteristic
251C23×C113C22×D411yescharacteristic
252C23×C113C22×Q811yescharacteristic
253C23×C113C2×#4111yescharacteristic
254C23×C113C2×#4111yescharacteristic
255C23×C113C2×#4111yescharacteristic
256C23×C113C2×#4111yescharacteristic
257C23×C113C2×#4111yescharacteristic
258C23×C113C2×#4111yescharacteristic
259C23×C113H(5,𝔽2)11yescharacteristic
260C23×C113H(5,𝔽2)11yescharacteristic
261C23×C1132−1+411yescharacteristic
262C23×C1132−1+411yescharacteristic
263C2×C4×C113—22no—
264C2×C4×C113—22no—
265C2×C4×C113—22no—
266C2×C4×C113—22no—
267C2×C4×C113—22no—
268C2×C4×C113—22no—
269C2×C4×C113—22no—
270C2×C4×C113—22no—
271C2×C4×C113—22no—
272C2×C4×C113—22no—
273C2×C4×C113—22no—
274C2×C4×C113—22no—
275C2×C4×C113—22no—
276C2×C4×C113—22no—
277C2×C4×C113—22no—
278C2×C4×C113—22no—
279C2×C4×C113—22no—
280C2×C4×C113—22no—
281C2×C4×C113—22no—
282C2×C4×C113—22no—
283C2×C4×C113—22no—
284C2×C4×C113—22no—
285C2×C4×C113—22no—
286C2×C4×C113—22no—
287C2×C4×C113—24no—
288C2×C4×C113—24no—
289C2×C4×C113—24no—
290C2×C4×C113—24no—
291C2×C4×C113—24no—
292C2×C4×C113—24no—
293C2×C4×C113—41no—
294C2×C4×C113—41no—
295C2×C4×C113—41no—
296C2×C4×C113—41no—
297C2×C4×C113—42no—
298C2×C4×C113—42no—
299C2×C4×C113—42no—
300C2×C4×C113—42no—
301C2×C4×C113—42no—
302C2×C4×C113—41no—
303C2×C4×C113—42no—
304C2×C4×C113—41no—
305C2×C4×C113—42no—
306C2×C4×C113—42no—
307C2×C4×C113—41no—
308C2×C4×C113—41no—
309C2×C4×C113—416no—
310C2×C4×C113—42no—
311C2×C4×C113—42no—
312C2×C4×C113—42no—
313C2×C4×C113—42no—
314C2×C4×C113—42no—
315C2×C4×C113—42no—
316C2×C4×C113—42no—
317C2×C4×C113—42no—
318C2×C4×C113—42no—
319C2×C4×C113—42no—
320C2×C4×C113—42no—
321C2×C4×C113—42no—
322C2×C4×C113—42no—
323C2×C4×C113—42no—
324C2×C4×C113C2×C4⋊C414yes—
325C2×C4×C113C2×C4⋊C414yes—
326C2×C4×C113#11714yes—
327C2×C4×C113#11714yes—
328C2×C4×C113C4×D414yes—
329C2×C4×C113C4×D414yes—
330C2×C4×C113#12114yes—
331C2×C4×C113#12314yes—
332C2×C4×C113#12414yes—
333C2×C4×C113#12614yes—
334C22×C113—24no—
335C22×C113—24no—
336C22×C113—24no—
337C22×C113—42no—
338C22×C113—42no—
339C22×C113—42no—
340C22×C113—42no—
341C22×C113—42no—
342C22×C113—42no—
343C22×C113—42no—
344C22×C113—42no—
345C22×C113—42no—
346C22×C113—42no—
347C22×C113—42no—
348C22×C113—42no—
349C22×C113C22×C4⋊C411yescharacteristic
350C22×C113C2×#11711yescharacteristic
351C22×C113C2×#11711yescharacteristic
352C22×C113C2×C4×D411yescharacteristic
353C22×C113C2×C4×D411yescharacteristic
354C22×C113#52011yescharacteristic
355C22×C113#52011yescharacteristic
356C22×C113C2×#12111yescharacteristic
357C22×C113C2×#12311yescharacteristic
358C22×C113C2×#12411yescharacteristic
359C22×C113C2×#12611yescharacteristic
360C22×C113#53211yescharacteristic
361C22×C113#53211yescharacteristic
362C22×C113#53311yescharacteristic
363C22×C113#53311yescharacteristic
364C22×C113#54011yescharacteristic
365C22×C113#54111yescharacteristic
366C22×C113#54211yescharacteristic
367C22×C113#54211yescharacteristic
368C22×C113D4211yescharacteristic
369C22×C113D4211yescharacteristic
370C22×C113#54611yescharacteristic
371C22×C113#54711yescharacteristic
372C22×C113#54711yescharacteristic
373C22×C113#54711yescharacteristic
374C22×C113#54811yescharacteristic
375C22×C113D4×Q811yescharacteristic
376C22×C113D4×Q811yescharacteristic
377C22×C113#55011yescharacteristic
378C22×C113#55211yescharacteristic
379C22×C113#55311yescharacteristic
380C22×C113#55411yescharacteristic
381C22×C113#55411yescharacteristic
382C22×C113#55511yescharacteristic
383C22×C113#55611yescharacteristic
384C4×C113—24no—
385C4×C113—24no—
386C4×C113—24no—
387C4×C113—42no—
388C4×C113—44no—
389C4×C113—44no—
390C4×C113—42no—
391C4×C113—82no—
392C4×C113—82no—
393C4×C113#38818yescomplemented
394#13876C11311yesmaximal, characteristic, direct product factor, Sylow
395C2×C113—44no—
396C2×C113#228511yescharacteristic
397C2×C113C2×#38811yescharacteristic
398C2×C113#231411yescharacteristic
399C2×C113D4×C4⋊C411yescharacteristic
400C2×C113D4×C4⋊C411yescharacteristic
401C2×C113#235211yescharacteristic
402C2×C113#235411yescharacteristic
403C2×C113#242211yescharacteristic
404C2×C113#242311yescharacteristic
405C2×C113#242811yescharacteristic
406C2×C113#242911yescharacteristic
407C2×C113#249111yescharacteristic
408C2×C113#249211yescharacteristic
409C2×C113#249611yescharacteristic
410C2×C113#249711yescharacteristic
411C2×#388C2×C11312yes—
412C2×#384C2×C11311yescharacteristic, complemented
413C2×#380C2×C11311yescharacteristic
414C2×#380C2×C11311yescharacteristic
415C2×C4×C4⋊C4C2×C11311yescharacteristic, complemented
416C2×C4×C22⋊C4C2×C11311yescharacteristic
417#1442C2×C11312yescomplemented
418#1439C2×C11312yes—
419#1436C2×C11312yescomplemented
420C4⋊#95C2×C11311yescharacteristic, complemented
421C4⋊#95C2×C11311yescharacteristic, complemented
422C113#1387611yescharacteristic, direct product factor, Sylow
423C24×C4C22×C11311yescharacteristic
424C22×C4⋊C4C22×C11311yescharacteristic
425C22×C4⋊C4C22×C11311yescharacteristic
426C22×C4⋊C4C22×C11312yes—
427C22×C4⋊C4C22×C11312yes—
428C22×C4⋊C4C22×C11311yescharacteristic
429C22×C4⋊C4C22×C11311yescharacteristic
430C22×C22⋊C4C22×C11312yes—
431C22×C22⋊C4C22×C11312yes—
432C22×C22⋊C4C22×C11311yescharacteristic
433C22×C22⋊C4C22×C11311yescharacteristic
434C22×C42C22×C11312yes—
435C22×C42C22×C11311yescharacteristic
436C22×C42C22×C11311yescharacteristic
437#388—28no—
438#384—24no—
439#380—24no—
440#380—24no—
441C4×C4⋊C4—24no—
442C4×C22⋊C4C4×C11318yescomplemented
443C2×#95C22×C11312yes—
444C2×#95C22×C11312yes—
445C2×#95C22×C11312yes—
446C2×#95C22×C11312yes—
447C2×#95C22×C11312yes—
448C2×#95C22×C11312yes—
449C2×#95C22×C11312yes—
450C2×#95C22×C11311yescharacteristic
451C2×#95C22×C11311yescharacteristic
452C25C23×C11311yescharacteristic
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4C2×C4×C11314yes—
460C23×C4C23×C11312yes—
461C23×C4C23×C11312yes—
462C23×C4C23×C11311yescharacteristic
463C23×C4C23×C11311yescharacteristic
464C23×C4C23×C11312yes—
465C23×C4C23×C11312yes—
466C23×C4C23×C11311yescharacteristic
467C23×C4C23×C11311yescharacteristic
468C23×C4C23×C11311yescharacteristic
469C23×C4C23×C11311yescharacteristic
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4D4×C11314yes—
487C2×C4⋊C4D4×C11314yes—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4C2×C4×C11314yes—
497C2×C22⋊C4C2×C4×C11314yes—
498C2×C22⋊C4D4×C11314yes—
499C2×C22⋊C4Q8×C11314yes—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—24no—
505C2×C42—24no—
506C2×C42—42no—
507C2×C42C2×C4×C11314yes—
508C2×C42C2×C4×C11314yes—
509#95—24no—
510#95—24no—
511#95—24no—
512#95—24no—
513#95—24no—
514#95—24no—
515#95—42no—
516#95C2×C4×C11314yes—
517#95C2×C4×C11314yes—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24C22×C4×C11312yes—
531C24C2×D4×C11312yes—
532C24C2×Q8×C11312yes—
533C24C24×C11311yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4C22×C4×C11312yes—
592C22×C4C22×C4×C11312yes—
593C22×C4C22×C4×C11312yes—
594C22×C4C22×C4×C11312yes—
595C22×C4C22×C4×C11312yes—
596C22×C4C22×C4×C11312yes—
597C22×C4C2×D4×C11314yes—
598C22×C4C2×D4×C11314yes—
599C22×C4C2×D4×C11312yes—
600C22×C4C2×D4×C11312yes—
601C22×C4C2×D4×C11312yes—
602C22×C4C2×D4×C11312yes—
603C22×C4C2×Q8×C11312yes—
604C22×C4C2×Q8×C11312yes—
605C22×C4#41×C11312yes—
606C22×C4#41×C11312yes—
607C22×C4#41×C11312yes—
608C22×C4#41×C11312yes—
609C22×C4#41×C11312yes—
610C22×C4#41×C11312yes—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4C4⋊C4×C113116yescomplemented
621C42—28no—
622C42—28no—
623C42—48no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C2×C4⋊C4×C11314yes—
659C23C23×C4×C11311yescharacteristic
660C23C22×D4×C11311yescharacteristic
661C23C22×D4×C11311yescharacteristic
662C23C22×D4×C11311yescharacteristic
663C23C22×Q8×C11311yescharacteristic
664C23C2×#41×C11311yescharacteristic
665C23C2×#41×C11311yescharacteristic
666C23C2×#41×C11311yescharacteristic
667C23C2×#41×C11311yescharacteristic
668C23C2×#41×C11311yescharacteristic
669C23C2×#41×C11311yescharacteristic
670C23H(5,𝔽2)×C11311yescharacteristic
671C23H(5,𝔽2)×C11311yescharacteristic
672C232−1+4×C11311yescharacteristic
673C232−1+4×C11311yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4C2×C4⋊C4×C11314yes—
736C2×C4C2×C4⋊C4×C11314yes—
737C2×C4#117×C11314yes—
738C2×C4#117×C11314yes—
739C2×C4C4×D4×C11314yes—
740C2×C4C4×D4×C11314yes—
741C2×C4#121×C11314yes—
742C2×C4#123×C11314yes—
743C2×C4#124×C11314yes—
744C2×C4#126×C11314yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C22×C4⋊C4×C11311yescharacteristic
761C22C2×#117×C11311yescharacteristic
762C22C2×#117×C11311yescharacteristic
763C22C2×C4×D4×C11311yescharacteristic
764C22C2×C4×D4×C11311yescharacteristic
765C22#520×C11311yescharacteristic
766C22#520×C11311yescharacteristic
767C22C2×#121×C11311yescharacteristic
768C22C2×#123×C11311yescharacteristic
769C22C2×#124×C11311yescharacteristic
770C22C2×#126×C11311yescharacteristic
771C22#532×C11311yescharacteristic
772C22#532×C11311yescharacteristic
773C22#533×C11311yescharacteristic
774C22#533×C11311yescharacteristic
775C22#540×C11311yescharacteristic
776C22#541×C11311yescharacteristic
777C22#542×C11311yescharacteristic
778C22#542×C11311yescharacteristic
779C22D42×C11311yescharacteristic
780C22D42×C11311yescharacteristic
781C22#546×C11311yescharacteristic
782C22#547×C11311yescharacteristic
783C22#547×C11311yescharacteristic
784C22#547×C11311yescharacteristic
785C22#548×C11311yescharacteristic
786C22D4×Q8×C11311yescharacteristic
787C22D4×Q8×C11311yescharacteristic
788C22#550×C11311yescharacteristic
789C22#552×C11311yescharacteristic
790C22#553×C11311yescharacteristic
791C22#554×C11311yescharacteristic
792C22#554×C11311yescharacteristic
793C22#555×C11311yescharacteristic
794C22#556×C11311yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—44no—
801C4—44no—
802C4—82no—
803C4—82no—
804C4#388×C11318yescomplemented
805C2—44no—
806C2C113×#228511yescharacteristic
807C2C2×#388×C11311yescharacteristic
808C2C113×#231411yescharacteristic
809C2D4×C4⋊C4×C11311yescharacteristic
810C2D4×C4⋊C4×C11311yescharacteristic
811C2C113×#235211yescharacteristic
812C2C113×#235411yescharacteristic
813C2C113×#242211yescharacteristic
814C2C113×#242311yescharacteristic
815C2C113×#242811yescharacteristic
816C2C113×#242911yescharacteristic
817C2C113×#249111yescharacteristic
818C2C113×#249211yescharacteristic
819C2C113×#249611yescharacteristic
820C2C113×#249711yescharacteristic
subgroupG/H
center, socleC24×C113C24
commutatorC23C23×C4×C113
Frattini, cosocleC24C24×C113
prime radicalC25×C113C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#384×C113C2semidirect
5. C2×C4×C4⋊C4×C113C2semidirect
7. C113×#1442C2semidirect
9. C113×#1436C2semidirect
10. C113×C4⋊#95C2semidirect
11. C113×C4⋊#95C2semidirect
31. C4×C22⋊C4×C113C4semidirect
209. C22⋊C4×C113C4⋊C4semidirect
393. C4×C113#388semidirect
394. #13876C113direct (N × H)
412. C2×#384C2×C113semidirect
415. C2×C4×C4⋊C4C2×C113semidirect
417. #1442C2×C113semidirect
419. #1436C2×C113semidirect
420. C4⋊#95C2×C113semidirect
421. C4⋊#95C2×C113semidirect
422. C113#13876direct (N × H)
442. C4×C22⋊C4C4×C113semidirect
620. C22⋊C4C4⋊C4×C113semidirect
804. C4#388×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1132
C2×#384×C1132
C2×#380×C1132
C2×C4×C4⋊C4×C1132
C2×C4×C22⋊C4×C1132
C113×#14422
C113×#14392
C113×#14362
C113×C4⋊#952
#13876113