Finite Group Databasebeta

← C131×#22400 #45708284

Subgroups — C131×#22400 #45708284

Order 33536.

1582 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C131C211yesmaximal, characteristic
2C2×#436×C131C211yesmaximal, characteristic, complemented
3C2×#435×C131C211yesmaximal, characteristic, complemented
4C2×#408×C131C211yesmaximal, characteristic, complemented
5C2×#407×C131C211yesmaximal, characteristic, complemented
6#1955×C131C211yesmaximal, characteristic, complemented
7#1954×C131C211yesmaximal, characteristic, complemented
8#1870×C131C211yesmaximal, characteristic, complemented
9#1870×C131C211yesmaximal, characteristic, complemented
10#1870×C131C211yesmaximal, characteristic, complemented
11#1869×C131C211yesmaximal, characteristic, complemented
12#1798×C131C211yesmaximal, characteristic, complemented
13#1780×C131C211yesmaximal, characteristic, complemented
14#1779×C131C211yesmaximal, characteristic, complemented
15#1750×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C24×C4×C131C2211yescharacteristic
18C22×M16×C131C2211yescharacteristic
19C22×M16×C131C2211yescharacteristic
20C22×M16×C131C2211yescharacteristic, complemented
21C23×C8×C131C2211yescharacteristic, complemented
22#525×C131—24no—
23#525×C131—24no—
24C2×#123×C131C411yescharacteristic
25C2×#123×C131C411yescharacteristic
26C2×C22⋊Q8×C131C411yescharacteristic
27C2×C22⋊Q8×C131C411yescharacteristic
28C2×#121×C131C411yescharacteristic
29C2×#121×C131C411yescharacteristic
30C2×#120×C131C411yescharacteristic
31C2×#120×C131C411yescharacteristic
32C2×C4×D4×C131C2211yescharacteristic
33C2×C4×D4×C131C2211yescharacteristic
34C2×C4×D4×C131C2211yescharacteristic
35C2×C4×D4×C131C2211yescharacteristic
36C2×#117×C131C2211yescharacteristic
37#436×C131—24no—
38#435×C131—24no—
39C2×C4⋊C8×C131C2211yescharacteristic, complemented
40C2×C4⋊C8×C131C2211yescharacteristic, complemented
41#408×C131—24no—
42#407×C131—24no—
43C2×C22⋊C8×C131C2211yescharacteristic
44C2×C22⋊C8×C131C2211yescharacteristic
45C2×C22⋊C8×C131C2211yescharacteristic
46C2×C22⋊C8×C131C2211yescharacteristic
47C2×C22⋊C8×C131C2211yescharacteristic
48C2×C22⋊C8×C131C2211yescharacteristic
49C2×C22⋊C8×C131C2211yescharacteristic
50C2×C22⋊C8×C131C2211yescharacteristic
51C2×C22⋊C8×C131C2211yescharacteristic
52C2×C22⋊C8×C131C2211yescharacteristic
53C2×C22⋊C8×C131C2211yescharacteristic, complemented
54C2×C22⋊C8×C131C2211yescharacteristic, complemented
55C2×C22⋊C8×C131C2211yescharacteristic, complemented
56C2×C22⋊C8×C131C2211yescharacteristic, complemented
57C2×C22⋊C8×C131C2211yescharacteristic, complemented
58C2×C22⋊C8×C131C2211yescharacteristic, complemented
59C2×#97×C131C2211yescharacteristic, complemented
60C2×C4×C8×C131C2211yescharacteristic, complemented
61#336×C131C2211yescharacteristic, complemented
62#336×C131C2211yescharacteristic, complemented
63#336×C131C2211yescharacteristic, complemented
64#336×C131C2211yescharacteristic, complemented
65C25×C131C2×C411yescharacteristic
66C2×#41×C131—22no—
67C2×#41×C131—22no—
68C2×#41×C131—22no—
69C2×#41×C131—22no—
70C2×#41×C131—41no—
71C2×#41×C131—41no—
72C22×Q8×C131C2×C411yescharacteristic
73C22×D4×C131C2×C411yescharacteristic
74C22×D4×C131C2×C411yescharacteristic
75C22×D4×C131C2×C411yescharacteristic
76C22×D4×C131C2×C411yescharacteristic
77C22×D4×C131C2×C411yescharacteristic
78C22×D4×C131C2×C411yescharacteristic
79C22×D4×C131C2×C411yescharacteristic
80C23×C4×C131—22no—
81C23×C4×C131—22no—
82C23×C4×C131—22no—
83C23×C4×C131—22no—
84C23×C4×C131—41no—
85C23×C4×C131—41no—
86C23×C4×C131C2×C411yescharacteristic
87C23×C4×C131C2×C411yescharacteristic
88C23×C4×C131C2×C411yescharacteristic
89C23×C4×C131C2311yescharacteristic
90C23×C4×C131C2311yescharacteristic
91C23×C4×C131C2311yescharacteristic
92C23×C4×C131C2311yescharacteristic
93C23×C4×C131C2311yescharacteristic
94C2×M16×C131—22no—
95C2×M16×C131—22no—
96C2×M16×C131—22no—
97C2×M16×C131—22no—
98C2×M16×C131—22no—
99C2×M16×C131—22no—
100C2×M16×C131—41no—
101C2×M16×C131—41no—
102C2×M16×C131—41no—
103C22×C8×C131—22no—
104C22×C8×C131—22no—
105C22×C8×C131—41no—
106C22×C8×C131C2311yescharacteristic
107C22×C8×C131C2311yescharacteristic
108C22×C8×C131C2311yescharacteristic
109C22×C8×C131C2311yescharacteristic
110C22×C8×C131C2311yescharacteristic
111C22×C8×C131C2311yescharacteristic
112C22×C8×C131C2311yescharacteristic
113C22×C8×C131C2311yescharacteristic
114#123×C131—24no—
115#123×C131—24no—
116C22⋊Q8×C131—24no—
117C22⋊Q8×C131—24no—
118#121×C131—24no—
119#121×C131—24no—
120#120×C131—24no—
121#120×C131—24no—
122C4×D4×C131—22no—
123C4×D4×C131—22no—
124C4×D4×C131—22no—
125C4×D4×C131—22no—
126C4×D4×C131—22no—
127C4×D4×C131—22no—
128C4×D4×C131D414yes—
129C4×D4×C131D414yes—
130#117×C131—22no—
131#117×C131—22no—
132C2×C4⋊C4×C131C2×C411yescharacteristic
133C2×C4⋊C4×C131C2×C411yescharacteristic
134C2×C4⋊C4×C131C2×C411yescharacteristic
135C2×C4⋊C4×C131C2×C411yescharacteristic
136C2×C4⋊C4×C131C2×C411yescharacteristic
137C2×C4⋊C4×C131C2×C411yescharacteristic
138C2×C22⋊C4×C131C2×C411yescharacteristic
139C2×C22⋊C4×C131C2×C411yescharacteristic
140C2×C22⋊C4×C131C2×C411yescharacteristic
141C2×C22⋊C4×C131C2×C411yescharacteristic
142C2×C22⋊C4×C131C2×C411yescharacteristic
143C2×C22⋊C4×C131C2×C411yescharacteristic
144C2×C22⋊C4×C131C2×C411yescharacteristic
145C2×C22⋊C4×C131C2×C411yescharacteristic
146C2×C22⋊C4×C131C2×C411yescharacteristic
147C2×C22⋊C4×C131C2×C411yescharacteristic
148C2×C42×C131C2311yescharacteristic
149C2×C42×C131C2311yescharacteristic
150C4⋊C8×C131—22no—
151C4⋊C8×C131—22no—
152C22⋊C8×C131—22no—
153C22⋊C8×C131—22no—
154C22⋊C8×C131—22no—
155C22⋊C8×C131—22no—
156C22⋊C8×C131—22no—
157C22⋊C8×C131—22no—
158C22⋊C8×C131—22no—
159C22⋊C8×C131—22no—
160C22⋊C8×C131—22no—
161C22⋊C8×C131—22no—
162C22⋊C8×C131—22no—
163C22⋊C8×C131—41no—
164C22⋊C8×C131—41no—
165C22⋊C8×C131—41no—
166C22⋊C8×C131—41no—
167C22⋊C8×C131D414yescomplemented
168#97×C131—22no—
169C4×C8×C131—22no—
170C24×C131—22no—
171C24×C131—22no—
172C24×C131—22no—
173C24×C131—41no—
174C24×C131—41no—
175C24×C131—41no—
176C24×C131—41no—
177C24×C131C22×C411yescharacteristic
178C24×C131C22×C411yescharacteristic
179C24×C131C22×C411yescharacteristic
180C24×C131C22×C411yescharacteristic
181C24×C131C22×C411yescharacteristic
182#41×C131—44no—
183#41×C131—44no—
184#41×C131—44no—
185#41×C131—44no—
186C2×Q8×C131—22no—
187C2×Q8×C131—22no—
188C2×Q8×C131—41no—
189C2×D4×C131—22no—
190C2×D4×C131—22no—
191C2×D4×C131—22no—
192C2×D4×C131—22no—
193C2×D4×C131—22no—
194C2×D4×C131—22no—
195C2×D4×C131—22no—
196C2×D4×C131—22no—
197C2×D4×C131—22no—
198C2×D4×C131—22no—
199C2×D4×C131—22no—
200C2×D4×C131—41no—
201C2×D4×C131—41no—
202C2×D4×C131—41no—
203C2×D4×C131—41no—
204C2×D4×C131—41no—
205C2×D4×C131—41no—
206C2×D4×C131—41no—
207C2×D4×C131—41no—
208C2×D4×C131—41no—
209C2×D4×C131C22⋊C414yes—
210C22×C4×C131—21no—
211C22×C4×C131—21no—
212C22×C4×C131—21no—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—21no—
217C22×C4×C131—21no—
218C22×C4×C131—21no—
219C22×C4×C131—21no—
220C22×C4×C131—21no—
221C22×C4×C131—21no—
222C22×C4×C131—22no—
223C22×C4×C131—22no—
224C22×C4×C131—22no—
225C22×C4×C131—22no—
226C22×C4×C131—22no—
227C22×C4×C131—22no—
228C22×C4×C131—21no—
229C22×C4×C131—21no—
230C22×C4×C131—21no—
231C22×C4×C131—21no—
232C22×C4×C131—21no—
233C22×C4×C131—21no—
234C22×C4×C131—21no—
235C22×C4×C131—21no—
236C22×C4×C131—21no—
237C22×C4×C131—21no—
238C22×C4×C131—21no—
239C22×C4×C131—21no—
240C22×C4×C131—41no—
241C22×C4×C131—41no—
242C22×C4×C131—41no—
243C22×C4×C131—44no—
244C22×C4×C131—44no—
245C22×C4×C131—44no—
246C22×C4×C131—44no—
247C22×C4×C131C22×C411yescharacteristic
248C22×C4×C131C22×C411yescharacteristic
249C22×C4×C131C22×C411yescharacteristic
250C22×C4×C131C22×C411yescharacteristic
251C22×C4×C131C22×C411yescharacteristic
252C22×C4×C131C22×C411yescharacteristic
253C22×C4×C131C22×C411yescharacteristic
254C22×C4×C131C22×C411yescharacteristic
255C22×C4×C131C22×C411yescharacteristic
256C22×C4×C131C2×D412yes—
257C22×C4×C131C2×D412yes—
258C22×C4×C131C2×D412yes—
259C22×C4×C131C2×D412yes—
260C22×C4×C131C2×D412yes—
261C22×C4×C131#4112yes—
262C22×C4×C131C2411yescharacteristic
263M16×C131—44no—
264M16×C131—44no—
265M16×C131—44no—
266C2×C8×C131—21no—
267C2×C8×C131—21no—
268C2×C8×C131—21no—
269C2×C8×C131—21no—
270C2×C8×C131—21no—
271C2×C8×C131—21no—
272C2×C8×C131—21no—
273C2×C8×C131—21no—
274C2×C8×C131—21no—
275C2×C8×C131—21no—
276C2×C8×C131—21no—
277C2×C8×C131—21no—
278C2×C8×C131—21no—
279C2×C8×C131—21no—
280C2×C8×C131—21no—
281C2×C8×C131—21no—
282C2×C8×C131—21no—
283C2×C8×C131—21no—
284C2×C8×C131—21no—
285C2×C8×C131—21no—
286C2×C8×C131—21no—
287C2×C8×C131—21no—
288C2×C8×C131—44no—
289C2×C8×C131C2×D412yes—
290C2×C8×C131C2×D412yes—
291C4⋊C4×C131—22no—
292C4⋊C4×C131—22no—
293C4⋊C4×C131—22no—
294C4⋊C4×C131—22no—
295C4⋊C4×C131—22no—
296C4⋊C4×C131C22⋊C414yes—
297C22⋊C4×C131—22no—
298C22⋊C4×C131—22no—
299C22⋊C4×C131—22no—
300C22⋊C4×C131—22no—
301C22⋊C4×C131—22no—
302C22⋊C4×C131—22no—
303C22⋊C4×C131—22no—
304C22⋊C4×C131—22no—
305C22⋊C4×C131C22⋊C414yes—
306C22⋊C4×C131C22⋊C414yes—
307C42×C131—21no—
308C42×C131—21no—
309C42×C131C2×D412yes—
310C42×C131C2×D412yes—
311C23×C131—21no—
312C23×C131—21no—
313C23×C131—21no—
314C23×C131—21no—
315C23×C131—21no—
316C23×C131—21no—
317C23×C131—21no—
318C23×C131—21no—
319C23×C131—21no—
320C23×C131—21no—
321C23×C131—21no—
322C23×C131—21no—
323C23×C131—21no—
324C23×C131—21no—
325C23×C131—21no—
326C23×C131—21no—
327C23×C131—21no—
328C23×C131—21no—
329C23×C131—21no—
330C23×C131—21no—
331C23×C131—21no—
332C23×C131—21no—
333C23×C131—21no—
334C23×C131—21no—
335C23×C131—21no—
336C23×C131—21no—
337C23×C131—21no—
338C23×C131—21no—
339C23×C131—21no—
340C23×C131—21no—
341C23×C131—21no—
342C23×C131—44no—
343C23×C131—44no—
344C23×C131—44no—
345C23×C131—44no—
346C23×C131—44no—
347C23×C131—44no—
348C23×C131—44no—
349C23×C131C2×C22⋊C412yes—
350C23×C131C2×C22⋊C412yes—
351C23×C131C4×D412yes—
352C23×C131#13112yes—
353C23×C131C23×C411yescharacteristic
354Q8×C131—44no—
355D4×C131—44no—
356D4×C131—44no—
357D4×C131—44no—
358D4×C131—44no—
359D4×C131—44no—
360D4×C131—44no—
361D4×C131—44no—
362C2×C4×C131—21no—
363C2×C4×C131—21no—
364C2×C4×C131—21no—
365C2×C4×C131—21no—
366C2×C4×C131—21no—
367C2×C4×C131—21no—
368C2×C4×C131—21no—
369C2×C4×C131—21no—
370C2×C4×C131—21no—
371C2×C4×C131—21no—
372C2×C4×C131—22no—
373C2×C4×C131—22no—
374C2×C4×C131—22no—
375C2×C4×C131—22no—
376C2×C4×C131—22no—
377C2×C4×C131—22no—
378C2×C4×C131—22no—
379C2×C4×C131—22no—
380C2×C4×C131—22no—
381C2×C4×C131—22no—
382C2×C4×C131—22no—
383C2×C4×C131—22no—
384C2×C4×C131—21no—
385C2×C4×C131—21no—
386C2×C4×C131—21no—
387C2×C4×C131—21no—
388C2×C4×C131—21no—
389C2×C4×C131—21no—
390C2×C4×C131—21no—
391C2×C4×C131—21no—
392C2×C4×C131—21no—
393C2×C4×C131—21no—
394C2×C4×C131—21no—
395C2×C4×C131—21no—
396C2×C4×C131—44no—
397C2×C4×C131—44no—
398C2×C4×C131—44no—
399C2×C4×C131—41no—
400C2×C4×C131—41no—
401C2×C4×C131—41no—
402C2×C4×C131—41no—
403C2×C4×C131—41no—
404C2×C4×C131—41no—
405C2×C4×C131—41no—
406C2×C4×C131—41no—
407C2×C4×C131C2×C22⋊C412yes—
408C2×C4×C131C2×C22⋊C412yes—
409C2×C4×C131C2×C22⋊C412yes—
410C2×C4×C131C2×C22⋊C412yes—
411C2×C4×C131C4×D412yes—
412C2×C4×C131C22×D411yescharacteristic
413C2×C4×C131C22×D411yescharacteristic
414C2×C4×C131C22×D411yescharacteristic
415C2×C4×C131C2×#4111yescharacteristic
416C2×C4×C131H(5,𝔽2)11yescharacteristic
417C2×C4×C131H(5,𝔽2)11yescharacteristic
418C8×C131—22no—
419C8×C131—22no—
420C8×C131—41no—
421C8×C131—41no—
422C8×C131—41no—
423C8×C131—41no—
424C8×C131—41no—
425C8×C131—41no—
426C22×C131—22no—
427C22×C131—22no—
428C22×C131—22no—
429C22×C131—22no—
430C22×C131—22no—
431C22×C131—22no—
432C22×C131—22no—
433C22×C131—22no—
434C22×C131—22no—
435C22×C131—22no—
436C22×C131—22no—
437C22×C131—22no—
438C22×C131—416no—
439C22×C131—41no—
440C22×C131—41no—
441C22×C131—41no—
442C22×C131—41no—
443C22×C131—41no—
444C22×C131—41no—
445C22×C131—41no—
446C22×C131—41no—
447C22×C131—41no—
448C22×C131—41no—
449C22×C131—41no—
450C22×C131—41no—
451C22×C131—41no—
452C22×C131—41no—
453C22×C131—41no—
454C22×C131—41no—
455C22×C131—41no—
456C22×C131—41no—
457C22×C131—41no—
458C22×C131—41no—
459C22×C131—41no—
460C22×C131—41no—
461C22×C131—41no—
462C22×C131C22×C22⋊C411yescharacteristic
463C22×C131C2×C4×D411yescharacteristic
464C22×C131#51811yescharacteristic
465C22×C131C2×#13111yescharacteristic
466C22×C131#56811yescharacteristic
467C22×C131#56811yescharacteristic
468C22×C131#56811yescharacteristic
469C4×C131—22no—
470C4×C131—22no—
471C4×C131—22no—
472C4×C131—22no—
473C4×C131—22no—
474C4×C131—41no—
475C4×C131—41no—
476C4×C131—41no—
477C4×C131—41no—
478C4×C131D4211yescharacteristic
479C4×C131D4211yescharacteristic
480C4×C131#54611yescharacteristic
481C4×C131#54611yescharacteristic
482C2×C131—42no—
483C2×C131—42no—
484C2×C131—42no—
485C2×C131—42no—
486C2×C131—81no—
487C2×C131D4×C22⋊C411yescharacteristic
488C2×C131#287911yescharacteristic
489C2×C131#288011yescharacteristic
490C2×C131#293011yescharacteristic
491C2×C131#293311yescharacteristic
492C2×C131#297611yescharacteristic
493C2×C131#297811yescharacteristic
494#22400C13111yesmaximal, characteristic, direct product factor, Sylow
495C131#2240011yescharacteristic, direct product factor, Sylow
496C2×#525C2×C13111yescharacteristic
497C2×#436C2×C13111yescharacteristic, complemented
498C2×#435C2×C13111yescharacteristic, complemented
499C2×#408C2×C13111yescharacteristic, complemented
500C2×#407C2×C13111yescharacteristic, complemented
501#1955C2×C13111yescharacteristic, complemented
502#1954C2×C13111yescharacteristic, complemented
503#1870C2×C13111yescharacteristic, complemented
504#1870C2×C13111yescharacteristic, complemented
505#1870C2×C13111yescharacteristic, complemented
506#1869C2×C13111yescharacteristic, complemented
507#1798C2×C13111yescharacteristic, complemented
508#1780C2×C13111yescharacteristic, complemented
509#1779C2×C13111yescharacteristic, complemented
510#1750C2×C13111yescharacteristic, complemented
511C22×#41C22×C13111yescharacteristic
512C24×C4C22×C13111yescharacteristic
513C22×M16C22×C13111yescharacteristic
514C22×M16C22×C13111yescharacteristic
515C22×M16C22×C13111yescharacteristic, complemented
516C23×C8C22×C13111yescharacteristic, complemented
517#525—24no—
518#525—24no—
519C2×#123C4×C13111yescharacteristic
520C2×#123C4×C13111yescharacteristic
521C2×C22⋊Q8C4×C13111yescharacteristic
522C2×C22⋊Q8C4×C13111yescharacteristic
523C2×#121C4×C13111yescharacteristic
524C2×#121C4×C13111yescharacteristic
525C2×#120C4×C13111yescharacteristic
526C2×#120C4×C13111yescharacteristic
527C2×C4×D4C22×C13111yescharacteristic
528C2×C4×D4C22×C13111yescharacteristic
529C2×C4×D4C22×C13111yescharacteristic
530C2×C4×D4C22×C13111yescharacteristic
531C2×#117C22×C13111yescharacteristic
532#436—24no—
533#435—24no—
534C2×C4⋊C8C22×C13111yescharacteristic, complemented
535C2×C4⋊C8C22×C13111yescharacteristic, complemented
536#408—24no—
537#407—24no—
538C2×C22⋊C8C22×C13111yescharacteristic
539C2×C22⋊C8C22×C13111yescharacteristic
540C2×C22⋊C8C22×C13111yescharacteristic
541C2×C22⋊C8C22×C13111yescharacteristic
542C2×C22⋊C8C22×C13111yescharacteristic
543C2×C22⋊C8C22×C13111yescharacteristic
544C2×C22⋊C8C22×C13111yescharacteristic
545C2×C22⋊C8C22×C13111yescharacteristic
546C2×C22⋊C8C22×C13111yescharacteristic
547C2×C22⋊C8C22×C13111yescharacteristic
548C2×C22⋊C8C22×C13111yescharacteristic, complemented
549C2×C22⋊C8C22×C13111yescharacteristic, complemented
550C2×C22⋊C8C22×C13111yescharacteristic, complemented
551C2×C22⋊C8C22×C13111yescharacteristic, complemented
552C2×C22⋊C8C22×C13111yescharacteristic, complemented
553C2×C22⋊C8C22×C13111yescharacteristic, complemented
554C2×#97C22×C13111yescharacteristic, complemented
555C2×C4×C8C22×C13111yescharacteristic, complemented
556#336C22×C13111yescharacteristic, complemented
557#336C22×C13111yescharacteristic, complemented
558#336C22×C13111yescharacteristic, complemented
559#336C22×C13111yescharacteristic, complemented
560C25C2×C4×C13111yescharacteristic
561C2×#41—22no—
562C2×#41—22no—
563C2×#41—22no—
564C2×#41—22no—
565C2×#41—41no—
566C2×#41—41no—
567C22×Q8C2×C4×C13111yescharacteristic
568C22×D4C2×C4×C13111yescharacteristic
569C22×D4C2×C4×C13111yescharacteristic
570C22×D4C2×C4×C13111yescharacteristic
571C22×D4C2×C4×C13111yescharacteristic
572C22×D4C2×C4×C13111yescharacteristic
573C22×D4C2×C4×C13111yescharacteristic
574C22×D4C2×C4×C13111yescharacteristic
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—41no—
580C23×C4—41no—
581C23×C4C2×C4×C13111yescharacteristic
582C23×C4C2×C4×C13111yescharacteristic
583C23×C4C2×C4×C13111yescharacteristic
584C23×C4C23×C13111yescharacteristic
585C23×C4C23×C13111yescharacteristic
586C23×C4C23×C13111yescharacteristic
587C23×C4C23×C13111yescharacteristic
588C23×C4C23×C13111yescharacteristic
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—22no—
592C2×M16—22no—
593C2×M16—22no—
594C2×M16—22no—
595C2×M16—41no—
596C2×M16—41no—
597C2×M16—41no—
598C22×C8—22no—
599C22×C8—22no—
600C22×C8—41no—
601C22×C8C23×C13111yescharacteristic
602C22×C8C23×C13111yescharacteristic
603C22×C8C23×C13111yescharacteristic
604C22×C8C23×C13111yescharacteristic
605C22×C8C23×C13111yescharacteristic
606C22×C8C23×C13111yescharacteristic
607C22×C8C23×C13111yescharacteristic
608C22×C8C23×C13111yescharacteristic
609#123—24no—
610#123—24no—
611C22⋊Q8—24no—
612C22⋊Q8—24no—
613#121—24no—
614#121—24no—
615#120—24no—
616#120—24no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4D4×C13114yes—
624C4×D4D4×C13114yes—
625#117—22no—
626#117—22no—
627C2×C4⋊C4C2×C4×C13111yescharacteristic
628C2×C4⋊C4C2×C4×C13111yescharacteristic
629C2×C4⋊C4C2×C4×C13111yescharacteristic
630C2×C4⋊C4C2×C4×C13111yescharacteristic
631C2×C4⋊C4C2×C4×C13111yescharacteristic
632C2×C4⋊C4C2×C4×C13111yescharacteristic
633C2×C22⋊C4C2×C4×C13111yescharacteristic
634C2×C22⋊C4C2×C4×C13111yescharacteristic
635C2×C22⋊C4C2×C4×C13111yescharacteristic
636C2×C22⋊C4C2×C4×C13111yescharacteristic
637C2×C22⋊C4C2×C4×C13111yescharacteristic
638C2×C22⋊C4C2×C4×C13111yescharacteristic
639C2×C22⋊C4C2×C4×C13111yescharacteristic
640C2×C22⋊C4C2×C4×C13111yescharacteristic
641C2×C22⋊C4C2×C4×C13111yescharacteristic
642C2×C22⋊C4C2×C4×C13111yescharacteristic
643C2×C42C23×C13111yescharacteristic
644C2×C42C23×C13111yescharacteristic
645C4⋊C8—22no—
646C4⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8—22no—
650C22⋊C8—22no—
651C22⋊C8—22no—
652C22⋊C8—22no—
653C22⋊C8—22no—
654C22⋊C8—22no—
655C22⋊C8—22no—
656C22⋊C8—22no—
657C22⋊C8—22no—
658C22⋊C8—41no—
659C22⋊C8—41no—
660C22⋊C8—41no—
661C22⋊C8—41no—
662C22⋊C8D4×C13114yescomplemented
663#97—22no—
664C4×C8—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—41no—
669C24—41no—
670C24—41no—
671C24—41no—
672C24C22×C4×C13111yescharacteristic
673C24C22×C4×C13111yescharacteristic
674C24C22×C4×C13111yescharacteristic
675C24C22×C4×C13111yescharacteristic
676C24C22×C4×C13111yescharacteristic
677#41—44no—
678#41—44no—
679#41—44no—
680#41—44no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—41no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4—41no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4C22⋊C4×C13114yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—41no—
736C22×C4—41no—
737C22×C4—41no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4C22×C4×C13111yescharacteristic
743C22×C4C22×C4×C13111yescharacteristic
744C22×C4C22×C4×C13111yescharacteristic
745C22×C4C22×C4×C13111yescharacteristic
746C22×C4C22×C4×C13111yescharacteristic
747C22×C4C22×C4×C13111yescharacteristic
748C22×C4C22×C4×C13111yescharacteristic
749C22×C4C22×C4×C13111yescharacteristic
750C22×C4C22×C4×C13111yescharacteristic
751C22×C4C2×D4×C13112yes—
752C22×C4C2×D4×C13112yes—
753C22×C4C2×D4×C13112yes—
754C22×C4C2×D4×C13112yes—
755C22×C4C2×D4×C13112yes—
756C22×C4#41×C13112yes—
757C22×C4C24×C13111yescharacteristic
758M16—44no—
759M16—44no—
760M16—44no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—44no—
784C2×C8C2×D4×C13112yes—
785C2×C8C2×D4×C13112yes—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4C22⋊C4×C13114yes—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4C22⋊C4×C13114yes—
801C22⋊C4C22⋊C4×C13114yes—
802C42—21no—
803C42—21no—
804C42C2×D4×C13112yes—
805C42C2×D4×C13112yes—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—44no—
838C23—44no—
839C23—44no—
840C23—44no—
841C23—44no—
842C23—44no—
843C23—44no—
844C23C2×C22⋊C4×C13112yes—
845C23C2×C22⋊C4×C13112yes—
846C23C4×D4×C13112yes—
847C23#131×C13112yes—
848C23C23×C4×C13111yescharacteristic
849Q8—44no—
850D4—44no—
851D4—44no—
852D4—44no—
853D4—44no—
854D4—44no—
855D4—44no—
856D4—44no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4C2×C22⋊C4×C13112yes—
903C2×C4C2×C22⋊C4×C13112yes—
904C2×C4C2×C22⋊C4×C13112yes—
905C2×C4C2×C22⋊C4×C13112yes—
906C2×C4C4×D4×C13112yes—
907C2×C4C22×D4×C13111yescharacteristic
908C2×C4C22×D4×C13111yescharacteristic
909C2×C4C22×D4×C13111yescharacteristic
910C2×C4C2×#41×C13111yescharacteristic
911C2×C4H(5,𝔽2)×C13111yescharacteristic
912C2×C4H(5,𝔽2)×C13111yescharacteristic
913C8—22no—
914C8—22no—
915C8—41no—
916C8—41no—
917C8—41no—
918C8—41no—
919C8—41no—
920C8—41no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—416no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22C22×C22⋊C4×C13111yescharacteristic
958C22C2×C4×D4×C13111yescharacteristic
959C22#518×C13111yescharacteristic
960C22C2×#131×C13111yescharacteristic
961C22#568×C13111yescharacteristic
962C22#568×C13111yescharacteristic
963C22#568×C13111yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—22no—
968C4—22no—
969C4—41no—
970C4—41no—
971C4—41no—
972C4—41no—
973C4D42×C13111yescharacteristic
974C4D42×C13111yescharacteristic
975C4#546×C13111yescharacteristic
976C4#546×C13111yescharacteristic
977C2—42no—
978C2—42no—
979C2—42no—
980C2—42no—
981C2—81no—
982C2D4×C22⋊C4×C13111yescharacteristic
983C2#2879×C13111yescharacteristic
984C2#2880×C13111yescharacteristic
985C2#2930×C13111yescharacteristic
986C2#2933×C13111yescharacteristic
987C2#2976×C13111yescharacteristic
988C2#2978×C13111yescharacteristic
subgroupG/H
centerC22×C4×C131C24
commutatorC23C23×C4×C131
Frattini, cosocleC22×C4C24×C131
socleC23×C131C23×C4
prime radicalC2×#525×C131C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#436×C131C2semidirect
3. C2×#435×C131C2semidirect
4. C2×#408×C131C2semidirect
5. C2×#407×C131C2semidirect
6. #1955×C131C2semidirect
7. #1954×C131C2semidirect
8. #1870×C131C2semidirect
9. #1870×C131C2semidirect
10. #1870×C131C2semidirect
11. #1869×C131C2semidirect
12. #1798×C131C2semidirect
13. #1780×C131C2semidirect
14. #1779×C131C2semidirect
15. #1750×C131C2semidirect
20. C22×M16×C131C22semidirect
21. C23×C8×C131C22semidirect
39. C2×C4⋊C8×C131C22semidirect
40. C2×C4⋊C8×C131C22semidirect
53. C2×C22⋊C8×C131C22semidirect
54. C2×C22⋊C8×C131C22semidirect
55. C2×C22⋊C8×C131C22semidirect
56. C2×C22⋊C8×C131C22semidirect
57. C2×C22⋊C8×C131C22semidirect
58. C2×C22⋊C8×C131C22semidirect
59. C2×#97×C131C22semidirect
60. C2×C4×C8×C131C22semidirect
61. #336×C131C22semidirect
62. #336×C131C22semidirect
63. #336×C131C22semidirect
64. #336×C131C22semidirect
167. C22⋊C8×C131D4semidirect
494. #22400C131direct (N × H)
495. C131#22400direct (N × H)
497. C2×#436C2×C131semidirect
498. C2×#435C2×C131semidirect
499. C2×#408C2×C131semidirect
500. C2×#407C2×C131semidirect
501. #1955C2×C131semidirect
502. #1954C2×C131semidirect
503. #1870C2×C131semidirect
504. #1870C2×C131semidirect
505. #1870C2×C131semidirect
506. #1869C2×C131semidirect
507. #1798C2×C131semidirect
508. #1780C2×C131semidirect
509. #1779C2×C131semidirect
510. #1750C2×C131semidirect
515. C22×M16C22×C131semidirect
516. C23×C8C22×C131semidirect
534. C2×C4⋊C8C22×C131semidirect
535. C2×C4⋊C8C22×C131semidirect
548. C2×C22⋊C8C22×C131semidirect
549. C2×C22⋊C8C22×C131semidirect
550. C2×C22⋊C8C22×C131semidirect
551. C2×C22⋊C8C22×C131semidirect
552. C2×C22⋊C8C22×C131semidirect
553. C2×C22⋊C8C22×C131semidirect
554. C2×#97C22×C131semidirect
555. C2×C4×C8C22×C131semidirect
556. #336C22×C131semidirect
557. #336C22×C131semidirect
558. #336C22×C131semidirect
559. #336C22×C131semidirect
662. C22⋊C8D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1312
C2×#436×C1312
C2×#435×C1312
C2×#408×C1312
C2×#407×C1312
#1955×C1312
#1954×C1312
#1870×C1312
#1869×C1312
#1798×C1312
#1780×C1312
#1779×C1312
#1750×C1312
#22400131