Finite Group Databasebeta

← C113×#14442 #43282462

Subgroups — C113×#14442 #43282462

Order 28928.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C113C211yesmaximal, characteristic, complemented
2C2×#388×C113C211yesmaximal, characteristic
3C2×#388×C113C211yesmaximal, characteristic
4C2×#385×C113C211yesmaximal, characteristic
5C2×#385×C113C211yesmaximal, characteristic
6C113×#1444C211yesmaximal, characteristic, complemented
7C113×#1442C211yesmaximal, characteristic, complemented
8C113×#1442C211yesmaximal, characteristic, complemented
9C113×#1441C211yesmaximal, characteristic, complemented
10C113×#1439C211yesmaximal, characteristic
11C113×#1439C211yesmaximal, characteristic
12C113×#1436C211yesmaximal, characteristic, complemented
13C113×C4⋊#95C211yesmaximal, characteristic, complemented
14C113×C4⋊#95C211yesmaximal, characteristic, complemented
15C113×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C113C2211yescharacteristic
17C22×C4⋊C4×C113C2211yescharacteristic
18C22×C4⋊C4×C113C2211yescharacteristic
19C22×C4⋊C4×C113C2211yescharacteristic
20C22×C4⋊C4×C113C2211yescharacteristic
21C22×C4⋊C4×C113C2211yescharacteristic
22C22×C4⋊C4×C113C2211yescharacteristic
23C22×C4⋊C4×C113C2211yescharacteristic
24C22×C4⋊C4×C113C2211yescharacteristic
25C22×C22⋊C4×C113C2211yescharacteristic
26C22×C22⋊C4×C113C2211yescharacteristic
27C22×C22⋊C4×C113C2211yescharacteristic
28C22×C22⋊C4×C113C2211yescharacteristic
29C22×C22⋊C4×C113C2211yescharacteristic
30C22×C22⋊C4×C113C2211yescharacteristic
31C22×C42×C113C2211yescharacteristic
32C22×C42×C113C2211yescharacteristic
33#389×C113—24no—
34#388×C113—24no—
35#388×C113C418yescomplemented
36#385×C113—24no—
37#385×C113—24no—
38C2×#95×C113C2211yescharacteristic
39C2×#95×C113C2211yescharacteristic
40C2×#95×C113C2211yescharacteristic
41C2×#95×C113C2211yescharacteristic
42C2×#95×C113C2211yescharacteristic
43C2×#95×C113C2211yescharacteristic
44C2×#95×C113C2211yescharacteristic
45C2×#95×C113C2211yescharacteristic
46C2×#95×C113C2211yescharacteristic
47C2×#95×C113C2211yescharacteristic
48C2×#95×C113C2211yescharacteristic
49C2×#95×C113C2211yescharacteristic
50C2×#95×C113C2211yescharacteristic
51C2×#95×C113C2211yescharacteristic
52C2×#95×C113C2211yescharacteristic
53C2×#95×C113C2211yescharacteristic
54C2×#95×C113C2211yescharacteristic
55C2×#95×C113C2211yescharacteristic
56C25×C113C2311yescharacteristic
57C23×C4×C113—22no—
58C23×C4×C113—22no—
59C23×C4×C113—22no—
60C23×C4×C113—41no—
61C23×C4×C113—41no—
62C23×C4×C113—41no—
63C23×C4×C113—41no—
64C23×C4×C113C2311yescharacteristic
65C23×C4×C113C2311yescharacteristic
66C23×C4×C113C2311yescharacteristic
67C23×C4×C113C2311yescharacteristic
68C23×C4×C113C2311yescharacteristic
69C23×C4×C113C2311yescharacteristic
70C23×C4×C113C2311yescharacteristic
71C23×C4×C113C2311yescharacteristic
72C23×C4×C113C2311yescharacteristic
73C23×C4×C113C2311yescharacteristic
74C23×C4×C113C2311yescharacteristic
75C23×C4×C113C2311yescharacteristic
76C23×C4×C113C2311yescharacteristic
77C23×C4×C113C2311yescharacteristic
78C2×C4⋊C4×C113—22no—
79C2×C4⋊C4×C113—22no—
80C2×C4⋊C4×C113—22no—
81C2×C4⋊C4×C113—22no—
82C2×C4⋊C4×C113—22no—
83C2×C4⋊C4×C113—22no—
84C2×C4⋊C4×C113—22no—
85C2×C4⋊C4×C113—22no—
86C2×C4⋊C4×C113—22no—
87C2×C4⋊C4×C113—22no—
88C2×C4⋊C4×C113—22no—
89C2×C4⋊C4×C113—22no—
90C2×C4⋊C4×C113—41no—
91C2×C4⋊C4×C113—41no—
92C2×C4⋊C4×C113—41no—
93C2×C4⋊C4×C113—41no—
94C2×C4⋊C4×C113—41no—
95C2×C4⋊C4×C113—41no—
96C2×C4⋊C4×C113—41no—
97C2×C4⋊C4×C113—41no—
98C2×C4⋊C4×C113—41no—
99C2×C4⋊C4×C113—41no—
100C2×C4⋊C4×C113C2×C414yescomplemented
101C2×C4⋊C4×C113D414yes—
102C2×C22⋊C4×C113—22no—
103C2×C22⋊C4×C113—22no—
104C2×C22⋊C4×C113—22no—
105C2×C22⋊C4×C113—22no—
106C2×C22⋊C4×C113—22no—
107C2×C22⋊C4×C113—22no—
108C2×C22⋊C4×C113—22no—
109C2×C22⋊C4×C113—41no—
110C2×C22⋊C4×C113—41no—
111C2×C22⋊C4×C113—41no—
112C2×C22⋊C4×C113—41no—
113C2×C22⋊C4×C113—41no—
114C2×C22⋊C4×C113—41no—
115C2×C22⋊C4×C113C2×C414yes—
116C2×C22⋊C4×C113C2×C414yes—
117C2×C22⋊C4×C113C2×C414yes—
118C2×C22⋊C4×C113D414yes—
119C2×C22⋊C4×C113Q814yes—
120C2×C42×C113—22no—
121C2×C42×C113—22no—
122C2×C42×C113—41no—
123C2×C42×C113—41no—
124C2×C42×C113—41no—
125C2×C42×C113C2×C414yescomplemented
126#95×C113—22no—
127#95×C113—22no—
128#95×C113—22no—
129#95×C113—22no—
130#95×C113—22no—
131#95×C113—22no—
132#95×C113—22no—
133#95×C113—22no—
134#95×C113—22no—
135#95×C113—41no—
136#95×C113—41no—
137#95×C113—41no—
138#95×C113—41no—
139#95×C113—41no—
140#95×C113—41no—
141#95×C113—41no—
142#95×C113C2×C414yescomplemented
143#95×C113C2×C414yescomplemented
144C24×C113—21no—
145C24×C113—21no—
146C24×C113—21no—
147C24×C113—21no—
148C24×C113—21no—
149C24×C113—21no—
150C24×C113—21no—
151C24×C113—21no—
152C24×C113—21no—
153C24×C113—21no—
154C24×C113—21no—
155C24×C113—21no—
156C24×C113C22×C412yes—
157C24×C113C2×D412yes—
158C24×C113C2×Q812yes—
159C24×C113C2411yescharacteristic
160C22×C4×C113—21no—
161C22×C4×C113—21no—
162C22×C4×C113—21no—
163C22×C4×C113—21no—
164C22×C4×C113—21no—
165C22×C4×C113—21no—
166C22×C4×C113—21no—
167C22×C4×C113—21no—
168C22×C4×C113—21no—
169C22×C4×C113—21no—
170C22×C4×C113—21no—
171C22×C4×C113—21no—
172C22×C4×C113—21no—
173C22×C4×C113—21no—
174C22×C4×C113—21no—
175C22×C4×C113—21no—
176C22×C4×C113—21no—
177C22×C4×C113—21no—
178C22×C4×C113—21no—
179C22×C4×C113—21no—
180C22×C4×C113—21no—
181C22×C4×C113—21no—
182C22×C4×C113—21no—
183C22×C4×C113—21no—
184C22×C4×C113—21no—
185C22×C4×C113—21no—
186C22×C4×C113—21no—
187C22×C4×C113—21no—
188C22×C4×C113—21no—
189C22×C4×C113—21no—
190C22×C4×C113—21no—
191C22×C4×C113—21no—
192C22×C4×C113—21no—
193C22×C4×C113—21no—
194C22×C4×C113—21no—
195C22×C4×C113—21no—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113—21no—
206C22×C4×C113—21no—
207C22×C4×C113—21no—
208C22×C4×C113—21no—
209C22×C4×C113—21no—
210C22×C4×C113—21no—
211C22×C4×C113—21no—
212C22×C4×C113—21no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—21no—
217C22×C4×C113—21no—
218C22×C4×C113—21no—
219C22×C4×C113—21no—
220C22×C4×C113—21no—
221C22×C4×C113—21no—
222C22×C4×C113—21no—
223C22×C4×C113—21no—
224C22×C4×C113—21no—
225C22×C4×C113—21no—
226C22×C4×C113—21no—
227C22×C4×C113—21no—
228C22×C4×C113—21no—
229C22×C4×C113—21no—
230C22×C4×C113—21no—
231C22×C4×C113—21no—
232C22×C4×C113—21no—
233C22×C4×C113—21no—
234C22×C4×C113—21no—
235C22×C4×C113—21no—
236C22×C4×C113—21no—
237C22×C4×C113—21no—
238C22×C4×C113—21no—
239C22×C4×C113—21no—
240C22×C4×C113—21no—
241C22×C4×C113—21no—
242C22×C4×C113—44no—
243C22×C4×C113—44no—
244C22×C4×C113—44no—
245C22×C4×C113—44no—
246C22×C4×C113—44no—
247C22×C4×C113—44no—
248C22×C4×C113—44no—
249C22×C4×C113C22×C412yes—
250C22×C4×C113C22×C412yes—
251C22×C4×C113C22×C412yes—
252C22×C4×C113C22×C412yes—
253C22×C4×C113C22×C412yes—
254C22×C4×C113C22×C412yes—
255C22×C4×C113C2×D412yes—
256C22×C4×C113C2×D412yes—
257C22×C4×C113C2×D412yes—
258C22×C4×C113C2×D412yes—
259C22×C4×C113C2×D412yes—
260C22×C4×C113C2×Q812yes—
261C22×C4×C113C2×Q812yes—
262C22×C4×C113#4112yes—
263C22×C4×C113#4112yes—
264C22×C4×C113#4112yes—
265C4⋊C4×C113—28no—
266C4⋊C4×C113—44no—
267C4⋊C4×C113—44no—
268C4⋊C4×C113—44no—
269C4⋊C4×C113—44no—
270C4⋊C4×C113—44no—
271C4⋊C4×C113—44no—
272C4⋊C4×C113—44no—
273C22⋊C4×C113—28no—
274C22⋊C4×C113—44no—
275C22⋊C4×C113—44no—
276C22⋊C4×C113—44no—
277C22⋊C4×C113—44no—
278C22⋊C4×C113C4⋊C4116yescomplemented
279C42×C113—44no—
280C42×C113—44no—
281C23×C113—22no—
282C23×C113—22no—
283C23×C113—22no—
284C23×C113—22no—
285C23×C113—22no—
286C23×C113—22no—
287C23×C113—22no—
288C23×C113—22no—
289C23×C113—22no—
290C23×C113—22no—
291C23×C113—22no—
292C23×C113—22no—
293C23×C113—22no—
294C23×C113—22no—
295C23×C113—22no—
296C23×C113—22no—
297C23×C113—22no—
298C23×C113—22no—
299C23×C113—41no—
300C23×C113—41no—
301C23×C113—41no—
302C23×C113—41no—
303C23×C113—41no—
304C23×C113—41no—
305C23×C113—41no—
306C23×C113—41no—
307C23×C113—41no—
308C23×C113—41no—
309C23×C113—41no—
310C23×C113—41no—
311C23×C113—41no—
312C23×C113—41no—
313C23×C113—41no—
314C23×C113—41no—
315C23×C113C2×C4⋊C414yes—
316C23×C113C23×C411yescharacteristic
317C23×C113C22×D411yescharacteristic
318C23×C113C22×D411yescharacteristic
319C23×C113C22×Q811yescharacteristic
320C23×C113C2×#4111yescharacteristic
321C23×C113C2×#4111yescharacteristic
322C23×C113C2×#4111yescharacteristic
323C23×C113H(5,𝔽2)11yescharacteristic
324C23×C113H(5,𝔽2)11yescharacteristic
325C23×C113H(5,𝔽2)11yescharacteristic
326C23×C113H(5,𝔽2)11yescharacteristic
327C23×C113H(5,𝔽2)11yescharacteristic
328C23×C1132−1+411yescharacteristic
329C23×C1132−1+411yescharacteristic
330C23×C1132−1+411yescharacteristic
331C2×C4×C113—22no—
332C2×C4×C113—22no—
333C2×C4×C113—22no—
334C2×C4×C113—22no—
335C2×C4×C113—22no—
336C2×C4×C113—22no—
337C2×C4×C113—22no—
338C2×C4×C113—22no—
339C2×C4×C113—22no—
340C2×C4×C113—22no—
341C2×C4×C113—22no—
342C2×C4×C113—22no—
343C2×C4×C113—22no—
344C2×C4×C113—22no—
345C2×C4×C113—22no—
346C2×C4×C113—22no—
347C2×C4×C113—22no—
348C2×C4×C113—22no—
349C2×C4×C113—22no—
350C2×C4×C113—22no—
351C2×C4×C113—22no—
352C2×C4×C113—22no—
353C2×C4×C113—22no—
354C2×C4×C113—22no—
355C2×C4×C113—22no—
356C2×C4×C113—22no—
357C2×C4×C113—22no—
358C2×C4×C113—22no—
359C2×C4×C113—22no—
360C2×C4×C113—22no—
361C2×C4×C113—22no—
362C2×C4×C113—22no—
363C2×C4×C113—22no—
364C2×C4×C113—22no—
365C2×C4×C113—22no—
366C2×C4×C113—22no—
367C2×C4×C113—22no—
368C2×C4×C113—22no—
369C2×C4×C113—22no—
370C2×C4×C113—416no—
371C2×C4×C113—41no—
372C2×C4×C113—41no—
373C2×C4×C113—41no—
374C2×C4×C113—41no—
375C2×C4×C113—41no—
376C2×C4×C113—41no—
377C2×C4×C113—41no—
378C2×C4×C113—41no—
379C2×C4×C113—41no—
380C2×C4×C113—41no—
381C2×C4×C113—41no—
382C2×C4×C113—41no—
383C2×C4×C113—41no—
384C2×C4×C113—41no—
385C2×C4×C113—41no—
386C2×C4×C113—41no—
387C2×C4×C113—41no—
388C2×C4×C113—41no—
389C2×C4×C113—41no—
390C2×C4×C113—41no—
391C2×C4×C113—41no—
392C2×C4×C113—41no—
393C2×C4×C113—41no—
394C2×C4×C113—41no—
395C2×C4×C113—41no—
396C2×C4×C113—41no—
397C2×C4×C113—41no—
398C2×C4×C113—41no—
399C2×C4×C113—41no—
400C2×C4×C113—41no—
401C2×C4×C113—41no—
402C2×C4×C113—41no—
403C2×C4×C113—41no—
404C2×C4×C113—41no—
405C2×C4×C113—41no—
406C2×C4×C113—41no—
407C2×C4×C113—41no—
408C2×C4×C113—41no—
409C2×C4×C113—41no—
410C2×C4×C113—41no—
411C2×C4×C113—41no—
412C2×C4×C113—41no—
413C2×C4×C113—41no—
414C2×C4×C113—41no—
415C2×C4×C113—41no—
416C2×C4×C113—41no—
417C2×C4×C113—41no—
418C2×C4×C113—41no—
419C2×C4×C113—41no—
420C2×C4×C113—41no—
421C2×C4×C113—41no—
422C2×C4×C113—41no—
423C2×C4×C113—41no—
424C2×C4×C113—41no—
425C2×C4×C113—41no—
426C2×C4×C113—41no—
427C2×C4×C113C2×C4⋊C414yes—
428C2×C4×C113C2×C4⋊C414yes—
429C2×C4×C113C4×D414yes—
430C22×C113—24no—
431C22×C113—24no—
432C22×C113—24no—
433C22×C113—42no—
434C22×C113—42no—
435C22×C113—42no—
436C22×C113—42no—
437C22×C113—42no—
438C22×C113—42no—
439C22×C113—42no—
440C22×C113—42no—
441C22×C113—42no—
442C22×C113—42no—
443C22×C113—42no—
444C22×C113—42no—
445C22×C113C22×C4⋊C411yescharacteristic
446C22×C113C2×C4×D411yescharacteristic
447C22×C113C4×#4111yescharacteristic
448C22×C113#51811yescharacteristic
449C22×C113#52011yescharacteristic
450C22×C113#52011yescharacteristic
451C22×C113#52011yescharacteristic
452C22×C113#53411yescharacteristic
453C22×C113#53511yescharacteristic
454C22×C113#53611yescharacteristic
455C22×C113#53711yescharacteristic
456C22×C113#53811yescharacteristic
457C22×C113#53811yescharacteristic
458C22×C113#53911yescharacteristic
459C22×C113#53911yescharacteristic
460C22×C113#54111yescharacteristic
461C22×C113#54211yescharacteristic
462C22×C113#54411yescharacteristic
463C22×C113#54411yescharacteristic
464C22×C113D4211yescharacteristic
465C22×C113#54611yescharacteristic
466C22×C113#54611yescharacteristic
467C22×C113#54611yescharacteristic
468C22×C113#54711yescharacteristic
469C22×C113#54811yescharacteristic
470C22×C113D4×Q811yescharacteristic
471C22×C113#55411yescharacteristic
472C22×C113#55411yescharacteristic
473C22×C113#55411yescharacteristic
474C22×C113#55611yescharacteristic
475C22×C113#55911yescharacteristic
476C22×C113#56011yescharacteristic
477C22×C113#56211yescharacteristic
478C22×C113#56211yescharacteristic
479C22×C113#56311yescharacteristic
480C4×C113—24no—
481C4×C113—24no—
482C4×C113—24no—
483C4×C113—42no—
484C4×C113—42no—
485C4×C113—42no—
486C4×C113—42no—
487C4×C113—42no—
488C4×C113—42no—
489C4×C113—42no—
490C4×C113—81no—
491C4×C113—81no—
492C4×C113—81no—
493C4×C113—81no—
494#14442C11311yesmaximal, characteristic, direct product factor, Sylow
495C2×C113—44no—
496C2×C113#231711yescharacteristic
497C2×C113#232511yescharacteristic
498C2×C113#233411yescharacteristic
499C2×C113D4×C4⋊C411yescharacteristic
500C2×C113#234911yescharacteristic
501C2×C113#236711yescharacteristic
502C2×C113#237611yescharacteristic
503C2×C113#267811yescharacteristic
504C2×C113#268111yescharacteristic
505C2×C113#268911yescharacteristic
506C2×C113#270411yescharacteristic
507C2×C113#271011yescharacteristic
508C2×C113#272911yescharacteristic
509C2×C113#278811yescharacteristic
510C2×C113#280711yescharacteristic
511C2×#389C2×C11311yescharacteristic, complemented
512C2×#388C2×C11311yescharacteristic
513C2×#388C2×C11311yescharacteristic
514C2×#385C2×C11311yescharacteristic
515C2×#385C2×C11311yescharacteristic
516#1444C2×C11311yescharacteristic, complemented
517#1442C2×C11311yescharacteristic, complemented
518#1442C2×C11311yescharacteristic, complemented
519#1441C2×C11311yescharacteristic, complemented
520#1439C2×C11311yescharacteristic
521#1439C2×C11311yescharacteristic
522#1436C2×C11311yescharacteristic, complemented
523C4⋊#95C2×C11311yescharacteristic, complemented
524C4⋊#95C2×C11311yescharacteristic, complemented
525C22⋊#95C2×C11311yescharacteristic
526C113#1444211yescharacteristic, direct product factor, Sylow
527C24×C4C22×C11311yescharacteristic
528C22×C4⋊C4C22×C11311yescharacteristic
529C22×C4⋊C4C22×C11311yescharacteristic
530C22×C4⋊C4C22×C11311yescharacteristic
531C22×C4⋊C4C22×C11311yescharacteristic
532C22×C4⋊C4C22×C11311yescharacteristic
533C22×C4⋊C4C22×C11311yescharacteristic
534C22×C4⋊C4C22×C11311yescharacteristic
535C22×C4⋊C4C22×C11311yescharacteristic
536C22×C22⋊C4C22×C11311yescharacteristic
537C22×C22⋊C4C22×C11311yescharacteristic
538C22×C22⋊C4C22×C11311yescharacteristic
539C22×C22⋊C4C22×C11311yescharacteristic
540C22×C22⋊C4C22×C11311yescharacteristic
541C22×C22⋊C4C22×C11311yescharacteristic
542C22×C42C22×C11311yescharacteristic
543C22×C42C22×C11311yescharacteristic
544#389—24no—
545#388—24no—
546#388C4×C11318yescomplemented
547#385—24no—
548#385—24no—
549C2×#95C22×C11311yescharacteristic
550C2×#95C22×C11311yescharacteristic
551C2×#95C22×C11311yescharacteristic
552C2×#95C22×C11311yescharacteristic
553C2×#95C22×C11311yescharacteristic
554C2×#95C22×C11311yescharacteristic
555C2×#95C22×C11311yescharacteristic
556C2×#95C22×C11311yescharacteristic
557C2×#95C22×C11311yescharacteristic
558C2×#95C22×C11311yescharacteristic
559C2×#95C22×C11311yescharacteristic
560C2×#95C22×C11311yescharacteristic
561C2×#95C22×C11311yescharacteristic
562C2×#95C22×C11311yescharacteristic
563C2×#95C22×C11311yescharacteristic
564C2×#95C22×C11311yescharacteristic
565C2×#95C22×C11311yescharacteristic
566C2×#95C22×C11311yescharacteristic
567C25C23×C11311yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4C23×C11311yescharacteristic
576C23×C4C23×C11311yescharacteristic
577C23×C4C23×C11311yescharacteristic
578C23×C4C23×C11311yescharacteristic
579C23×C4C23×C11311yescharacteristic
580C23×C4C23×C11311yescharacteristic
581C23×C4C23×C11311yescharacteristic
582C23×C4C23×C11311yescharacteristic
583C23×C4C23×C11311yescharacteristic
584C23×C4C23×C11311yescharacteristic
585C23×C4C23×C11311yescharacteristic
586C23×C4C23×C11311yescharacteristic
587C23×C4C23×C11311yescharacteristic
588C23×C4C23×C11311yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4C2×C4×C11314yescomplemented
612C2×C4⋊C4D4×C11314yes—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4C2×C4×C11314yes—
627C2×C22⋊C4C2×C4×C11314yes—
628C2×C22⋊C4C2×C4×C11314yes—
629C2×C22⋊C4D4×C11314yes—
630C2×C22⋊C4Q8×C11314yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42C2×C4×C11314yescomplemented
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95C2×C4×C11314yescomplemented
654#95C2×C4×C11314yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C11312yes—
668C24C2×D4×C11312yes—
669C24C2×Q8×C11312yes—
670C24C24×C11311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
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—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
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—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C22×C4×C11312yes—
761C22×C4C22×C4×C11312yes—
762C22×C4C22×C4×C11312yes—
763C22×C4C22×C4×C11312yes—
764C22×C4C22×C4×C11312yes—
765C22×C4C22×C4×C11312yes—
766C22×C4C2×D4×C11312yes—
767C22×C4C2×D4×C11312yes—
768C22×C4C2×D4×C11312yes—
769C22×C4C2×D4×C11312yes—
770C22×C4C2×D4×C11312yes—
771C22×C4C2×Q8×C11312yes—
772C22×C4C2×Q8×C11312yes—
773C22×C4#41×C11312yes—
774C22×C4#41×C11312yes—
775C22×C4#41×C11312yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4C4⋊C4×C113116yescomplemented
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C11314yes—
827C23C23×C4×C11311yescharacteristic
828C23C22×D4×C11311yescharacteristic
829C23C22×D4×C11311yescharacteristic
830C23C22×Q8×C11311yescharacteristic
831C23C2×#41×C11311yescharacteristic
832C23C2×#41×C11311yescharacteristic
833C23C2×#41×C11311yescharacteristic
834C23H(5,𝔽2)×C11311yescharacteristic
835C23H(5,𝔽2)×C11311yescharacteristic
836C23H(5,𝔽2)×C11311yescharacteristic
837C23H(5,𝔽2)×C11311yescharacteristic
838C23H(5,𝔽2)×C11311yescharacteristic
839C232−1+4×C11311yescharacteristic
840C232−1+4×C11311yescharacteristic
841C232−1+4×C11311yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
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—22no—
880C2×C4—22no—
881C2×C4—416no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
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×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4C2×C4⋊C4×C11314yes—
939C2×C4C2×C4⋊C4×C11314yes—
940C2×C4C4×D4×C11314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C11311yescharacteristic
957C22C2×C4×D4×C11311yescharacteristic
958C22C4×#41×C11311yescharacteristic
959C22#518×C11311yescharacteristic
960C22#520×C11311yescharacteristic
961C22#520×C11311yescharacteristic
962C22#520×C11311yescharacteristic
963C22#534×C11311yescharacteristic
964C22#535×C11311yescharacteristic
965C22#536×C11311yescharacteristic
966C22#537×C11311yescharacteristic
967C22#538×C11311yescharacteristic
968C22#538×C11311yescharacteristic
969C22#539×C11311yescharacteristic
970C22#539×C11311yescharacteristic
971C22#541×C11311yescharacteristic
972C22#542×C11311yescharacteristic
973C22#544×C11311yescharacteristic
974C22#544×C11311yescharacteristic
975C22D42×C11311yescharacteristic
976C22#546×C11311yescharacteristic
977C22#546×C11311yescharacteristic
978C22#546×C11311yescharacteristic
979C22#547×C11311yescharacteristic
980C22#548×C11311yescharacteristic
981C22D4×Q8×C11311yescharacteristic
982C22#554×C11311yescharacteristic
983C22#554×C11311yescharacteristic
984C22#554×C11311yescharacteristic
985C22#556×C11311yescharacteristic
986C22#559×C11311yescharacteristic
987C22#560×C11311yescharacteristic
988C22#562×C11311yescharacteristic
989C22#562×C11311yescharacteristic
990C22#563×C11311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C113×#231711yescharacteristic
1007C2C113×#232511yescharacteristic
1008C2C113×#233411yescharacteristic
1009C2D4×C4⋊C4×C11311yescharacteristic
1010C2C113×#234911yescharacteristic
1011C2C113×#236711yescharacteristic
1012C2C113×#237611yescharacteristic
1013C2C113×#267811yescharacteristic
1014C2C113×#268111yescharacteristic
1015C2C113×#268911yescharacteristic
1016C2C113×#270411yescharacteristic
1017C2C113×#271011yescharacteristic
1018C2C113×#272911yescharacteristic
1019C2C113×#278811yescharacteristic
1020C2C113×#280711yescharacteristic
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
1. C2×#389×C113C2semidirect
6. C113×#1444C2semidirect
7. C113×#1442C2semidirect
8. C113×#1442C2semidirect
9. C113×#1441C2semidirect
12. C113×#1436C2semidirect
13. C113×C4⋊#95C2semidirect
14. C113×C4⋊#95C2semidirect
35. #388×C113C4semidirect
100. C2×C4⋊C4×C113C2×C4semidirect
125. C2×C42×C113C2×C4semidirect
142. #95×C113C2×C4semidirect
143. #95×C113C2×C4semidirect
278. C22⋊C4×C113C4⋊C4semidirect
494. #14442C113direct (N × H)
511. C2×#389C2×C113semidirect
516. #1444C2×C113semidirect
517. #1442C2×C113semidirect
518. #1442C2×C113semidirect
519. #1441C2×C113semidirect
522. #1436C2×C113semidirect
523. C4⋊#95C2×C113semidirect
524. C4⋊#95C2×C113semidirect
526. C113#14442direct (N × H)
546. #388C4×C113semidirect
611. C2×C4⋊C4C2×C4×C113semidirect
636. C2×C42C2×C4×C113semidirect
653. #95C2×C4×C113semidirect
654. #95C2×C4×C113semidirect
789. C22⋊C4C4⋊C4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1132
C2×#388×C1132
C2×#385×C1132
C113×#14442
C113×#14422
C113×#14412
C113×#14392
C113×#14362
C113×C4⋊#952
C113×C22⋊#952
#14442113