Finite Group Databasebeta

← C113×#17559 #43285579

Subgroups — C113×#17559 #43285579

Order 28928.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C113C211yesmaximal, characteristic
2C2×#407×C113C211yesmaximal, characteristic, complemented
3C113×#2280C211yesmaximal, characteristic, complemented
4C113×#1513C214yesmaximal, complemented
5C113×#1511C212yesmaximal, complemented
6C113×#1510C212yesmaximal, complemented
7C113×#1501C214yesmaximal, complemented
8C22×#41×C113C411yescharacteristic, complemented
9C24×C4×C113C2211yescharacteristic
10C22×M16×C113—21no—
11#525×C113—21no—
12#525×C113—21no—
13#525×C113—21no—
14#525×C113—21no—
15#525×C113C412yescomplemented
16#525×C113C412yescomplemented
17#525×C113C2212yes—
18#525×C113C2212yes—
19C2×#123×C113—21no—
20C2×C22⋊Q8×C113C411yescharacteristic, complemented
21C2×C22⋊Q8×C113C2211yescharacteristic
22C2×#121×C113C411yescharacteristic, complemented
23C2×#121×C113C2211yescharacteristic
24C2×#120×C113—21no—
25C2×C4×D4×C113—21no—
26C2×C4×D4×C113—21no—
27C2×#117×C113—21no—
28C2×#117×C113C411yescharacteristic, complemented
29#407×C113—21no—
30#407×C113—21no—
31#407×C113C2212yes—
32#407×C113C2212yescomplemented
33C2×C22⋊C8×C113—21no—
34C2×C22⋊C8×C113C2212yescomplemented
35#381×C113C2212yes—
36#380×C113—21no—
37#380×C113C2212yescomplemented
38#379×C113—21no—
39C4×C22⋊C4×C113—21no—
40C4×C22⋊C4×C113C2212yescomplemented
41#328×C113C2218yescomplemented
42#327×C113C2218yescomplemented
43C25×C113D411yescharacteristic
44C2×#41×C113—21no—
45C2×#41×C113—21no—
46C2×#41×C113—44no—
47C2×#41×C113C2×C412yes—
48C2×#41×C113C2×C412yes—
49C22×Q8×C113C2×C411yescharacteristic
50C22×D4×C113—21no—
51C22×D4×C113—21no—
52C22×D4×C113—21no—
53C22×D4×C113C2×C411yescharacteristic
54C23×C4×C113—21no—
55C23×C4×C113—44no—
56C23×C4×C113C2×C411yescharacteristic
57C23×C4×C113C2×C411yescharacteristic
58C23×C4×C113C2×C411yescharacteristic
59C23×C4×C113C2×C411yescharacteristic
60C23×C4×C113D411yescharacteristic
61C23×C4×C113D411yescharacteristic
62C23×C4×C113D411yescharacteristic
63C23×C4×C113D411yescharacteristic
64C23×C4×C113D411yescharacteristic
65C23×C4×C113D411yescharacteristic
66C23×C4×C113D411yescharacteristic
67C23×C4×C113C2311yescharacteristic
68C23×C4×C113C2311yescharacteristic
69C23×C4×C113C2311yescharacteristic
70C2×M16×C113—22no—
71C2×M16×C113—22no—
72C2×M16×C113—44no—
73C22×C8×C113—22no—
74#123×C113—22no—
75#123×C113—22no—
76#123×C113—22no—
77#123×C113—22no—
78C22⋊Q8×C113—21no—
79C22⋊Q8×C113—21no—
80C22⋊Q8×C113—21no—
81C22⋊Q8×C113—21no—
82C22⋊Q8×C113C2×C412yes—
83C22⋊Q8×C113C2×C412yes—
84C22⋊Q8×C113C2×C412yes—
85C22⋊Q8×C113C2312yes—
86#121×C113—21no—
87#121×C113—21no—
88#121×C113—21no—
89#121×C113—21no—
90#121×C113C2×C412yes—
91#121×C113C2×C412yes—
92#121×C113C2×C412yes—
93#121×C113C2312yes—
94#120×C113—22no—
95#120×C113—22no—
96#120×C113—22no—
97#120×C113—22no—
98C4×D4×C113—22no—
99C4×D4×C113—22no—
100C4×D4×C113—22no—
101C4×D4×C113—22no—
102C4×D4×C113—22no—
103C4×D4×C113—22no—
104C4×D4×C113—22no—
105C4×D4×C113—22no—
106#117×C113—21no—
107#117×C113—21no—
108#117×C113—44no—
109#117×C113C2×C412yes—
110#117×C113C2×C412yes—
111C2×C4⋊C4×C113—21no—
112C2×C4⋊C4×C113—21no—
113C2×C4⋊C4×C113—22no—
114C2×C4⋊C4×C113C2×C411yescharacteristic
115C2×C4⋊C4×C113C2×C411yescharacteristic
116C2×C22⋊C4×C113—21no—
117C2×C22⋊C4×C113—21no—
118C2×C22⋊C4×C113—21no—
119C2×C22⋊C4×C113—21no—
120C2×C22⋊C4×C113—21no—
121C2×C22⋊C4×C113—22no—
122C2×C22⋊C4×C113—22no—
123C2×C22⋊C4×C113—22no—
124C2×C42×C113—21no—
125C2×C42×C113—22no—
126C22⋊C8×C113—22no—
127C22⋊C8×C113—22no—
128C22⋊C8×C113—22no—
129C22⋊C8×C113C2314yes—
130#95×C113—22no—
131#95×C113C2314yes—
132C24×C113—21no—
133C24×C113—42no—
134C24×C113—42no—
135C24×C113—42no—
136C24×C113C22⋊C411yescharacteristic
137C24×C113C22⋊C411yescharacteristic
138C24×C113C22⋊C411yescharacteristic
139C24×C113C22⋊C411yescharacteristic
140C24×C113C2×D411yescharacteristic
141C24×C113C2×D411yescharacteristic
142C24×C113C2×D411yescharacteristic
143#41×C113—44no—
144#41×C113—44no—
145#41×C113—44no—
146#41×C113—44no—
147C2×Q8×C113—21no—
148C2×Q8×C113—42no—
149C2×Q8×C113C22×C412yes—
150C2×D4×C113—22no—
151C2×D4×C113—22no—
152C2×D4×C113—22no—
153C2×D4×C113—22no—
154C2×D4×C113—22no—
155C2×D4×C113—22no—
156C2×D4×C113—21no—
157C2×D4×C113—42no—
158C2×D4×C113—44no—
159C2×D4×C113—44no—
160C2×D4×C113—44no—
161C2×D4×C113C22×C412yes—
162C22×C4×C113—24no—
163C22×C4×C113—24no—
164C22×C4×C113—24no—
165C22×C4×C113—21no—
166C22×C4×C113—21no—
167C22×C4×C113—21no—
168C22×C4×C113—22no—
169C22×C4×C113—22no—
170C22×C4×C113—24no—
171C22×C4×C113—42no—
172C22×C4×C113—42no—
173C22×C4×C113—42no—
174C22×C4×C113—42no—
175C22×C4×C113—42no—
176C22×C4×C113—42no—
177C22×C4×C113—42no—
178C22×C4×C113—42no—
179C22×C4×C113—42no—
180C22×C4×C113—42no—
181C22×C4×C113—42no—
182C22×C4×C113—44no—
183C22×C4×C113C22⋊C411yescharacteristic
184C22×C4×C113C22⋊C411yescharacteristic
185C22×C4×C113C22⋊C411yescharacteristic
186C22×C4×C113C22⋊C411yescharacteristic
187C22×C4×C113C22⋊C411yescharacteristic
188C22×C4×C113C22⋊C411yescharacteristic
189C22×C4×C113C22⋊C411yescharacteristic
190C22×C4×C113C22⋊C411yescharacteristic
191C22×C4×C113C22⋊C411yescharacteristic
192C22×C4×C113C22⋊C411yescharacteristic
193C22×C4×C113C22⋊C411yescharacteristic
194C22×C4×C113C22⋊C411yescharacteristic
195C22×C4×C113C22×C411yescharacteristic
196C22×C4×C113C22×C411yescharacteristic
197C22×C4×C113C22×C411yescharacteristic
198C22×C4×C113C22×C411yescharacteristic
199C22×C4×C113C22×C411yescharacteristic
200C22×C4×C113C22×C411yescharacteristic
201C22×C4×C113C2×D411yescharacteristic
202C22×C4×C113C2×D411yescharacteristic
203C22×C4×C113C2×D411yescharacteristic
204C22×C4×C113C2×D411yescharacteristic
205C22×C4×C113C2×D411yescharacteristic
206C22×C4×C113C2×D411yescharacteristic
207C22×C4×C113C2×D411yescharacteristic
208C22×C4×C113C2×D411yescharacteristic
209C22×C4×C113C2×D411yescharacteristic
210C22×C4×C113C2411yescharacteristic
211M16×C113—44no—
212M16×C113—44no—
213C2×C8×C113—24no—
214C2×C8×C113—44no—
215C4⋊C4×C113—22no—
216C4⋊C4×C113—22no—
217C4⋊C4×C113—22no—
218C4⋊C4×C113—21no—
219C4⋊C4×C113—21no—
220C4⋊C4×C113—22no—
221C4⋊C4×C113—44no—
222C4⋊C4×C113C22×C412yes—
223C4⋊C4×C113C22×C412yes—
224C22⋊C4×C113—22no—
225C22⋊C4×C113—22no—
226C22⋊C4×C113—22no—
227C22⋊C4×C113—22no—
228C22⋊C4×C113—22no—
229C22⋊C4×C113—22no—
230C22⋊C4×C113—22no—
231C22⋊C4×C113—22no—
232C22⋊C4×C113—22no—
233C22⋊C4×C113—22no—
234C22⋊C4×C113—44no—
235C22⋊C4×C113—44no—
236C22⋊C4×C113—44no—
237C42×C113—22no—
238C42×C113—22no—
239C42×C113—44no—
240C23×C113—22no—
241C23×C113—22no—
242C23×C113—22no—
243C23×C113—22no—
244C23×C113—22no—
245C23×C113—22no—
246C23×C113—22no—
247C23×C113—22no—
248C23×C113—22no—
249C23×C113—22no—
250C23×C113—41no—
251C23×C113—41no—
252C23×C113—41no—
253C23×C113—41no—
254C23×C113—41no—
255C23×C113—41no—
256C23×C113—41no—
257C23×C113—41no—
258C23×C113—41no—
259C23×C113—41no—
260C23×C113—41no—
261C23×C113—41no—
262C23×C113—42no—
263C23×C113—42no—
264C23×C113—416no—
265C23×C113—42no—
266C23×C113C2×C22⋊C411yescharacteristic
267C23×C113C2×C22⋊C411yescharacteristic
268C23×C113C2×C22⋊C411yescharacteristic
269C23×C113C2×C22⋊C411yescharacteristic
270C23×C113C2×C22⋊C411yescharacteristic
271C23×C113C2×C22⋊C411yescharacteristic
272C23×C113C22×D411yescharacteristic
273Q8×C113—42no—
274Q8×C113—42no—
275D4×C113—42no—
276D4×C113—42no—
277D4×C113—44no—
278D4×C113—44no—
279D4×C113—44no—
280D4×C113—44no—
281D4×C113—44no—
282D4×C113—44no—
283C2×C4×C113—22no—
284C2×C4×C113—22no—
285C2×C4×C113—22no—
286C2×C4×C113—22no—
287C2×C4×C113—22no—
288C2×C4×C113—22no—
289C2×C4×C113—22no—
290C2×C4×C113—22no—
291C2×C4×C113—22no—
292C2×C4×C113—22no—
293C2×C4×C113—22no—
294C2×C4×C113—22no—
295C2×C4×C113—22no—
296C2×C4×C113—22no—
297C2×C4×C113—22no—
298C2×C4×C113—22no—
299C2×C4×C113—22no—
300C2×C4×C113—22no—
301C2×C4×C113—41no—
302C2×C4×C113—41no—
303C2×C4×C113—41no—
304C2×C4×C113—41no—
305C2×C4×C113—41no—
306C2×C4×C113—41no—
307C2×C4×C113—41no—
308C2×C4×C113—41no—
309C2×C4×C113—41no—
310C2×C4×C113—41no—
311C2×C4×C113—41no—
312C2×C4×C113—41no—
313C2×C4×C113—42no—
314C2×C4×C113—42no—
315C2×C4×C113—42no—
316C2×C4×C113—44no—
317C2×C4×C113—44no—
318C2×C4×C113—44no—
319C2×C4×C113—44no—
320C2×C4×C113—44no—
321C2×C4×C113#9914yes—
322C2×C4×C113C2×C22⋊C411yescharacteristic
323C2×C4×C113C2×C22⋊C411yescharacteristic
324C2×C4×C113C2×C22⋊C411yescharacteristic
325C2×C4×C113C2×C22⋊C411yescharacteristic
326C2×C4×C113C2×C22⋊C411yescharacteristic
327C2×C4×C113C2×C22⋊C411yescharacteristic
328C2×C4×C113C23×C411yescharacteristic
329C2×C4×C113C22×D411yescharacteristic
330C8×C113—44no—
331C22×C113—21no—
332C22×C113—21no—
333C22×C113—21no—
334C22×C113—21no—
335C22×C113—21no—
336C22×C113—21no—
337C22×C113—21no—
338C22×C113—21no—
339C22×C113—21no—
340C22×C113—21no—
341C22×C113—21no—
342C22×C113—21no—
343C22×C113—21no—
344C22×C113—21no—
345C22×C113—21no—
346C22×C113—21no—
347C22×C113—21no—
348C22×C113—21no—
349C22×C113—44no—
350C22×C113—44no—
351C22×C113—44no—
352C22×C113—44no—
353C22×C113—44no—
354C22×C113—44no—
355C22×C113—44no—
356C22×C113—42no—
357C22×C113—42no—
358C22×C113—42no—
359C22×C113—84no—
360C22×C113C2×#9912yes—
361C22×C113#42112yes—
362C22×C113C22×C22⋊C411yescharacteristic
363C22×C113#57512yes—
364C4×C113—21no—
365C4×C113—21no—
366C4×C113—21no—
367C4×C113—21no—
368C4×C113—21no—
369C4×C113—21no—
370C4×C113—42no—
371C4×C113—42no—
372C4×C113—42no—
373C4×C113—84no—
374C4×C113C2×#9912yes—
375C4×C113C2×#9912yes—
376#17559C11311yesmaximal, characteristic, direct product factor, Sylow
377C2×C113—22no—
378C2×C113—22no—
379C2×C113—22no—
380C2×C113—41no—
381C2×C113—41no—
382C2×C113—41no—
383C2×C113—41no—
384C2×C113—82no—
385C2×C113C22×#9911yescharacteristic
386C2×C113#289611yescharacteristic
387C2×C113C2×#42111yescharacteristic
388C2×#525C2×C11311yescharacteristic
389C2×#407C2×C11311yescharacteristic, complemented
390#2280C2×C11311yescharacteristic, complemented
391#1513C2×C11314yescomplemented
392#1511C2×C11312yescomplemented
393#1510C2×C11312yescomplemented
394#1501C2×C11314yescomplemented
395C113#1755911yescharacteristic, direct product factor, Sylow
396C22×#41C4×C11311yescharacteristic, complemented
397C24×C4C22×C11311yescharacteristic
398C22×M16—21no—
399#525—21no—
400#525—21no—
401#525—21no—
402#525—21no—
403#525C4×C11312yescomplemented
404#525C4×C11312yescomplemented
405#525C22×C11312yes—
406#525C22×C11312yes—
407C2×#123—21no—
408C2×C22⋊Q8C4×C11311yescharacteristic, complemented
409C2×C22⋊Q8C22×C11311yescharacteristic
410C2×#121C4×C11311yescharacteristic, complemented
411C2×#121C22×C11311yescharacteristic
412C2×#120—21no—
413C2×C4×D4—21no—
414C2×C4×D4—21no—
415C2×#117—21no—
416C2×#117C4×C11311yescharacteristic, complemented
417#407—21no—
418#407—21no—
419#407C22×C11312yes—
420#407C22×C11312yescomplemented
421C2×C22⋊C8—21no—
422C2×C22⋊C8C22×C11312yescomplemented
423#381C22×C11312yes—
424#380—21no—
425#380C22×C11312yescomplemented
426#379—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4C22×C11312yescomplemented
429#328C22×C11318yescomplemented
430#327C22×C11318yescomplemented
431C25D4×C11311yescharacteristic
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—44no—
435C2×#41C2×C4×C11312yes—
436C2×#41C2×C4×C11312yes—
437C22×Q8C2×C4×C11311yescharacteristic
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C2×C4×C11311yescharacteristic
442C23×C4—21no—
443C23×C4—44no—
444C23×C4C2×C4×C11311yescharacteristic
445C23×C4C2×C4×C11311yescharacteristic
446C23×C4C2×C4×C11311yescharacteristic
447C23×C4C2×C4×C11311yescharacteristic
448C23×C4D4×C11311yescharacteristic
449C23×C4D4×C11311yescharacteristic
450C23×C4D4×C11311yescharacteristic
451C23×C4D4×C11311yescharacteristic
452C23×C4D4×C11311yescharacteristic
453C23×C4D4×C11311yescharacteristic
454C23×C4D4×C11311yescharacteristic
455C23×C4C23×C11311yescharacteristic
456C23×C4C23×C11311yescharacteristic
457C23×C4C23×C11311yescharacteristic
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—44no—
461C22×C8—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—22no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8C2×C4×C11312yes—
471C22⋊Q8C2×C4×C11312yes—
472C22⋊Q8C2×C4×C11312yes—
473C22⋊Q8C23×C11312yes—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121C2×C4×C11312yes—
479#121C2×C4×C11312yes—
480#121C2×C4×C11312yes—
481#121C23×C11312yes—
482#120—22no—
483#120—22no—
484#120—22no—
485#120—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494#117—21no—
495#117—21no—
496#117—44no—
497#117C2×C4×C11312yes—
498#117C2×C4×C11312yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4C2×C4×C11311yescharacteristic
503C2×C4⋊C4C2×C4×C11311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C42—21no—
513C2×C42—22no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8C23×C11314yes—
518#95—22no—
519#95C23×C11314yes—
520C24—21no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24C22⋊C4×C11311yescharacteristic
525C24C22⋊C4×C11311yescharacteristic
526C24C22⋊C4×C11311yescharacteristic
527C24C22⋊C4×C11311yescharacteristic
528C24C2×D4×C11311yescharacteristic
529C24C2×D4×C11311yescharacteristic
530C24C2×D4×C11311yescharacteristic
531#41—44no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—42no—
537C2×Q8C22×C4×C11312yes—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4C22×C4×C11312yes—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—44no—
571C22×C4C22⋊C4×C11311yescharacteristic
572C22×C4C22⋊C4×C11311yescharacteristic
573C22×C4C22⋊C4×C11311yescharacteristic
574C22×C4C22⋊C4×C11311yescharacteristic
575C22×C4C22⋊C4×C11311yescharacteristic
576C22×C4C22⋊C4×C11311yescharacteristic
577C22×C4C22⋊C4×C11311yescharacteristic
578C22×C4C22⋊C4×C11311yescharacteristic
579C22×C4C22⋊C4×C11311yescharacteristic
580C22×C4C22⋊C4×C11311yescharacteristic
581C22×C4C22⋊C4×C11311yescharacteristic
582C22×C4C22⋊C4×C11311yescharacteristic
583C22×C4C22×C4×C11311yescharacteristic
584C22×C4C22×C4×C11311yescharacteristic
585C22×C4C22×C4×C11311yescharacteristic
586C22×C4C22×C4×C11311yescharacteristic
587C22×C4C22×C4×C11311yescharacteristic
588C22×C4C22×C4×C11311yescharacteristic
589C22×C4C2×D4×C11311yescharacteristic
590C22×C4C2×D4×C11311yescharacteristic
591C22×C4C2×D4×C11311yescharacteristic
592C22×C4C2×D4×C11311yescharacteristic
593C22×C4C2×D4×C11311yescharacteristic
594C22×C4C2×D4×C11311yescharacteristic
595C22×C4C2×D4×C11311yescharacteristic
596C22×C4C2×D4×C11311yescharacteristic
597C22×C4C2×D4×C11311yescharacteristic
598C22×C4C24×C11311yescharacteristic
599M16—44no—
600M16—44no—
601C2×C8—24no—
602C2×C8—44no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—22no—
609C4⋊C4—44no—
610C4⋊C4C22×C4×C11312yes—
611C4⋊C4C22×C4×C11312yes—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C42—22no—
626C42—22no—
627C42—44no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—42no—
651C23—42no—
652C23—416no—
653C23—42no—
654C23C2×C22⋊C4×C11311yescharacteristic
655C23C2×C22⋊C4×C11311yescharacteristic
656C23C2×C22⋊C4×C11311yescharacteristic
657C23C2×C22⋊C4×C11311yescharacteristic
658C23C2×C22⋊C4×C11311yescharacteristic
659C23C2×C22⋊C4×C11311yescharacteristic
660C23C22×D4×C11311yescharacteristic
661Q8—42no—
662Q8—42no—
663D4—42no—
664D4—42no—
665D4—44no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—44no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
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—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4#99×C11314yes—
710C2×C4C2×C22⋊C4×C11311yescharacteristic
711C2×C4C2×C22⋊C4×C11311yescharacteristic
712C2×C4C2×C22⋊C4×C11311yescharacteristic
713C2×C4C2×C22⋊C4×C11311yescharacteristic
714C2×C4C2×C22⋊C4×C11311yescharacteristic
715C2×C4C2×C22⋊C4×C11311yescharacteristic
716C2×C4C23×C4×C11311yescharacteristic
717C2×C4C22×D4×C11311yescharacteristic
718C8—44no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22C2×#99×C11312yes—
749C22#421×C11312yes—
750C22C22×C22⋊C4×C11311yescharacteristic
751C22#575×C11312yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—84no—
762C4C2×#99×C11312yes—
763C4C2×#99×C11312yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—82no—
772C2C22×#99×C11311yescharacteristic
773C2C113×#289611yescharacteristic
774C2C2×#421×C11311yescharacteristic
subgroupG/H
centerC2×C4×C113C2×C22⋊C4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
socleC22×C113C22×C22⋊C4
prime radicalC2×#525×C113C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C113 ◁ C24×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#407×C113C2semidirect
3. C113×#2280C2semidirect
4. C113×#1513C2semidirect
5. C113×#1511C2semidirect
6. C113×#1510C2semidirect
7. C113×#1501C2semidirect
8. C22×#41×C113C4semidirect
15. #525×C113C4semidirect
16. #525×C113C4semidirect
20. C2×C22⋊Q8×C113C4semidirect
22. C2×#121×C113C4semidirect
28. C2×#117×C113C4semidirect
32. #407×C113C22semidirect
34. C2×C22⋊C8×C113C22semidirect
37. #380×C113C22semidirect
40. C4×C22⋊C4×C113C22semidirect
41. #328×C113C22semidirect
42. #327×C113C22semidirect
376. #17559C113direct (N × H)
389. C2×#407C2×C113semidirect
390. #2280C2×C113semidirect
391. #1513C2×C113semidirect
392. #1511C2×C113semidirect
393. #1510C2×C113semidirect
394. #1501C2×C113semidirect
395. C113#17559direct (N × H)
396. C22×#41C4×C113semidirect
403. #525C4×C113semidirect
404. #525C4×C113semidirect
408. C2×C22⋊Q8C4×C113semidirect
410. C2×#121C4×C113semidirect
416. C2×#117C4×C113semidirect
420. #407C22×C113semidirect
422. C2×C22⋊C8C22×C113semidirect
425. #380C22×C113semidirect
428. C4×C22⋊C4C22×C113semidirect
429. #328C22×C113semidirect
430. #327C22×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1132
C2×#407×C1132
C113×#22802
C113×#15132
C113×#15112
C113×#15102
C113×#15012
#17559113