Finite Group Databasebeta

← C113×#17381 #43285401

Subgroups — C113×#17381 #43285401

Order 28928.

1446 conjugacy classes of subgroups.

The subgroup lattice has 766 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
3C22×C22⋊C8×C113C211yesmaximal, characteristic, complemented
4C113×#1472C212yesmaximal, complemented
5C113×#1471C212yesmaximal, complemented
6C113×#1468C214yesmaximal, complemented
7C113×#1459C214yesmaximal, complemented
8C22×#41×C113C411yescharacteristic
9C24×C4×C113C2211yescharacteristic
10C22×M16×C113—21no—
11C23×C8×C113—21no—
12#525×C113—21no—
13#525×C113—21no—
14#525×C113—21no—
15#525×C113—21no—
16#525×C113—21no—
17#525×C113—21no—
18#525×C113—21no—
19#525×C113—21no—
20C2×#123×C113C2212yes—
21C2×C22⋊Q8×C113C411yescharacteristic
22C2×C22⋊Q8×C113C2211yescharacteristic
23C2×#121×C113C411yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×#120×C113C412yes—
26C2×C4×D4×C113C412yes—
27C2×C4×D4×C113C2212yes—
28C2×#117×C113C411yescharacteristic
29#407×C113—21no—
30#407×C113—21no—
31#407×C113C2212yes—
32#407×C113C2212yes—
33C2×C22⋊C8×C113—21no—
34C2×C22⋊C8×C113—21no—
35C2×C22⋊C8×C113—21no—
36C2×C22⋊C8×C113—21no—
37C2×C22⋊C8×C113C2212yes—
38C2×C22⋊C8×C113C2212yes—
39C2×C22⋊C8×C113C2212yes—
40C2×C22⋊C8×C113C2212yes—
41#324×C113C2218yescomplemented
42#323×C113C2218yescomplemented
43C25×C113C2×C411yescharacteristic
44C2×#41×C113—21no—
45C2×#41×C113—21no—
46C2×#41×C113—21no—
47C2×#41×C113—21no—
48C2×#41×C113—44no—
49C22×Q8×C113C2×C411yescharacteristic
50C22×D4×C113C2×C412yes—
51C22×D4×C113C2×C412yes—
52C22×D4×C113C2×C412yes—
53C22×D4×C113C2×C411yescharacteristic
54C23×C4×C113—44no—
55C23×C4×C113C2×C411yescharacteristic
56C23×C4×C113C2×C412yes—
57C23×C4×C113C2×C411yescharacteristic
58C23×C4×C113C2×C411yescharacteristic
59C23×C4×C113D411yescharacteristic
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—
74C22×C8×C113—22no—
75C22×C8×C113—22no—
76C22×C8×C113—22no—
77C22×C8×C113—44no—
78#123×C113—22no—
79#123×C113—22no—
80#123×C113—22no—
81#123×C113—22no—
82C22⋊Q8×C113—21no—
83C22⋊Q8×C113—21no—
84C22⋊Q8×C113—21no—
85C22⋊Q8×C113—21no—
86C22⋊Q8×C113—21no—
87C22⋊Q8×C113—21no—
88C22⋊Q8×C113—21no—
89C22⋊Q8×C113—21no—
90#121×C113—21no—
91#121×C113—21no—
92#121×C113—21no—
93#121×C113—21no—
94#121×C113—21no—
95#121×C113—21no—
96#121×C113—21no—
97#121×C113—21no—
98#120×C113—22no—
99#120×C113—22no—
100#120×C113—22no—
101#120×C113—22no—
102C4×D4×C113—22no—
103C4×D4×C113—22no—
104C4×D4×C113—22no—
105C4×D4×C113—22no—
106C4×D4×C113—22no—
107C4×D4×C113—22no—
108C4×D4×C113—22no—
109C4×D4×C113—22no—
110#117×C113—21no—
111#117×C113—21no—
112#117×C113—21no—
113#117×C113—21no—
114C2×C4⋊C4×C113C2×C411yescharacteristic
115C2×C4⋊C4×C113C2×C411yescharacteristic
116C2×C4⋊C4×C113C2×C412yes—
117C2×C4⋊C4×C113C2312yes—
118C2×C22⋊C4×C113C2×C412yes—
119C2×C22⋊C4×C113C2×C412yes—
120C2×C22⋊C4×C113C2×C412yes—
121C2×C22⋊C4×C113C2×C412yes—
122C2×C22⋊C4×C113C2312yes—
123C2×C42×C113C2×C412yes—
124C22⋊C8×C113—22no—
125C22⋊C8×C113—22no—
126C22⋊C8×C113—22no—
127C22⋊C8×C113—22no—
128C22⋊C8×C113—22no—
129C22⋊C8×C113—22no—
130C22⋊C8×C113C2314yes—
131C22⋊C8×C113C2314yes—
132C24×C113—24no—
133C24×C113—42no—
134C24×C113—42no—
135C24×C113C22⋊C411yescharacteristic
136C24×C113C22⋊C411yescharacteristic
137C24×C113C22⋊C411yescharacteristic
138C24×C113C22⋊C411yescharacteristic
139C24×C113C22×C411yescharacteristic
140C24×C113C22×C411yescharacteristic
141C24×C113C22×C412yes—
142C24×C113C22×C411yescharacteristic
143#41×C113—44no—
144#41×C113—44no—
145#41×C113—44no—
146#41×C113—44no—
147C2×Q8×C113—21no—
148C2×Q8×C113—21no—
149C2×Q8×C113—42no—
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—28no—
157C2×D4×C113—21no—
158C2×D4×C113—21no—
159C2×D4×C113—42no—
160C2×D4×C113—44no—
161C2×D4×C113—44no—
162C22×C4×C113—24no—
163C22×C4×C113—24no—
164C22×C4×C113—24no—
165C22×C4×C113—22no—
166C22×C4×C113—22no—
167C22×C4×C113—42no—
168C22×C4×C113—42no—
169C22×C4×C113—42no—
170C22×C4×C113—42no—
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—44no—
179C22×C4×C113C22⋊C411yescharacteristic
180C22×C4×C113C22⋊C411yescharacteristic
181C22×C4×C113C22⋊C411yescharacteristic
182C22×C4×C113C22⋊C411yescharacteristic
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×C412yes—
192C22×C4×C113C22×C411yescharacteristic
193C22×C4×C113C22×C411yescharacteristic
194C22×C4×C113C22×C412yes—
195C22×C4×C113C22×C412yes—
196C22×C4×C113C22×C411yescharacteristic
197C22×C4×C113C2×D411yescharacteristic
198C22×C4×C113C2×D411yescharacteristic
199C22×C4×C113C2×D411yescharacteristic
200C22×C4×C113C2×D411yescharacteristic
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×C113C2411yescharacteristic
210M16×C113—44no—
211M16×C113—44no—
212C2×C8×C113—24no—
213C2×C8×C113—24no—
214C2×C8×C113—44no—
215C2×C8×C113—44no—
216C2×C8×C113—44no—
217C2×C8×C113—44no—
218C4⋊C4×C113—21no—
219C4⋊C4×C113—21no—
220C4⋊C4×C113—21no—
221C4⋊C4×C113—21no—
222C4⋊C4×C113—22no—
223C4⋊C4×C113—22no—
224C4⋊C4×C113—22no—
225C4⋊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—22no—
235C22⋊C4×C113—22no—
236C42×C113—22no—
237C42×C113—22no—
238C23×C113—22no—
239C23×C113—22no—
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—22no—
251C23×C113—24no—
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—416no—
261C23×C113—42no—
262C23×C113—42no—
263C23×C113C2×C22⋊C411yescharacteristic
264C23×C113C2×C22⋊C411yescharacteristic
265C23×C113C2×C22⋊C411yescharacteristic
266C23×C113C2×C22⋊C411yescharacteristic
267C23×C113C2×C22⋊C411yescharacteristic
268C23×C113C2×C22⋊C411yescharacteristic
269C23×C113#13114yes—
270C23×C113C23×C411yescharacteristic
271Q8×C113—42no—
272Q8×C113—42no—
273D4×C113—42no—
274D4×C113—44no—
275D4×C113—44no—
276D4×C113—44no—
277D4×C113—44no—
278D4×C113—44no—
279D4×C113—44no—
280D4×C113—42no—
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—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—24no—
300C2×C4×C113—41no—
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—44no—
313C2×C4×C113—44no—
314C2×C4×C113—42no—
315C2×C4×C113—42no—
316C2×C4×C113#9914yes—
317C2×C4×C113C2×C22⋊C411yescharacteristic
318C2×C4×C113C2×C22⋊C411yescharacteristic
319C2×C4×C113C2×C22⋊C411yescharacteristic
320C2×C4×C113C2×C22⋊C411yescharacteristic
321C2×C4×C113C2×C22⋊C411yescharacteristic
322C2×C4×C113C2×C22⋊C411yescharacteristic
323C2×C4×C113C22×D411yescharacteristic
324C2×C4×C113C22×D411yescharacteristic
325C8×C113—44no—
326C8×C113—44no—
327C22×C113—28no—
328C22×C113—21no—
329C22×C113—21no—
330C22×C113—21no—
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—44no—
345C22×C113—44no—
346C22×C113—44no—
347C22×C113—44no—
348C22×C113—44no—
349C22×C113—44no—
350C22×C113—42no—
351C22×C113—42no—
352C22×C113—42no—
353C22×C113—84no—
354C22×C113#40812yes—
355C22×C113#40812yes—
356C22×C113C2×#9912yes—
357C22×C113#41312yes—
358C22×C113C22×C22⋊C411yescharacteristic
359C22×C113C2×#13112yes—
360C4×C113—21no—
361C4×C113—21no—
362C4×C113—21no—
363C4×C113—21no—
364C4×C113—21no—
365C4×C113—21no—
366C4×C113—42no—
367C4×C113—42no—
368C4×C113—42no—
369C4×C113C2×#9912yes—
370C4×C113C2×#9912yes—
371#17381C11311yesmaximal, characteristic, direct product factor, Sylow
372C2×C113—22no—
373C2×C113—22no—
374C2×C113—22no—
375C2×C113—22no—
376C2×C113—22no—
377C2×C113—41no—
378C2×C113—41no—
379C2×C113—82no—
380C2×C113C2×#40811yescharacteristic
381C2×C113C22×#9911yescharacteristic
382C2×C113C2×#41311yescharacteristic
383C2×#525C2×C11311yescharacteristic
384C2×#407C2×C11311yescharacteristic, complemented
385C22×C22⋊C8C2×C11311yescharacteristic, complemented
386#1472C2×C11312yescomplemented
387#1471C2×C11312yescomplemented
388#1468C2×C11314yescomplemented
389#1459C2×C11314yescomplemented
390C113#1738111yescharacteristic, direct product factor, Sylow
391C22×#41C4×C11311yescharacteristic
392C24×C4C22×C11311yescharacteristic
393C22×M16—21no—
394C23×C8—21no—
395#525—21no—
396#525—21no—
397#525—21no—
398#525—21no—
399#525—21no—
400#525—21no—
401#525—21no—
402#525—21no—
403C2×#123C22×C11312yes—
404C2×C22⋊Q8C4×C11311yescharacteristic
405C2×C22⋊Q8C22×C11311yescharacteristic
406C2×#121C4×C11311yescharacteristic
407C2×#121C22×C11311yescharacteristic
408C2×#120C4×C11312yes—
409C2×C4×D4C4×C11312yes—
410C2×C4×D4C22×C11312yes—
411C2×#117C4×C11311yescharacteristic
412#407—21no—
413#407—21no—
414#407C22×C11312yes—
415#407C22×C11312yes—
416C2×C22⋊C8—21no—
417C2×C22⋊C8—21no—
418C2×C22⋊C8—21no—
419C2×C22⋊C8—21no—
420C2×C22⋊C8C22×C11312yes—
421C2×C22⋊C8C22×C11312yes—
422C2×C22⋊C8C22×C11312yes—
423C2×C22⋊C8C22×C11312yes—
424#324C22×C11318yescomplemented
425#323C22×C11318yescomplemented
426C25C2×C4×C11311yescharacteristic
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—44no—
432C22×Q8C2×C4×C11311yescharacteristic
433C22×D4C2×C4×C11312yes—
434C22×D4C2×C4×C11312yes—
435C22×D4C2×C4×C11312yes—
436C22×D4C2×C4×C11311yescharacteristic
437C23×C4—44no—
438C23×C4C2×C4×C11311yescharacteristic
439C23×C4C2×C4×C11312yes—
440C23×C4C2×C4×C11311yescharacteristic
441C23×C4C2×C4×C11311yescharacteristic
442C23×C4D4×C11311yescharacteristic
443C23×C4D4×C11311yescharacteristic
444C23×C4D4×C11311yescharacteristic
445C23×C4D4×C11311yescharacteristic
446C23×C4D4×C11311yescharacteristic
447C23×C4D4×C11311yescharacteristic
448C23×C4D4×C11311yescharacteristic
449C23×C4D4×C11311yescharacteristic
450C23×C4C23×C11311yescharacteristic
451C23×C4C23×C11311yescharacteristic
452C23×C4C23×C11311yescharacteristic
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—44no—
456C22×C8—22no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—22no—
460C22×C8—44no—
461#123—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473#121—21no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#120—22no—
482#120—22no—
483#120—22no—
484#120—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493#117—21no—
494#117—21no—
495#117—21no—
496#117—21no—
497C2×C4⋊C4C2×C4×C11311yescharacteristic
498C2×C4⋊C4C2×C4×C11311yescharacteristic
499C2×C4⋊C4C2×C4×C11312yes—
500C2×C4⋊C4C23×C11312yes—
501C2×C22⋊C4C2×C4×C11312yes—
502C2×C22⋊C4C2×C4×C11312yes—
503C2×C22⋊C4C2×C4×C11312yes—
504C2×C22⋊C4C2×C4×C11312yes—
505C2×C22⋊C4C23×C11312yes—
506C2×C42C2×C4×C11312yes—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513C22⋊C8C23×C11314yes—
514C22⋊C8C23×C11314yes—
515C24—24no—
516C24—42no—
517C24—42no—
518C24C22⋊C4×C11311yescharacteristic
519C24C22⋊C4×C11311yescharacteristic
520C24C22⋊C4×C11311yescharacteristic
521C24C22⋊C4×C11311yescharacteristic
522C24C22×C4×C11311yescharacteristic
523C24C22×C4×C11311yescharacteristic
524C24C22×C4×C11312yes—
525C24C22×C4×C11311yescharacteristic
526#41—44no—
527#41—44no—
528#41—44no—
529#41—44no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—42no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—28no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—44no—
544C2×D4—44no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—44no—
562C22×C4C22⋊C4×C11311yescharacteristic
563C22×C4C22⋊C4×C11311yescharacteristic
564C22×C4C22⋊C4×C11311yescharacteristic
565C22×C4C22⋊C4×C11311yescharacteristic
566C22×C4C22⋊C4×C11311yescharacteristic
567C22×C4C22⋊C4×C11311yescharacteristic
568C22×C4C22⋊C4×C11311yescharacteristic
569C22×C4C22⋊C4×C11311yescharacteristic
570C22×C4C22⋊C4×C11311yescharacteristic
571C22×C4C22⋊C4×C11311yescharacteristic
572C22×C4C22⋊C4×C11311yescharacteristic
573C22×C4C22⋊C4×C11311yescharacteristic
574C22×C4C22×C4×C11312yes—
575C22×C4C22×C4×C11311yescharacteristic
576C22×C4C22×C4×C11311yescharacteristic
577C22×C4C22×C4×C11312yes—
578C22×C4C22×C4×C11312yes—
579C22×C4C22×C4×C11311yescharacteristic
580C22×C4C2×D4×C11311yescharacteristic
581C22×C4C2×D4×C11311yescharacteristic
582C22×C4C2×D4×C11311yescharacteristic
583C22×C4C2×D4×C11311yescharacteristic
584C22×C4C2×D4×C11311yescharacteristic
585C22×C4C2×D4×C11311yescharacteristic
586C22×C4C2×D4×C11311yescharacteristic
587C22×C4C2×D4×C11311yescharacteristic
588C22×C4C2×D4×C11311yescharacteristic
589C22×C4C2×D4×C11311yescharacteristic
590C22×C4C2×D4×C11311yescharacteristic
591C22×C4C2×D4×C11311yescharacteristic
592C22×C4C24×C11311yescharacteristic
593M16—44no—
594M16—44no—
595C2×C8—24no—
596C2×C8—24no—
597C2×C8—44no—
598C2×C8—44no—
599C2×C8—44no—
600C2×C8—44no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C42—22no—
620C42—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—416no—
644C23—42no—
645C23—42no—
646C23C2×C22⋊C4×C11311yescharacteristic
647C23C2×C22⋊C4×C11311yescharacteristic
648C23C2×C22⋊C4×C11311yescharacteristic
649C23C2×C22⋊C4×C11311yescharacteristic
650C23C2×C22⋊C4×C11311yescharacteristic
651C23C2×C22⋊C4×C11311yescharacteristic
652C23#131×C11314yes—
653C23C23×C4×C11311yescharacteristic
654Q8—42no—
655Q8—42no—
656D4—42no—
657D4—44no—
658D4—44no—
659D4—44no—
660D4—44no—
661D4—44no—
662D4—44no—
663D4—42no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
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—24no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4#99×C11314yes—
700C2×C4C2×C22⋊C4×C11311yescharacteristic
701C2×C4C2×C22⋊C4×C11311yescharacteristic
702C2×C4C2×C22⋊C4×C11311yescharacteristic
703C2×C4C2×C22⋊C4×C11311yescharacteristic
704C2×C4C2×C22⋊C4×C11311yescharacteristic
705C2×C4C2×C22⋊C4×C11311yescharacteristic
706C2×C4C22×D4×C11311yescharacteristic
707C2×C4C22×D4×C11311yescharacteristic
708C8—44no—
709C8—44no—
710C22—28no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—84no—
737C22#408×C11312yes—
738C22#408×C11312yes—
739C22C2×#99×C11312yes—
740C22#413×C11312yes—
741C22C22×C22⋊C4×C11311yescharacteristic
742C22C2×#131×C11312yes—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4C2×#99×C11312yes—
753C4C2×#99×C11312yes—
754C2—22no—
755C2—22no—
756C2—22no—
757C2—22no—
758C2—22no—
759C2—41no—
760C2—41no—
761C2—82no—
762C2C2×#408×C11311yescharacteristic
763C2C22×#99×C11311yescharacteristic
764C2C2×#413×C11311yescharacteristic
subgroupG/H
centerC2×C4×C113C2×C22⋊C4
commutatorC23C23×C4×C113
Frattini, cosocleC22×C4C24×C113
socleC22×C113C22×C22⋊C4
prime radicalC2×#525×C113C2
LCSG ▷ C23 ▷ C2 ▷ 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. C22×C22⋊C8×C113C2semidirect
4. C113×#1472C2semidirect
5. C113×#1471C2semidirect
6. C113×#1468C2semidirect
7. C113×#1459C2semidirect
41. #324×C113C22semidirect
42. #323×C113C22semidirect
371. #17381C113direct (N × H)
384. C2×#407C2×C113semidirect
385. C22×C22⋊C8C2×C113semidirect
386. #1472C2×C113semidirect
387. #1471C2×C113semidirect
388. #1468C2×C113semidirect
389. #1459C2×C113semidirect
390. C113#17381direct (N × H)
424. #324C22×C113semidirect
425. #323C22×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
C22×C22⋊C8×C1132
C113×#14722
C113×#14712
C113×#14682
C113×#14592
#17381113