Finite Group Databasebeta

← C113×#22427 #43290447

Subgroups — C113×#22427 #43290447

Order 28928.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C113C211yesmaximal, characteristic
2C2×#436×C113C211yesmaximal, characteristic, complemented
3C2×#417×C113C211yesmaximal, characteristic, complemented
4C2×#418×C113C211yesmaximal, characteristic, complemented
5C113×#2352C211yesmaximal, characteristic, complemented
6C113×#1983C211yesmaximal, characteristic, complemented
7C113×#1958C211yesmaximal, characteristic, complemented
8C113×#1895C211yesmaximal, characteristic, complemented
9C113×#1894C211yesmaximal, characteristic, complemented
10C113×#1874C211yesmaximal, characteristic, complemented
11C113×#1873C211yesmaximal, characteristic, complemented
12C113×#1804C211yesmaximal, characteristic, complemented
13C113×#1788C211yesmaximal, characteristic, complemented
14C113×#1786C211yesmaximal, characteristic, complemented
15C4×#102×C113C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×D4×C113C2211yescharacteristic
18C22×M16×C113C2211yescharacteristic
19C22×M16×C113C2211yescharacteristic, complemented
20#546×C113—24no—
21#546×C113C418yescomplemented
22C2×#124×C113C2211yescharacteristic
23C2×#123×C113—21no—
24C2×C22⋊Q8×C113C2211yescharacteristic
25C2×#121×C113—21no—
26C2×#121×C113C2211yescharacteristic
27C2×#120×C113—21no—
28C2×C4×D4×C113C2211yescharacteristic
29C2×C4×D4×C113C2211yescharacteristic
30C2×#117×C113C2211yescharacteristic
31C22×C4⋊C4×C113C2211yescharacteristic, complemented
32C22×C22⋊C4×C113—21no—
33#436×C113—24no—
34C2×C4⋊C8×C113C2211yescharacteristic, complemented
35#418×C113—24no—
36#417×C113—24no—
37C2×#103×C113C2211yescharacteristic, complemented
38C2×#103×C113C2211yescharacteristic, complemented
39C2×#103×C113C2211yescharacteristic, complemented
40C2×#103×C113C2211yescharacteristic, complemented
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×#102×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic
46C2×#102×C113C2211yescharacteristic
47C2×#102×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49C2×C22⋊C8×C113C2211yescharacteristic
50C2×C22⋊C8×C113C2211yescharacteristic, complemented
51C2×C4×C8×C113C2211yescharacteristic, complemented
52#388×C113—21no—
53#387×C113—21no—
54#386×C113—21no—
55#382×C113C2211yescharacteristic, complemented
56#380×C113C2211yescharacteristic
57#380×C113C2211yescharacteristic, complemented
58C4×C4⋊C4×C113C2211yescharacteristic, complemented
59C4×C22⋊C4×C113—21no—
60#340×C113C2211yescharacteristic, complemented
61#340×C113C2211yescharacteristic, complemented
62#340×C113C2211yescharacteristic, complemented
63#340×C113C2211yescharacteristic, complemented
64C25×C113—21no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—41no—
69C2×#41×C113—41no—
70C2×#41×C113C2×C414yes—
71C22×Q8×C113C2311yescharacteristic
72C22×D4×C113—22no—
73C22×D4×C113—22no—
74C22×D4×C113—21no—
75C22×D4×C113—21no—
76C22×D4×C113—21no—
77C22×D4×C113—22no—
78C22×D4×C113—41no—
79C22×D4×C113—41no—
80C22×D4×C113C2×C414yescomplemented
81C22×D4×C113D411yescharacteristic
82C22×D4×C113C2311yescharacteristic
83C22×D4×C113C2311yescharacteristic
84C23×C4×C113—21no—
85C23×C4×C113—21no—
86C23×C4×C113—21no—
87C23×C4×C113C2311yescharacteristic
88C23×C4×C113C2311yescharacteristic
89C2×M16×C113—22no—
90C2×M16×C113—22no—
91C2×M16×C113—22no—
92C2×M16×C113—22no—
93C2×M16×C113—41no—
94C2×M16×C113—41no—
95C22×C8×C113C2311yescharacteristic
96C22×C8×C113C2311yescharacteristic
97C22×C8×C113C2311yescharacteristic
98C22×C8×C113C2311yescharacteristic
99#124×C113—22no—
100#124×C113C2×C414yescomplemented
101#123×C113—28no—
102C22⋊Q8×C113—22no—
103C22⋊Q8×C113C2×C414yescomplemented
104#121×C113—22no—
105#121×C113—28no—
106#121×C113C2×C414yes—
107#120×C113—28no—
108C4×D4×C113—22no—
109C4×D4×C113C2×C414yes—
110C4×D4×C113C2×C414yescomplemented
111C4×D4×C113D414yes—
112#117×C113—22no—
113#117×C113—41no—
114C2×C4⋊C4×C113—21no—
115C2×C4⋊C4×C113—22no—
116C2×C4⋊C4×C113—21no—
117C2×C4⋊C4×C113—41no—
118C2×C4⋊C4×C113D411yescharacteristic
119C2×C4⋊C4×C113C2311yescharacteristic
120C2×C4⋊C4×C113C2311yescharacteristic
121C2×C4⋊C4×C113C2311yescharacteristic
122C2×C4⋊C4×C113C2311yescharacteristic
123C2×C4⋊C4×C113C2311yescharacteristic
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113—21no—
129C2×C22⋊C4×C113—28no—
130C2×C22⋊C4×C113—21no—
131C2×C22⋊C4×C113—21no—
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113D411yescharacteristic
134C2×C22⋊C4×C113D411yescharacteristic
135C2×C42×C113—21no—
136C2×C42×C113—21no—
137C2×C42×C113C2311yescharacteristic
138C4⋊C8×C113—22no—
139#103×C113—22no—
140#103×C113—22no—
141#103×C113—41no—
142#103×C113—41no—
143#102×C113—22no—
144#102×C113—22no—
145#102×C113—22no—
146#102×C113—22no—
147#102×C113—22no—
148#102×C113—41no—
149#102×C113—41no—
150#102×C113D414yescomplemented
151C22⋊C8×C113—22no—
152C22⋊C8×C113—22no—
153C4×C8×C113—22no—
154#95×C113—21no—
155#95×C113—21no—
156#95×C113—21no—
157#95×C113—21no—
158#95×C113—21no—
159C24×C113—21no—
160C24×C113—21no—
161C24×C113—24no—
162C24×C113—42no—
163C24×C113—42no—
164C24×C113—42no—
165C24×C113—42no—
166C24×C113—81no—
167C24×C113—81no—
168C24×C113C2×D411yescharacteristic
169C24×C113C2×D411yescharacteristic
170#41×C113—28no—
171#41×C113—44no—
172#41×C113—44no—
173#41×C113—44no—
174C2×Q8×C113—21no—
175C2×Q8×C113—21no—
176C2×Q8×C113—21no—
177C2×Q8×C113—21no—
178C2×Q8×C113—21no—
179C2×Q8×C113C22×C412yes—
180C2×D4×C113—28no—
181C2×D4×C113—24no—
182C2×D4×C113—24no—
183C2×D4×C113—24no—
184C2×D4×C113—21no—
185C2×D4×C113—21no—
186C2×D4×C113—21no—
187C2×D4×C113—21no—
188C2×D4×C113—21no—
189C2×D4×C113—21no—
190C2×D4×C113—21no—
191C2×D4×C113—21no—
192C2×D4×C113—44no—
193C2×D4×C113—44no—
194C2×D4×C113—44no—
195C2×D4×C113—41no—
196C2×D4×C113—41no—
197C2×D4×C113—42no—
198C2×D4×C113—42no—
199C2×D4×C113—42no—
200C2×D4×C113—42no—
201C2×D4×C113—81no—
202C2×D4×C113—81no—
203C2×D4×C113C22⋊C414yes—
204C2×D4×C113C22×C412yes—
205C2×D4×C113C22×C412yes—
206C2×D4×C113C2×D412yes—
207C2×D4×C113#4112yes—
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—24no—
220C22×C4×C113—24no—
221C22×C4×C113—21no—
222C22×C4×C113—21no—
223C22×C4×C113—21no—
224C22×C4×C113—42no—
225C22×C4×C113—42no—
226C22×C4×C113—42no—
227C22×C4×C113—42no—
228C22×C4×C113—81no—
229C22×C4×C113—81no—
230C22×C4×C113—81no—
231C22×C4×C113C22×C412yes—
232C22×C4×C113C22×C412yes—
233C22×C4×C113C2×D411yescharacteristic
234C22×C4×C113C2×D411yescharacteristic
235C22×C4×C113C2×D411yescharacteristic
236C22×C4×C113C2×D411yescharacteristic
237C22×C4×C113C2×D412yes—
238C22×C4×C113C2×D412yes—
239C22×C4×C113C2411yescharacteristic
240M16×C113—44no—
241M16×C113—44no—
242C2×C8×C113—21no—
243C2×C8×C113—21no—
244C2×C8×C113—21no—
245C2×C8×C113—21no—
246C2×C8×C113—21no—
247C2×C8×C113—21no—
248C2×C8×C113—21no—
249C2×C8×C113—21no—
250C2×C8×C113—21no—
251C2×C8×C113—21no—
252C2×C8×C113—21no—
253C2×C8×C113C2×D412yes—
254C4⋊C4×C113—24no—
255C4⋊C4×C113—21no—
256C4⋊C4×C113—21no—
257C4⋊C4×C113—21no—
258C4⋊C4×C113—21no—
259C4⋊C4×C113—21no—
260C4⋊C4×C113—21no—
261C4⋊C4×C113—21no—
262C4⋊C4×C113—21no—
263C4⋊C4×C113—42no—
264C4⋊C4×C113C22⋊C414yes—
265C4⋊C4×C113C22×C412yes—
266C4⋊C4×C113C2×D412yes—
267C22⋊C4×C113—24no—
268C22⋊C4×C113—24no—
269C22⋊C4×C113—24no—
270C22⋊C4×C113—24no—
271C22⋊C4×C113—24no—
272C22⋊C4×C113—42no—
273C22⋊C4×C113—42no—
274C22⋊C4×C113—81no—
275C22⋊C4×C113C22⋊C414yes—
276C22⋊C4×C113C22⋊C414yes—
277C42×C113—42no—
278C42×C113—81no—
279C42×C113C22×C412yes—
280C42×C113C2×D412yes—
281C23×C113—22no—
282C23×C113—21no—
283C23×C113—21no—
284C23×C113—22no—
285C23×C113—21no—
286C23×C113—21no—
287C23×C113—22no—
288C23×C113—21no—
289C23×C113—21no—
290C23×C113—21no—
291C23×C113—21no—
292C23×C113—21no—
293C23×C113—21no—
294C23×C113—21no—
295C23×C113—21no—
296C23×C113—22no—
297C23×C113—48no—
298C23×C113—48no—
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—84no—
310C23×C113—84no—
311C23×C113—84no—
312C23×C113—84no—
313C23×C113—84no—
314C23×C113C2×C22⋊C412yes—
315C23×C113C2×C22⋊C412yes—
316C23×C113C22×D411yescharacteristic
317Q8×C113—22no—
318Q8×C113—22no—
319Q8×C113—41no—
320Q8×C113—41no—
321D4×C113—22no—
322D4×C113—22no—
323D4×C113—22no—
324D4×C113—22no—
325D4×C113—22no—
326D4×C113—44no—
327D4×C113—48no—
328D4×C113—48no—
329D4×C113—41no—
330D4×C113—41no—
331D4×C113—84no—
332D4×C113C4×D414yes—
333C2×C4×C113—21no—
334C2×C4×C113—21no—
335C2×C4×C113—21no—
336C2×C4×C113—21no—
337C2×C4×C113—21no—
338C2×C4×C113—21no—
339C2×C4×C113—21no—
340C2×C4×C113—21no—
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—48no—
353C2×C4×C113—41no—
354C2×C4×C113—41no—
355C2×C4×C113—41no—
356C2×C4×C113—41no—
357C2×C4×C113—41no—
358C2×C4×C113—41no—
359C2×C4×C113—41no—
360C2×C4×C113—41no—
361C2×C4×C113—41no—
362C2×C4×C113—41no—
363C2×C4×C113—41no—
364C2×C4×C113—41no—
365C2×C4×C113—41no—
366C2×C4×C113—41no—
367C2×C4×C113—41no—
368C2×C4×C113—84no—
369C2×C4×C113—84no—
370C2×C4×C113C2×C22⋊C412yes—
371C2×C4×C113C2×C22⋊C412yes—
372C2×C4×C113C2×C22⋊C412yes—
373C2×C4×C113C2×C22⋊C412yes—
374C2×C4×C113C23×C411yescharacteristic
375C2×C4×C113C22×D411yescharacteristic
376C2×C4×C113C22×D411yescharacteristic
377C2×C4×C113C2×#4111yescharacteristic
378C2×C4×C113H(5,𝔽2)11yescharacteristic
379C2×C4×C113H(5,𝔽2)11yescharacteristic
380C8×C113—22no—
381C8×C113—41no—
382C8×C113—41no—
383C8×C113—41no—
384C22×C113—22no—
385C22×C113—22no—
386C22×C113—24no—
387C22×C113—22no—
388C22×C113—22no—
389C22×C113—22no—
390C22×C113—22no—
391C22×C113—42no—
392C22×C113—42no—
393C22×C113—41no—
394C22×C113—41no—
395C22×C113—42no—
396C22×C113—41no—
397C22×C113—41no—
398C22×C113—42no—
399C22×C113—41no—
400C22×C113—41no—
401C22×C113—42no—
402C22×C113—41no—
403C22×C113—41no—
404C22×C113—42no—
405C22×C113—42no—
406C22×C113—42no—
407C22×C113—42no—
408C22×C113—816no—
409C22×C113—81no—
410C22×C113—81no—
411C22×C113—81no—
412C22×C113—81no—
413C22×C113C22×C22⋊C411yescharacteristic
414C22×C113D4211yescharacteristic
415C22×C113#54611yescharacteristic
416C22×C113#57511yescharacteristic
417C22×C113#57511yescharacteristic
418C22×C113#57611yescharacteristic
419C22×C113#57711yescharacteristic
420C4×C113—22no—
421C4×C113—22no—
422C4×C113—22no—
423C4×C113—22no—
424C4×C113—42no—
425C4×C113—42no—
426C4×C113—42no—
427C4×C113—81no—
428C4×C113—81no—
429C4×C113—81no—
430C4×C113C2×C4×D411yescharacteristic
431C4×C113#51811yescharacteristic
432C4×C113D4211yescharacteristic
433C4×C113#54611yescharacteristic
434#22427C11311yesmaximal, characteristic, direct product factor, Sylow
435C2×C113—42no—
436C2×C113—42no—
437C2×C113—44no—
438C2×C113—82no—
439C2×C113D4×C22⋊C411yescharacteristic
440C2×C113#289611yescharacteristic
441C2×C113#289711yescharacteristic
442C2×C113#327311yescharacteristic
443C2×C113#327511yescharacteristic
444C2×C113#332211yescharacteristic
445C2×C113#332311yescharacteristic
446C2×#546C2×C11311yescharacteristic
447C2×#436C2×C11311yescharacteristic, complemented
448C2×#417C2×C11311yescharacteristic, complemented
449C2×#418C2×C11311yescharacteristic, complemented
450#2352C2×C11311yescharacteristic, complemented
451#1983C2×C11311yescharacteristic, complemented
452#1958C2×C11311yescharacteristic, complemented
453#1895C2×C11311yescharacteristic, complemented
454#1894C2×C11311yescharacteristic, complemented
455#1874C2×C11311yescharacteristic, complemented
456#1873C2×C11311yescharacteristic, complemented
457#1804C2×C11311yescharacteristic, complemented
458#1788C2×C11311yescharacteristic, complemented
459#1786C2×C11311yescharacteristic, complemented
460C4×#102C2×C11311yescharacteristic, complemented
461C113#2242711yescharacteristic, direct product factor, Sylow
462C22×#41C22×C11311yescharacteristic
463C23×D4C22×C11311yescharacteristic
464C22×M16C22×C11311yescharacteristic
465C22×M16C22×C11311yescharacteristic, complemented
466#546—24no—
467#546C4×C11318yescomplemented
468C2×#124C22×C11311yescharacteristic
469C2×#123—21no—
470C2×C22⋊Q8C22×C11311yescharacteristic
471C2×#121—21no—
472C2×#121C22×C11311yescharacteristic
473C2×#120—21no—
474C2×C4×D4C22×C11311yescharacteristic
475C2×C4×D4C22×C11311yescharacteristic
476C2×#117C22×C11311yescharacteristic
477C22×C4⋊C4C22×C11311yescharacteristic, complemented
478C22×C22⋊C4—21no—
479#436—24no—
480C2×C4⋊C8C22×C11311yescharacteristic, complemented
481#418—24no—
482#417—24no—
483C2×#103C22×C11311yescharacteristic, complemented
484C2×#103C22×C11311yescharacteristic, complemented
485C2×#103C22×C11311yescharacteristic, complemented
486C2×#103C22×C11311yescharacteristic, complemented
487C2×#102C22×C11311yescharacteristic
488C2×#102C22×C11311yescharacteristic
489C2×#102C22×C11311yescharacteristic
490C2×#102C22×C11311yescharacteristic
491C2×#102C22×C11311yescharacteristic
492C2×#102C22×C11311yescharacteristic
493C2×#102C22×C11311yescharacteristic
494C2×#102C22×C11311yescharacteristic
495C2×C22⋊C8C22×C11311yescharacteristic
496C2×C22⋊C8C22×C11311yescharacteristic, complemented
497C2×C4×C8C22×C11311yescharacteristic, complemented
498#388—21no—
499#387—21no—
500#386—21no—
501#382C22×C11311yescharacteristic, complemented
502#380C22×C11311yescharacteristic
503#380C22×C11311yescharacteristic, complemented
504C4×C4⋊C4C22×C11311yescharacteristic, complemented
505C4×C22⋊C4—21no—
506#340C22×C11311yescharacteristic, complemented
507#340C22×C11311yescharacteristic, complemented
508#340C22×C11311yescharacteristic, complemented
509#340C22×C11311yescharacteristic, complemented
510C25—21no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C2×C4×C11314yes—
517C22×Q8C23×C11311yescharacteristic
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×C4×C11314yescomplemented
527C22×D4D4×C11311yescharacteristic
528C22×D4C23×C11311yescharacteristic
529C22×D4C23×C11311yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C23×C11311yescharacteristic
534C23×C4C23×C11311yescharacteristic
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8C23×C11311yescharacteristic
542C22×C8C23×C11311yescharacteristic
543C22×C8C23×C11311yescharacteristic
544C22×C8C23×C11311yescharacteristic
545#124—22no—
546#124C2×C4×C11314yescomplemented
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8C2×C4×C11314yescomplemented
550#121—22no—
551#121—28no—
552#121C2×C4×C11314yes—
553#120—28no—
554C4×D4—22no—
555C4×D4C2×C4×C11314yes—
556C4×D4C2×C4×C11314yescomplemented
557C4×D4D4×C11314yes—
558#117—22no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4D4×C11311yescharacteristic
565C2×C4⋊C4C23×C11311yescharacteristic
566C2×C4⋊C4C23×C11311yescharacteristic
567C2×C4⋊C4C23×C11311yescharacteristic
568C2×C4⋊C4C23×C11311yescharacteristic
569C2×C4⋊C4C23×C11311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C11311yescharacteristic
580C2×C22⋊C4D4×C11311yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42C23×C11311yescharacteristic
584C4⋊C8—22no—
585#103—22no—
586#103—22no—
587#103—41no—
588#103—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102—41no—
596#102D4×C11314yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599C4×C8—22no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×D4×C11311yescharacteristic
615C24C2×D4×C11311yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×C4×C11312yes—
626C2×D4—28no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊C4×C11314yes—
650C2×D4C22×C4×C11312yes—
651C2×D4C22×C4×C11312yes—
652C2×D4C2×D4×C11312yes—
653C2×D4#41×C11312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—81no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4C22×C4×C11312yes—
678C22×C4C22×C4×C11312yes—
679C22×C4C2×D4×C11311yescharacteristic
680C22×C4C2×D4×C11311yescharacteristic
681C22×C4C2×D4×C11311yescharacteristic
682C22×C4C2×D4×C11311yescharacteristic
683C22×C4C2×D4×C11312yes—
684C22×C4C2×D4×C11312yes—
685C22×C4C24×C11311yescharacteristic
686M16—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C11312yes—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4C22⋊C4×C11314yes—
711C4⋊C4C22×C4×C11312yes—
712C4⋊C4C2×D4×C11312yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C22⋊C4C22⋊C4×C11314yes—
722C22⋊C4C22⋊C4×C11314yes—
723C42—42no—
724C42—81no—
725C42C22×C4×C11312yes—
726C42C2×D4×C11312yes—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—48no—
744C23—48no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23C2×C22⋊C4×C11312yes—
761C23C2×C22⋊C4×C11312yes—
762C23C22×D4×C11311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—44no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4C4×D4×C11314yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4C2×C22⋊C4×C11312yes—
817C2×C4C2×C22⋊C4×C11312yes—
818C2×C4C2×C22⋊C4×C11312yes—
819C2×C4C2×C22⋊C4×C11312yes—
820C2×C4C23×C4×C11311yescharacteristic
821C2×C4C22×D4×C11311yescharacteristic
822C2×C4C22×D4×C11311yescharacteristic
823C2×C4C2×#41×C11311yescharacteristic
824C2×C4H(5,𝔽2)×C11311yescharacteristic
825C2×C4H(5,𝔽2)×C11311yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—41no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C22×C22⋊C4×C11311yescharacteristic
860C22D42×C11311yescharacteristic
861C22#546×C11311yescharacteristic
862C22#575×C11311yescharacteristic
863C22#575×C11311yescharacteristic
864C22#576×C11311yescharacteristic
865C22#577×C11311yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4C2×C4×D4×C11311yescharacteristic
877C4#518×C11311yescharacteristic
878C4D42×C11311yescharacteristic
879C4#546×C11311yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊C4×C11311yescharacteristic
885C2C113×#289611yescharacteristic
886C2C113×#289711yescharacteristic
887C2C113×#327311yescharacteristic
888C2C113×#327511yescharacteristic
889C2C113×#332211yescharacteristic
890C2C113×#332311yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
prime radicalC2×#546×C113C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#436×C113C2semidirect
3. C2×#417×C113C2semidirect
4. C2×#418×C113C2semidirect
5. C113×#2352C2semidirect
6. C113×#1983C2semidirect
7. C113×#1958C2semidirect
8. C113×#1895C2semidirect
9. C113×#1894C2semidirect
10. C113×#1874C2semidirect
11. C113×#1873C2semidirect
12. C113×#1804C2semidirect
13. C113×#1788C2semidirect
14. C113×#1786C2semidirect
15. C4×#102×C113C2semidirect
19. C22×M16×C113C22semidirect
21. #546×C113C4semidirect
31. C22×C4⋊C4×C113C22semidirect
34. C2×C4⋊C8×C113C22semidirect
37. C2×#103×C113C22semidirect
38. C2×#103×C113C22semidirect
39. C2×#103×C113C22semidirect
40. C2×#103×C113C22semidirect
50. C2×C22⋊C8×C113C22semidirect
51. C2×C4×C8×C113C22semidirect
55. #382×C113C22semidirect
57. #380×C113C22semidirect
58. C4×C4⋊C4×C113C22semidirect
60. #340×C113C22semidirect
61. #340×C113C22semidirect
62. #340×C113C22semidirect
63. #340×C113C22semidirect
80. C22×D4×C113C2×C4semidirect
100. #124×C113C2×C4semidirect
103. C22⋊Q8×C113C2×C4semidirect
110. C4×D4×C113C2×C4semidirect
150. #102×C113D4semidirect
434. #22427C113direct (N × H)
447. C2×#436C2×C113semidirect
448. C2×#417C2×C113semidirect
449. C2×#418C2×C113semidirect
450. #2352C2×C113semidirect
451. #1983C2×C113semidirect
452. #1958C2×C113semidirect
453. #1895C2×C113semidirect
454. #1894C2×C113semidirect
455. #1874C2×C113semidirect
456. #1873C2×C113semidirect
457. #1804C2×C113semidirect
458. #1788C2×C113semidirect
459. #1786C2×C113semidirect
460. C4×#102C2×C113semidirect
461. C113#22427direct (N × H)
465. C22×M16C22×C113semidirect
467. #546C4×C113semidirect
477. C22×C4⋊C4C22×C113semidirect
480. C2×C4⋊C8C22×C113semidirect
483. C2×#103C22×C113semidirect
484. C2×#103C22×C113semidirect
485. C2×#103C22×C113semidirect
486. C2×#103C22×C113semidirect
496. C2×C22⋊C8C22×C113semidirect
497. C2×C4×C8C22×C113semidirect
501. #382C22×C113semidirect
503. #380C22×C113semidirect
504. C4×C4⋊C4C22×C113semidirect
506. #340C22×C113semidirect
507. #340C22×C113semidirect
508. #340C22×C113semidirect
509. #340C22×C113semidirect
526. C22×D4C2×C4×C113semidirect
546. #124C2×C4×C113semidirect
549. C22⋊Q8C2×C4×C113semidirect
556. C4×D4C2×C4×C113semidirect
596. #102D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1132
C2×#436×C1132
C2×#417×C1132
C2×#418×C1132
C113×#23522
C113×#19832
C113×#19582
C113×#18952
C113×#18942
C113×#18742
C113×#18732
C113×#18042
C113×#17882
C113×#17862
C4×#102×C1132
#22427113