Finite Group Databasebeta

← C113×#24469 #43292489

Subgroups — C113×#24469 #43292489

Order 28928.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3489C211yesmaximal, characteristic, complemented
2C113×#3055C211yesmaximal, characteristic, complemented
3C2×#454×C113C211yesmaximal, characteristic, complemented
4C113×#3006C211yesmaximal, characteristic, complemented
5C2×#421×C113C211yesmaximal, characteristic, complemented
6C113×#2620C211yesmaximal, characteristic, complemented
7C113×#2039C211yesmaximal, characteristic, complemented
8C113×#2038C211yesmaximal, characteristic, complemented
9C113×#2006C211yesmaximal, characteristic, complemented
10C113×#2003C211yesmaximal, characteristic, complemented
11C113×#1901C211yesmaximal, characteristic, complemented
12C113×#1897C211yesmaximal, characteristic, complemented
13C113×#1883C211yesmaximal, characteristic, complemented
14C113×#1859C211yesmaximal, characteristic, complemented
15C113×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C113C2211yescharacteristic, complemented
21C22×M16×C113C2211yescharacteristic
22D4×Q8×C113—21no—
23#548×C113—21no—
24#547×C113—21no—
25#547×C113—22no—
26#546×C113—21no—
27#546×C113—22no—
28#537×C113—21no—
29#537×C113C2211yescharacteristic
30#536×C113—21no—
31#536×C113C2211yescharacteristic
32C2×#124×C113C2211yescharacteristic, complemented
33#525×C113—21no—
34#525×C113C2211yescharacteristic
35C2×C22⋊Q8×C113—21no—
36C2×C22⋊Q8×C113C2211yescharacteristic
37C2×#121×C113C2211yescharacteristic
38#520×C113C2211yescharacteristic
39C2×#117×C113C2211yescharacteristic
40#469×C113—21no—
41#468×C113—21no—
42#466×C113—21no—
43#465×C113—21no—
44#454×C113—24no—
45#449×C113—21no—
46#449×C113—21no—
47#448×C113—21no—
48#447×C113—21no—
49#428×C113C2211yescharacteristic, complemented
50#421×C113—24no—
51C2×#104×C113C2211yescharacteristic
52C2×#104×C113C2211yescharacteristic
53C2×#104×C113C2211yescharacteristic
54C2×#104×C113C2211yescharacteristic
55C2×#104×C113C2211yescharacteristic, complemented
56C2×#104×C113C2211yescharacteristic, complemented
57#418×C113C2211yescharacteristic, complemented
58#417×C113C2211yescharacteristic
59#417×C113C2211yescharacteristic
60#417×C113C2211yescharacteristic, complemented
61C2×#101×C113C2211yescharacteristic, complemented
62C2×#101×C113C2211yescharacteristic, complemented
63#407×C113C2211yescharacteristic
64#396×C113—22no—
65#394×C113—22no—
66#391×C113C2211yescharacteristic, complemented
67#390×C113C2211yescharacteristic, complemented
68#384×C113C2211yescharacteristic, complemented
69#343×C113C2211yescharacteristic, complemented
70#343×C113C2211yescharacteristic, complemented
71#339×C113C2211yescharacteristic, complemented
72#339×C113C2211yescharacteristic, complemented
732−1+4×C113—22no—
742−1+4×C113—22no—
752−1+4×C113—41no—
762−1+4×C113—41no—
77C2×#41×C113—21no—
78C2×#41×C113—21no—
79C2×#41×C113—21no—
80C2×#41×C113—22no—
81C2×#41×C113—21no—
82C2×#41×C113—22no—
83C2×#41×C113—22no—
84C2×#41×C113—41no—
85C2×#41×C113—41no—
86C2×#41×C113D411yescharacteristic
87C2×#41×C113D411yescharacteristic
88C2×#41×C113C2311yescharacteristic
89C2×#41×C113C2311yescharacteristic
90C2×#41×C113C2311yescharacteristic
91C22×Q8×C113—21no—
92C22×Q8×C113—21no—
93C22×Q8×C113D411yescharacteristic
94C22×Q8×C113C2311yescharacteristic
95C22×D4×C113—21no—
96C22×D4×C113—21no—
97C22×D4×C113D411yescharacteristic
98C22×D4×C113C2311yescharacteristic
99C23×C4×C113—21no—
100C23×C4×C113C2311yescharacteristic
101AGL(1,ℤ/8)×C113—22no—
102AGL(1,ℤ/8)×C113—22no—
103AGL(1,ℤ/8)×C113—22no—
104AGL(1,ℤ/8)×C113—41no—
105AGL(1,ℤ/8)×C113—41no—
106AGL(1,ℤ/8)×C113—41no—
107C2×SD16×C113—21no—
108C2×SD16×C113—21no—
109C2×SD16×C113—21no—
110C2×D8×C113—21no—
111C2×D8×C113—21no—
112C2×D8×C113—21no—
113C2×M16×C113—21no—
114C2×M16×C113—22no—
115C2×M16×C113—41no—
116C2×M16×C113C2311yescharacteristic
117C2×M16×C113C2311yescharacteristic
118C2×M16×C113C2311yescharacteristic
119C2×M16×C113C2311yescharacteristic
120C22×C8×C113—21no—
121C4⋊Q8×C113—22no—
122C4⋊Q8×C113—21no—
123#124×C113—22no—
124#124×C113—21no—
125#124×C113—22no—
126#124×C113—41no—
127#123×C113—22no—
128#123×C113—22no—
129#123×C113—22no—
130#123×C113—21no—
131#123×C113—22no—
132C22⋊Q8×C113—22no—
133C22⋊Q8×C113—22no—
134C22⋊Q8×C113—22no—
135C22⋊Q8×C113—21no—
136C22⋊Q8×C113—21no—
137C22⋊Q8×C113—21no—
138C22⋊Q8×C113—21no—
139C22⋊Q8×C113—21no—
140C22⋊Q8×C113—21no—
141C22⋊Q8×C113—21no—
142C22⋊Q8×C113—21no—
143C22⋊Q8×C113D411yescharacteristic
144C22⋊Q8×C113D411yescharacteristic
145#121×C113—22no—
146#121×C113—22no—
147#121×C113—22no—
148#121×C113—21no—
149#121×C113—21no—
150#121×C113—22no—
151#121×C113—21no—
152#121×C113—21no—
153#121×C113—21no—
154#121×C113—21no—
155#121×C113D411yescharacteristic
156#121×C113D411yescharacteristic
157#120×C113—22no—
158#120×C113—21no—
159C4×Q8×C113—21no—
160C4×D4×C113—22no—
161C4×D4×C113—22no—
162C4×D4×C113—21no—
163C4×D4×C113—22no—
164C4×D4×C113—21no—
165C4×D4×C113—21no—
166#117×C113—21no—
167#117×C113—22no—
168#117×C113—41no—
169#117×C113C2311yescharacteristic
170C2×C4⋊C4×C113—22no—
171C2×C4⋊C4×C113—21no—
172C2×C4⋊C4×C113—21no—
173C2×C4⋊C4×C113—22no—
174C2×C4⋊C4×C113D412yes—
175C2×C4⋊C4×C113C2311yescharacteristic
176C2×C4⋊C4×C113C2311yescharacteristic
177C2×C22⋊C4×C113—22no—
178C2×C22⋊C4×C113—21no—
179C2×C22⋊C4×C113—21no—
180C2×C22⋊C4×C113—22no—
181C2×C22⋊C4×C113—22no—
182C2×C22⋊C4×C113D412yes—
183C2×C42×C113C2311yescharacteristic
184C2×C42×C113C2311yescharacteristic
185#107×C113—21no—
186#106×C113—21no—
187#104×C113—22no—
188#104×C113—22no—
189#104×C113—22no—
190#104×C113—22no—
191#104×C113—41no—
192#104×C113D414yescomplemented
193#103×C113—21no—
194#103×C113—21no—
195#103×C113—21no—
196#102×C113—21no—
197#102×C113—21no—
198#102×C113—21no—
199#102×C113—21no—
200#102×C113—21no—
201#101×C113—22no—
202#101×C113—41no—
203C22⋊C8×C113—21no—
204C22⋊C8×C113—21no—
205#95×C113—22no—
206C24×C113—21no—
207C24×C113—21no—
208C24×C113C2×D411yescharacteristic
209#41×C113—21no—
210#41×C113—21no—
211#41×C113—22no—
212#41×C113—22no—
213#41×C113—21no—
214#41×C113—21no—
215#41×C113—21no—
216#41×C113—21no—
217#41×C113—21no—
218#41×C113—21no—
219#41×C113—21no—
220#41×C113—21no—
221#41×C113—42no—
222#41×C113—42no—
223#41×C113—41no—
224#41×C113—41no—
225#41×C113—42no—
226#41×C113—42no—
227#41×C113—42no—
228#41×C113—42no—
229#41×C113—44no—
230#41×C113—44no—
231#41×C113—42no—
232#41×C113—42no—
233#41×C113C2×D412yes—
234#41×C113#4112yes—
235C2×Q8×C113—22no—
236C2×Q8×C113—21no—
237C2×Q8×C113—21no—
238C2×Q8×C113—21no—
239C2×Q8×C113—21no—
240C2×Q8×C113—21no—
241C2×Q8×C113—21no—
242C2×Q8×C113—21no—
243C2×Q8×C113—22no—
244C2×Q8×C113—41no—
245C2×Q8×C113—42no—
246C2×Q8×C113—42no—
247C2×Q8×C113—42no—
248C2×Q8×C113—42no—
249C2×Q8×C113C2×D411yescharacteristic
250C2×Q8×C113C2×D411yescharacteristic
251C2×Q8×C113C2×D411yescharacteristic
252C2×D4×C113—21no—
253C2×D4×C113—22no—
254C2×D4×C113—22no—
255C2×D4×C113—21no—
256C2×D4×C113—21no—
257C2×D4×C113—21no—
258C2×D4×C113—21no—
259C2×D4×C113—21no—
260C2×D4×C113—22no—
261C2×D4×C113—21no—
262C2×D4×C113—21no—
263C2×D4×C113—21no—
264C2×D4×C113—21no—
265C2×D4×C113—21no—
266C2×D4×C113—21no—
267C2×D4×C113—21no—
268C2×D4×C113—21no—
269C2×D4×C113—41no—
270C2×D4×C113—42no—
271C2×D4×C113—42no—
272C2×D4×C113—41no—
273C2×D4×C113—41no—
274C2×D4×C113—82no—
275C2×D4×C113C2×D411yescharacteristic
276C2×D4×C113C2×D411yescharacteristic
277C2×D4×C113C2×D411yescharacteristic
278C22×C4×C113—21no—
279C22×C4×C113—21no—
280C22×C4×C113—21no—
281C22×C4×C113—21no—
282C22×C4×C113—21no—
283C22×C4×C113—22no—
284C22×C4×C113—22no—
285C22×C4×C113—21no—
286C22×C4×C113—21no—
287C22×C4×C113—22no—
288C22×C4×C113—21no—
289C22×C4×C113—21no—
290C22×C4×C113—21no—
291C22×C4×C113—21no—
292C22×C4×C113—21no—
293C22×C4×C113—21no—
294C22×C4×C113—42no—
295C22×C4×C113—42no—
296C22×C4×C113C2×D412yes—
297C22×C4×C113C2×D411yescharacteristic
298C22×C4×C113C2×D411yescharacteristic
299C22×C4×C113C2×D411yescharacteristic
300C22×C4×C113C2×D411yescharacteristic
301C22×C4×C113C2×D411yescharacteristic
302C22×C4×C113C2×D412yes—
303C22×C4×C113C2411yescharacteristic
304SD16×C113—42no—
305SD16×C113—42no—
306SD16×C113—42no—
307D8×C113—42no—
308D8×C113—42no—
309D8×C113—42no—
310M16×C113—21no—
311M16×C113—21no—
312M16×C113—21no—
313M16×C113—21no—
314M16×C113—21no—
315M16×C113—21no—
316M16×C113—21no—
317M16×C113—42no—
318M16×C113C2×D412yes—
319C2×C8×C113—21no—
320C2×C8×C113—21no—
321C2×C8×C113—21no—
322C2×C8×C113—21no—
323C2×C8×C113—42no—
324C4⋊C4×C113—22no—
325C4⋊C4×C113—22no—
326C4⋊C4×C113—22no—
327C4⋊C4×C113—22no—
328C4⋊C4×C113—21no—
329C4⋊C4×C113—22no—
330C4⋊C4×C113—22no—
331C4⋊C4×C113—21no—
332C4⋊C4×C113—21no—
333C4⋊C4×C113—21no—
334C4⋊C4×C113—21no—
335C4⋊C4×C113—21no—
336C4⋊C4×C113—42no—
337C4⋊C4×C113—82no—
338C4⋊C4×C113C2×D411yescharacteristic
339C4⋊C4×C113C2×D411yescharacteristic
340C22⋊C4×C113—22no—
341C22⋊C4×C113—22no—
342C22⋊C4×C113—22no—
343C22⋊C4×C113—22no—
344C22⋊C4×C113—22no—
345C22⋊C4×C113—21no—
346C22⋊C4×C113—22no—
347C22⋊C4×C113—22no—
348C22⋊C4×C113—21no—
349C22⋊C4×C113—21no—
350C22⋊C4×C113—21no—
351C22⋊C4×C113—21no—
352C22⋊C4×C113—44no—
353C22⋊C4×C113—42no—
354C22⋊C4×C113—41no—
355C22⋊C4×C113—41no—
356C22⋊C4×C113—82no—
357C42×C113—22no—
358C42×C113—21no—
359C42×C113—21no—
360C42×C113—21no—
361C42×C113—21no—
362C42×C113C2×D412yes—
363C23×C113—21no—
364C23×C113—21no—
365C23×C113—21no—
366C23×C113—21no—
367C23×C113—21no—
368C23×C113—41no—
369C23×C113—41no—
370C23×C113—42no—
371C23×C113—42no—
372C23×C113—42no—
373C23×C113—42no—
374C23×C113—41no—
375C23×C113—41no—
376C23×C113—41no—
377C23×C113—81no—
378C23×C113#12011yescharacteristic
379C23×C113#12011yescharacteristic
380C23×C113C22×D411yescharacteristic
381Q8×C113—21no—
382Q8×C113—21no—
383Q8×C113—21no—
384Q8×C113—21no—
385Q8×C113—21no—
386Q8×C113—42no—
387Q8×C113—44no—
388Q8×C113—41no—
389Q8×C113—41no—
390Q8×C113—41no—
391Q8×C113—41no—
392Q8×C113#12112yes—
393D4×C113—22no—
394D4×C113—22no—
395D4×C113—21no—
396D4×C113—21no—
397D4×C113—21no—
398D4×C113—21no—
399D4×C113—21no—
400D4×C113—42no—
401D4×C113—42no—
402D4×C113—42no—
403D4×C113—42no—
404D4×C113—44no—
405D4×C113—41no—
406D4×C113—41no—
407D4×C113—41no—
408D4×C113—41no—
409D4×C113—41no—
410D4×C113—41no—
411D4×C113—41no—
412D4×C113—41no—
413D4×C113—81no—
414D4×C113—82no—
415D4×C113—82no—
416D4×C113—82no—
417D4×C113#12112yes—
418C2×C4×C113—21no—
419C2×C4×C113—21no—
420C2×C4×C113—21no—
421C2×C4×C113—21no—
422C2×C4×C113—21no—
423C2×C4×C113—21no—
424C2×C4×C113—21no—
425C2×C4×C113—21no—
426C2×C4×C113—21no—
427C2×C4×C113—22no—
428C2×C4×C113—21no—
429C2×C4×C113—21no—
430C2×C4×C113—22no—
431C2×C4×C113—21no—
432C2×C4×C113—22no—
433C2×C4×C113—21no—
434C2×C4×C113—21no—
435C2×C4×C113—22no—
436C2×C4×C113—21no—
437C2×C4×C113—22no—
438C2×C4×C113—22no—
439C2×C4×C113—22no—
440C2×C4×C113—42no—
441C2×C4×C113—42no—
442C2×C4×C113—42no—
443C2×C4×C113—44no—
444C2×C4×C113—41no—
445C2×C4×C113—41no—
446C2×C4×C113—44no—
447C2×C4×C113—41no—
448C2×C4×C113—41no—
449C2×C4×C113—41no—
450C2×C4×C113—41no—
451C2×C4×C113—42no—
452C2×C4×C113—41no—
453C2×C4×C113—42no—
454C2×C4×C113—41no—
455C2×C4×C113—41no—
456C2×C4×C113—41no—
457C2×C4×C113—82no—
458C2×C4×C113#12011yescharacteristic
459C2×C4×C113#12011yescharacteristic
460C2×C4×C113C22×D411yescharacteristic
461C2×C4×C113C22×D411yescharacteristic
462C2×C4×C113C22×D411yescharacteristic
463C2×C4×C113C2×#4111yescharacteristic
464C2×C4×C113H(5,𝔽2)11yescharacteristic
465C2×C4×C113H(5,𝔽2)11yescharacteristic
466C8×C113—22no—
467C8×C113—41no—
468C8×C113—41no—
469C8×C113—41no—
470C22×C113—21no—
471C22×C113—21no—
472C22×C113—21no—
473C22×C113—21no—
474C22×C113—22no—
475C22×C113—21no—
476C22×C113—21no—
477C22×C113—21no—
478C22×C113—21no—
479C22×C113—41no—
480C22×C113—41no—
481C22×C113—41no—
482C22×C113—41no—
483C22×C113—41no—
484C22×C113—41no—
485C22×C113—41no—
486C22×C113—41no—
487C22×C113—81no—
488C22×C113—81no—
489C22×C113—82no—
490C22×C113—82no—
491C22×C113—84no—
492C22×C113—81no—
493C22×C113—81no—
494C22×C113—81no—
495C22×C113C2×#12011yescharacteristic
496C22×C113D4211yescharacteristic
497C22×C113#54611yescharacteristic
498C4×C113—21no—
499C4×C113—21no—
500C4×C113—22no—
501C4×C113—42no—
502C4×C113—42no—
503C4×C113—41no—
504C4×C113—41no—
505C4×C113—41no—
506C4×C113—42no—
507C4×C113—41no—
508C4×C113—81no—
509C4×C113—81no—
510C4×C113C2×#12111yescharacteristic
511C4×C113#53411yescharacteristic
512C4×C113D4211yescharacteristic
513C4×C113#54611yescharacteristic
514#24469C11311yesmaximal, characteristic, direct product factor, Sylow
515C2×C113—21no—
516C2×C113—21no—
517C2×C113—41no—
518C2×C113—41no—
519C2×C113—42no—
520C2×C113—81no—
521C2×C113—81no—
522C2×C113—161no—
523C2×C113#241011yescharacteristic
524C2×C113#302011yescharacteristic
525C2×C113#302111yescharacteristic
526#3489C2×C11311yescharacteristic, complemented
527#3055C2×C11311yescharacteristic, complemented
528C2×#454C2×C11311yescharacteristic, complemented
529#3006C2×C11311yescharacteristic, complemented
530C2×#421C2×C11311yescharacteristic, complemented
531#2620C2×C11311yescharacteristic, complemented
532#2039C2×C11311yescharacteristic, complemented
533#2038C2×C11311yescharacteristic, complemented
534#2006C2×C11311yescharacteristic, complemented
535#2003C2×C11311yescharacteristic, complemented
536#1901C2×C11311yescharacteristic, complemented
537#1897C2×C11311yescharacteristic, complemented
538#1883C2×C11311yescharacteristic, complemented
539#1859C2×C11311yescharacteristic, complemented
540#1793C2×C11311yescharacteristic, complemented
541C113#2446911yescharacteristic, direct product factor, Sylow
542C2×2−1+4C22×C11311yescharacteristic
543C22×#41C22×C11311yescharacteristic
544C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
545C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
546C2×AGL(1,ℤ/8)C22×C11311yescharacteristic, complemented
547C22×M16C22×C11311yescharacteristic
548D4×Q8—21no—
549#548—21no—
550#547—21no—
551#547—22no—
552#546—21no—
553#546—22no—
554#537—21no—
555#537C22×C11311yescharacteristic
556#536—21no—
557#536C22×C11311yescharacteristic
558C2×#124C22×C11311yescharacteristic, complemented
559#525—21no—
560#525C22×C11311yescharacteristic
561C2×C22⋊Q8—21no—
562C2×C22⋊Q8C22×C11311yescharacteristic
563C2×#121C22×C11311yescharacteristic
564#520C22×C11311yescharacteristic
565C2×#117C22×C11311yescharacteristic
566#469—21no—
567#468—21no—
568#466—21no—
569#465—21no—
570#454—24no—
571#449—21no—
572#449—21no—
573#448—21no—
574#447—21no—
575#428C22×C11311yescharacteristic, complemented
576#421—24no—
577C2×#104C22×C11311yescharacteristic
578C2×#104C22×C11311yescharacteristic
579C2×#104C22×C11311yescharacteristic
580C2×#104C22×C11311yescharacteristic
581C2×#104C22×C11311yescharacteristic, complemented
582C2×#104C22×C11311yescharacteristic, complemented
583#418C22×C11311yescharacteristic, complemented
584#417C22×C11311yescharacteristic
585#417C22×C11311yescharacteristic
586#417C22×C11311yescharacteristic, complemented
587C2×#101C22×C11311yescharacteristic, complemented
588C2×#101C22×C11311yescharacteristic, complemented
589#407C22×C11311yescharacteristic
590#396—22no—
591#394—22no—
592#391C22×C11311yescharacteristic, complemented
593#390C22×C11311yescharacteristic, complemented
594#384C22×C11311yescharacteristic, complemented
595#343C22×C11311yescharacteristic, complemented
596#343C22×C11311yescharacteristic, complemented
597#339C22×C11311yescharacteristic, complemented
598#339C22×C11311yescharacteristic, complemented
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C11311yescharacteristic
613C2×#41D4×C11311yescharacteristic
614C2×#41C23×C11311yescharacteristic
615C2×#41C23×C11311yescharacteristic
616C2×#41C23×C11311yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C11311yescharacteristic
620C22×Q8C23×C11311yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C11311yescharacteristic
624C22×D4C23×C11311yescharacteristic
625C23×C4—21no—
626C23×C4C23×C11311yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C11311yescharacteristic
643C2×M16C23×C11311yescharacteristic
644C2×M16C23×C11311yescharacteristic
645C2×M16C23×C11311yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C11311yescharacteristic
670C22⋊Q8D4×C11311yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C11311yescharacteristic
682#121D4×C11311yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C11311yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C11312yes—
701C2×C4⋊C4C23×C11311yescharacteristic
702C2×C4⋊C4C23×C11311yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C11312yes—
709C2×C42C23×C11311yescharacteristic
710C2×C42C23×C11311yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C11314yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C11311yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C11312yes—
760#41#41×C11312yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C11311yescharacteristic
776C2×Q8C2×D4×C11311yescharacteristic
777C2×Q8C2×D4×C11311yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C11311yescharacteristic
802C2×D4C2×D4×C11311yescharacteristic
803C2×D4C2×D4×C11311yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C11312yes—
823C22×C4C2×D4×C11311yescharacteristic
824C22×C4C2×D4×C11311yescharacteristic
825C22×C4C2×D4×C11311yescharacteristic
826C22×C4C2×D4×C11311yescharacteristic
827C22×C4C2×D4×C11311yescharacteristic
828C22×C4C2×D4×C11312yes—
829C22×C4C24×C11311yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C11312yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C11311yescharacteristic
865C4⋊C4C2×D4×C11311yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C11312yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C11311yescharacteristic
905C23#120×C11311yescharacteristic
906C23C22×D4×C11311yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C11312yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—44no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C11312yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—44no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C11311yescharacteristic
985C2×C4#120×C11311yescharacteristic
986C2×C4C22×D4×C11311yescharacteristic
987C2×C4C22×D4×C11311yescharacteristic
988C2×C4C22×D4×C11311yescharacteristic
989C2×C4C2×#41×C11311yescharacteristic
990C2×C4H(5,𝔽2)×C11311yescharacteristic
991C2×C4H(5,𝔽2)×C11311yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C11311yescharacteristic
1022C22D42×C11311yescharacteristic
1023C22#546×C11311yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C11311yescharacteristic
1037C4#534×C11311yescharacteristic
1038C4D42×C11311yescharacteristic
1039C4#546×C11311yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C113×#241011yescharacteristic
1049C2C113×#302011yescharacteristic
1050C2C113×#302111yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3489C2semidirect
2. C113×#3055C2semidirect
3. C2×#454×C113C2semidirect
4. C113×#3006C2semidirect
5. C2×#421×C113C2semidirect
6. C113×#2620C2semidirect
7. C113×#2039C2semidirect
8. C113×#2038C2semidirect
9. C113×#2006C2semidirect
10. C113×#2003C2semidirect
11. C113×#1901C2semidirect
12. C113×#1897C2semidirect
13. C113×#1883C2semidirect
14. C113×#1859C2semidirect
15. C113×#1793C2semidirect
20. C2×AGL(1,ℤ/8)×C113C22semidirect
32. C2×#124×C113C22semidirect
49. #428×C113C22semidirect
55. C2×#104×C113C22semidirect
56. C2×#104×C113C22semidirect
57. #418×C113C22semidirect
60. #417×C113C22semidirect
61. C2×#101×C113C22semidirect
62. C2×#101×C113C22semidirect
66. #391×C113C22semidirect
67. #390×C113C22semidirect
68. #384×C113C22semidirect
69. #343×C113C22semidirect
70. #343×C113C22semidirect
71. #339×C113C22semidirect
72. #339×C113C22semidirect
192. #104×C113D4semidirect
514. #24469C113direct (N × H)
526. #3489C2×C113semidirect
527. #3055C2×C113semidirect
528. C2×#454C2×C113semidirect
529. #3006C2×C113semidirect
530. C2×#421C2×C113semidirect
531. #2620C2×C113semidirect
532. #2039C2×C113semidirect
533. #2038C2×C113semidirect
534. #2006C2×C113semidirect
535. #2003C2×C113semidirect
536. #1901C2×C113semidirect
537. #1897C2×C113semidirect
538. #1883C2×C113semidirect
539. #1859C2×C113semidirect
540. #1793C2×C113semidirect
541. C113#24469direct (N × H)
546. C2×AGL(1,ℤ/8)C22×C113semidirect
558. C2×#124C22×C113semidirect
575. #428C22×C113semidirect
581. C2×#104C22×C113semidirect
582. C2×#104C22×C113semidirect
583. #418C22×C113semidirect
586. #417C22×C113semidirect
587. C2×#101C22×C113semidirect
588. C2×#101C22×C113semidirect
592. #391C22×C113semidirect
593. #390C22×C113semidirect
594. #384C22×C113semidirect
595. #343C22×C113semidirect
596. #343C22×C113semidirect
597. #339C22×C113semidirect
598. #339C22×C113semidirect
718. #104D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34892
C113×#30552
C2×#454×C1132
C113×#30062
C2×#421×C1132
C113×#26202
C113×#20392
C113×#20382
C113×#20062
C113×#20032
C113×#19012
C113×#18972
C113×#18832
C113×#18592
C113×#17932
#24469113