Finite Group Databasebeta

← C113×#26147 #43294167

Subgroups — C113×#26147 #43294167

Order 28928.

938 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C113C211yesmaximal, characteristic, complemented
2C2×#428×C113C211yesmaximal, characteristic, complemented
3C113×#2416C211yesmaximal, characteristic
4C113×#2352C211yesmaximal, characteristic, complemented
5C113×#2092C211yesmaximal, characteristic, complemented
6C113×#2085C211yesmaximal, characteristic, complemented
7C113×#2077C211yesmaximal, characteristic, complemented
8C113×#2034C211yesmaximal, characteristic, complemented
9C113×#1925C211yesmaximal, characteristic, complemented
10C113×#1921C211yesmaximal, characteristic, complemented
11C113×#1895C211yesmaximal, characteristic, complemented
12C113×#1875C211yesmaximal, characteristic, complemented
13C113×#1870C211yesmaximal, characteristic, complemented
14C113×#1852C211yesmaximal, characteristic, complemented
15C113×#1852C211yesmaximal, characteristic, complemented
16C22×M16×C113C2211yescharacteristic
17C2×#121×C113—21no—
18C2×#121×C113C2211yescharacteristic
19C2×#121×C113C2211yescharacteristic
20C2×C4×D4×C113C2211yescharacteristic
21C2×#117×C113C2211yescharacteristic
22C22×C4⋊C4×C113C2211yescharacteristic
23C22×C4⋊C4×C113C2211yescharacteristic
24#480×C113—24no—
25#428×C113—24no—
26C2×#107×C113C2211yescharacteristic
27C2×#107×C113C2211yescharacteristic
28C2×#107×C113C2211yescharacteristic
29C2×#107×C113C2211yescharacteristic
30C2×#106×C113C2211yescharacteristic
31C2×#106×C113C2211yescharacteristic
32C2×#102×C113C2211yescharacteristic
33C2×#102×C113C2211yescharacteristic
34C2×#102×C113C2211yescharacteristic
35C2×#102×C113C2211yescharacteristic
36C2×C22⋊C8×C113C2211yescharacteristic
37C2×C22⋊C8×C113C2211yescharacteristic
38C2×C22⋊C8×C113C2211yescharacteristic
39#396×C113—21no—
40#394×C113—21no—
41#390×C113C2211yescharacteristic
42#389×C113C2211yescharacteristic
43#388×C113—21no—
44#387×C113—21no—
45#386×C113—21no—
46#386×C113—21no—
47#382×C113C2211yescharacteristic
48#380×C113C2211yescharacteristic
49#380×C113C2211yescharacteristic
50#380×C113C2211yescharacteristic
51C4×C4⋊C4×C113C2211yescharacteristic
52C4×C22⋊C4×C113—21no—
53#340×C113C2211yescharacteristic
54#340×C113C2211yescharacteristic
55#340×C113C2211yescharacteristic
56#340×C113C2211yescharacteristic
57#340×C113C2211yescharacteristic
58#340×C113C2211yescharacteristic
59#336×C113C2211yescharacteristic
60#336×C113C2211yescharacteristic
61C22×D4×C113—21no—
62C22×D4×C113—21no—
63C22×D4×C113D411yescharacteristic
64C22×D4×C113C2311yescharacteristic
65C23×C4×C113—21no—
66C23×C4×C113—21no—
67C23×C4×C113C2311yescharacteristic
68C23×C4×C113C2311yescharacteristic
69C2×M16×C113—22no—
70C2×M16×C113—22no—
71C2×M16×C113—22no—
72C22×C8×C113C2311yescharacteristic
73C22×C8×C113C2311yescharacteristic
74C22×C8×C113C2311yescharacteristic
75C22×C8×C113C2311yescharacteristic
76#121×C113—22no—
77#121×C113—22no—
78#121×C113—22no—
79#121×C113—41no—
80#121×C113—44no—
81C4×D4×C113—22no—
82C4×D4×C113—22no—
83#117×C113—22no—
84#117×C113—41no—
85C2×C4⋊C4×C113—22no—
86C2×C4⋊C4×C113—22no—
87C2×C4⋊C4×C113—21no—
88C2×C4⋊C4×C113—21no—
89C2×C4⋊C4×C113—21no—
90C2×C4⋊C4×C113—41no—
91C2×C4⋊C4×C113—41no—
92C2×C4⋊C4×C113D411yescharacteristic
93C2×C4⋊C4×C113C2311yescharacteristic
94C2×C4⋊C4×C113C2311yescharacteristic
95C2×C4⋊C4×C113C2311yescharacteristic
96C2×C4⋊C4×C113C2311yescharacteristic
97C2×C4⋊C4×C113C2311yescharacteristic
98C2×C4⋊C4×C113C2311yescharacteristic
99C2×C4⋊C4×C113C2311yescharacteristic
100C2×C22⋊C4×C113—21no—
101C2×C22⋊C4×C113—21no—
102C2×C22⋊C4×C113—21no—
103C2×C22⋊C4×C113—21no—
104C2×C22⋊C4×C113—21no—
105C2×C22⋊C4×C113—21no—
106C2×C22⋊C4×C113—21no—
107C2×C22⋊C4×C113—21no—
108C2×C22⋊C4×C113D411yescharacteristic
109C2×C22⋊C4×C113D411yescharacteristic
110C2×C42×C113—21no—
111C2×C42×C113—21no—
112C2×C42×C113C2311yescharacteristic
113#107×C113—22no—
114#107×C113—22no—
115#107×C113—41no—
116#107×C113D414yescomplemented
117#106×C113—22no—
118#106×C113—22no—
119#102×C113—22no—
120#102×C113—22no—
121#102×C113—22no—
122#102×C113—41no—
123C22⋊C8×C113—22no—
124C22⋊C8×C113—22no—
125C22⋊C8×C113—22no—
126#95×C113—21no—
127#95×C113—21no—
128#95×C113—21no—
129#95×C113—21no—
130#95×C113—21no—
131#95×C113—21no—
132#95×C113—21no—
133C24×C113—21no—
134C24×C113C2×D411yescharacteristic
135C24×C113C2×D411yescharacteristic
136C2×D4×C113—22no—
137C2×D4×C113—22no—
138C2×D4×C113—21no—
139C2×D4×C113—21no—
140C2×D4×C113—21no—
141C2×D4×C113—21no—
142C2×D4×C113—21no—
143C2×D4×C113—21no—
144C2×D4×C113—41no—
145C2×D4×C113—42no—
146C2×D4×C113—42no—
147C2×D4×C113—42no—
148C2×D4×C113—42no—
149C2×D4×C113—42no—
150C2×D4×C113—81no—
151C22×C4×C113—21no—
152C22×C4×C113—21no—
153C22×C4×C113—21no—
154C22×C4×C113—21no—
155C22×C4×C113—21no—
156C22×C4×C113—21no—
157C22×C4×C113—21no—
158C22×C4×C113—21no—
159C22×C4×C113—21no—
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—42no—
169C22×C4×C113—42no—
170C22×C4×C113—42no—
171C22×C4×C113—42no—
172C22×C4×C113—81no—
173C22×C4×C113—81no—
174C22×C4×C113C2×D411yescharacteristic
175C22×C4×C113C2×D411yescharacteristic
176C22×C4×C113C2×D411yescharacteristic
177C22×C4×C113C2×D411yescharacteristic
178C22×C4×C113#4112yes—
179C22×C4×C113#4112yes—
180C22×C4×C113C2411yescharacteristic
181M16×C113—28no—
182C2×C8×C113—21no—
183C2×C8×C113—21no—
184C2×C8×C113—21no—
185C2×C8×C113—21no—
186C2×C8×C113—21no—
187C2×C8×C113—21no—
188C2×C8×C113—21no—
189C2×C8×C113—21no—
190C2×C8×C113—21no—
191C2×C8×C113—21no—
192C2×C8×C113C2×D412yes—
193C2×C8×C113#4112yes—
194C4⋊C4×C113—22no—
195C4⋊C4×C113—21no—
196C4⋊C4×C113—21no—
197C4⋊C4×C113—21no—
198C4⋊C4×C113—21no—
199C4⋊C4×C113—21no—
200C4⋊C4×C113—21no—
201C4⋊C4×C113—21no—
202C4⋊C4×C113—21no—
203C4⋊C4×C113—21no—
204C4⋊C4×C113—21no—
205C4⋊C4×C113—21no—
206C4⋊C4×C113—21no—
207C4⋊C4×C113—42no—
208C4⋊C4×C113—42no—
209C4⋊C4×C113—42no—
210C4⋊C4×C113C2×D412yes—
211C4⋊C4×C113C2×D412yes—
212C22⋊C4×C113—22no—
213C22⋊C4×C113—22no—
214C22⋊C4×C113—42no—
215C22⋊C4×C113—42no—
216C22⋊C4×C113—42no—
217C22⋊C4×C113—42no—
218C22⋊C4×C113—42no—
219C22⋊C4×C113—42no—
220C22⋊C4×C113—81no—
221C22⋊C4×C113—81no—
222C42×C113—21no—
223C42×C113—21no—
224C42×C113—42no—
225C42×C113—81no—
226C23×C113—21no—
227C23×C113—21no—
228C23×C113—21no—
229C23×C113—21no—
230C23×C113—21no—
231C23×C113—21no—
232C23×C113—21no—
233C23×C113—21no—
234C23×C113—21no—
235C23×C113—21no—
236C23×C113—21no—
237C23×C113—21no—
238C23×C113—41no—
239C23×C113—41no—
240C23×C113—41no—
241C23×C113—41no—
242C23×C113—41no—
243C23×C113—41no—
244C23×C113—41no—
245C23×C113#12312yes—
246C23×C113AGL(1,ℤ/8)12yes—
247C23×C113C22×D411yescharacteristic
248D4×C113—44no—
249D4×C113—41no—
250D4×C113—41no—
251D4×C113—41no—
252D4×C113—41no—
253D4×C113—84no—
254D4×C113—84no—
255C2×C4×C113—21no—
256C2×C4×C113—21no—
257C2×C4×C113—22no—
258C2×C4×C113—22no—
259C2×C4×C113—22no—
260C2×C4×C113—22no—
261C2×C4×C113—21no—
262C2×C4×C113—21no—
263C2×C4×C113—21no—
264C2×C4×C113—22no—
265C2×C4×C113—21no—
266C2×C4×C113—22no—
267C2×C4×C113—21no—
268C2×C4×C113—21no—
269C2×C4×C113—21no—
270C2×C4×C113—21no—
271C2×C4×C113—21no—
272C2×C4×C113—41no—
273C2×C4×C113—41no—
274C2×C4×C113—41no—
275C2×C4×C113—41no—
276C2×C4×C113—41no—
277C2×C4×C113—41no—
278C2×C4×C113—41no—
279C2×C4×C113—41no—
280C2×C4×C113—41no—
281C2×C4×C113—41no—
282C2×C4×C113—41no—
283C2×C4×C113—41no—
284C2×C4×C113—41no—
285C2×C4×C113—41no—
286C2×C4×C113—41no—
287C2×C4×C113—41no—
288C2×C4×C113—41no—
289C2×C4×C113—41no—
290C2×C4×C113—41no—
291C2×C4×C113—41no—
292C2×C4×C113—41no—
293C2×C4×C113—41no—
294C2×C4×C113—41no—
295C2×C4×C113—84no—
296C2×C4×C113—84no—
297C2×C4×C113#12312yes—
298C2×C4×C113C22×D411yescharacteristic
299C2×C4×C113C2×#4111yescharacteristic
300C2×C4×C113C2×#4111yescharacteristic
301C2×C4×C113C2×#4111yescharacteristic
302C2×C4×C113H(5,𝔽2)11yescharacteristic
303C2×C4×C1132−1+411yescharacteristic
304C8×C113—22no—
305C8×C113—22no—
306C8×C113—41no—
307C8×C113—41no—
308C22×C113—22no—
309C22×C113—22no—
310C22×C113—22no—
311C22×C113—22no—
312C22×C113—22no—
313C22×C113—22no—
314C22×C113—41no—
315C22×C113—41no—
316C22×C113—41no—
317C22×C113—41no—
318C22×C113—41no—
319C22×C113—41no—
320C22×C113—41no—
321C22×C113—41no—
322C22×C113—81no—
323C22×C113—81no—
324C22×C113—81no—
325C22×C113—81no—
326C22×C113—81no—
327C22×C113—81no—
328C22×C113—81no—
329C22×C113C2×#12311yescharacteristic
330C22×C113D4211yescharacteristic
331C22×C113#54711yescharacteristic
332C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C113#57511yescharacteristic
334C22×C113#57611yescharacteristic
335C22×C113#57811yescharacteristic
336C4×C113—22no—
337C4×C113—41no—
338C4×C113—41no—
339C4×C113—41no—
340C4×C113—42no—
341C4×C113—42no—
342C4×C113—81no—
343C4×C113—81no—
344C4×C113—81no—
345C4×C113—81no—
346C4×C113—81no—
347C4×C113#52511yescharacteristic
348C4×C113#53911yescharacteristic
349C4×C113#54811yescharacteristic
350C4×C113#55311yescharacteristic
351#26147C11311yesmaximal, characteristic, direct product factor, Sylow
352C2×C113—42no—
353C2×C113—42no—
354C2×C113—161no—
355C2×C113#244311yescharacteristic
356C2×C113#309411yescharacteristic
357C2×C113#309811yescharacteristic
358C2×C113#326411yescharacteristic
359C2×C113#327711yescharacteristic
360C2×C113#334311yescharacteristic
361C2×C113#335511yescharacteristic
362C2×#480C2×C11311yescharacteristic, complemented
363C2×#428C2×C11311yescharacteristic, complemented
364#2416C2×C11311yescharacteristic
365#2352C2×C11311yescharacteristic, complemented
366#2092C2×C11311yescharacteristic, complemented
367#2085C2×C11311yescharacteristic, complemented
368#2077C2×C11311yescharacteristic, complemented
369#2034C2×C11311yescharacteristic, complemented
370#1925C2×C11311yescharacteristic, complemented
371#1921C2×C11311yescharacteristic, complemented
372#1895C2×C11311yescharacteristic, complemented
373#1875C2×C11311yescharacteristic, complemented
374#1870C2×C11311yescharacteristic, complemented
375#1852C2×C11311yescharacteristic, complemented
376#1852C2×C11311yescharacteristic, complemented
377C113#2614711yescharacteristic, direct product factor, Sylow
378C22×M16C22×C11311yescharacteristic
379C2×#121—21no—
380C2×#121C22×C11311yescharacteristic
381C2×#121C22×C11311yescharacteristic
382C2×C4×D4C22×C11311yescharacteristic
383C2×#117C22×C11311yescharacteristic
384C22×C4⋊C4C22×C11311yescharacteristic
385C22×C4⋊C4C22×C11311yescharacteristic
386#480—24no—
387#428—24no—
388C2×#107C22×C11311yescharacteristic
389C2×#107C22×C11311yescharacteristic
390C2×#107C22×C11311yescharacteristic
391C2×#107C22×C11311yescharacteristic
392C2×#106C22×C11311yescharacteristic
393C2×#106C22×C11311yescharacteristic
394C2×#102C22×C11311yescharacteristic
395C2×#102C22×C11311yescharacteristic
396C2×#102C22×C11311yescharacteristic
397C2×#102C22×C11311yescharacteristic
398C2×C22⋊C8C22×C11311yescharacteristic
399C2×C22⋊C8C22×C11311yescharacteristic
400C2×C22⋊C8C22×C11311yescharacteristic
401#396—21no—
402#394—21no—
403#390C22×C11311yescharacteristic
404#389C22×C11311yescharacteristic
405#388—21no—
406#387—21no—
407#386—21no—
408#386—21no—
409#382C22×C11311yescharacteristic
410#380C22×C11311yescharacteristic
411#380C22×C11311yescharacteristic
412#380C22×C11311yescharacteristic
413C4×C4⋊C4C22×C11311yescharacteristic
414C4×C22⋊C4—21no—
415#340C22×C11311yescharacteristic
416#340C22×C11311yescharacteristic
417#340C22×C11311yescharacteristic
418#340C22×C11311yescharacteristic
419#340C22×C11311yescharacteristic
420#340C22×C11311yescharacteristic
421#336C22×C11311yescharacteristic
422#336C22×C11311yescharacteristic
423C22×D4—21no—
424C22×D4—21no—
425C22×D4D4×C11311yescharacteristic
426C22×D4C23×C11311yescharacteristic
427C23×C4—21no—
428C23×C4—21no—
429C23×C4C23×C11311yescharacteristic
430C23×C4C23×C11311yescharacteristic
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—22no—
434C22×C8C23×C11311yescharacteristic
435C22×C8C23×C11311yescharacteristic
436C22×C8C23×C11311yescharacteristic
437C22×C8C23×C11311yescharacteristic
438#121—22no—
439#121—22no—
440#121—22no—
441#121—41no—
442#121—44no—
443C4×D4—22no—
444C4×D4—22no—
445#117—22no—
446#117—41no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4D4×C11311yescharacteristic
455C2×C4⋊C4C23×C11311yescharacteristic
456C2×C4⋊C4C23×C11311yescharacteristic
457C2×C4⋊C4C23×C11311yescharacteristic
458C2×C4⋊C4C23×C11311yescharacteristic
459C2×C4⋊C4C23×C11311yescharacteristic
460C2×C4⋊C4C23×C11311yescharacteristic
461C2×C4⋊C4C23×C11311yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4D4×C11311yescharacteristic
471C2×C22⋊C4D4×C11311yescharacteristic
472C2×C42—21no—
473C2×C42—21no—
474C2×C42C23×C11311yescharacteristic
475#107—22no—
476#107—22no—
477#107—41no—
478#107D4×C11314yescomplemented
479#106—22no—
480#106—22no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102—41no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495C24—21no—
496C24C2×D4×C11311yescharacteristic
497C24C2×D4×C11311yescharacteristic
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—41no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4C2×D4×C11311yescharacteristic
537C22×C4C2×D4×C11311yescharacteristic
538C22×C4C2×D4×C11311yescharacteristic
539C22×C4C2×D4×C11311yescharacteristic
540C22×C4#41×C11312yes—
541C22×C4#41×C11312yes—
542C22×C4C24×C11311yescharacteristic
543M16—28no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8C2×D4×C11312yes—
555C2×C8#41×C11312yes—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4C2×D4×C11312yes—
573C4⋊C4C2×D4×C11312yes—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—42no—
587C42—81no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23#123×C11312yes—
608C23AGL(1,ℤ/8)×C11312yes—
609C23C22×D4×C11311yescharacteristic
610D4—44no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—84no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—84no—
658C2×C4—84no—
659C2×C4#123×C11312yes—
660C2×C4C22×D4×C11311yescharacteristic
661C2×C4C2×#41×C11311yescharacteristic
662C2×C4C2×#41×C11311yescharacteristic
663C2×C4C2×#41×C11311yescharacteristic
664C2×C4H(5,𝔽2)×C11311yescharacteristic
665C2×C42−1+4×C11311yescharacteristic
666C8—22no—
667C8—22no—
668C8—41no—
669C8—41no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C2×#123×C11311yescharacteristic
692C22D42×C11311yescharacteristic
693C22#547×C11311yescharacteristic
694C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
695C22#575×C11311yescharacteristic
696C22#576×C11311yescharacteristic
697C22#578×C11311yescharacteristic
698C4—22no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—42no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4#525×C11311yescharacteristic
710C4#539×C11311yescharacteristic
711C4#548×C11311yescharacteristic
712C4#553×C11311yescharacteristic
713C2—42no—
714C2—42no—
715C2—161no—
716C2C113×#244311yescharacteristic
717C2C113×#309411yescharacteristic
718C2C113×#309811yescharacteristic
719C2C113×#326411yescharacteristic
720C2C113×#327711yescharacteristic
721C2C113×#334311yescharacteristic
722C2C113×#335511yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#2416C2
LCSG ▷ C22×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
1. C2×#480×C113C2semidirect
2. C2×#428×C113C2semidirect
4. C113×#2352C2semidirect
5. C113×#2092C2semidirect
6. C113×#2085C2semidirect
7. C113×#2077C2semidirect
8. C113×#2034C2semidirect
9. C113×#1925C2semidirect
10. C113×#1921C2semidirect
11. C113×#1895C2semidirect
12. C113×#1875C2semidirect
13. C113×#1870C2semidirect
14. C113×#1852C2semidirect
15. C113×#1852C2semidirect
116. #107×C113D4semidirect
351. #26147C113direct (N × H)
362. C2×#480C2×C113semidirect
363. C2×#428C2×C113semidirect
365. #2352C2×C113semidirect
366. #2092C2×C113semidirect
367. #2085C2×C113semidirect
368. #2077C2×C113semidirect
369. #2034C2×C113semidirect
370. #1925C2×C113semidirect
371. #1921C2×C113semidirect
372. #1895C2×C113semidirect
373. #1875C2×C113semidirect
374. #1870C2×C113semidirect
375. #1852C2×C113semidirect
376. #1852C2×C113semidirect
377. C113#26147direct (N × H)
478. #107D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1132
C2×#428×C1132
C113×#24162
C113×#23522
C113×#20922
C113×#20852
C113×#20772
C113×#20342
C113×#19252
C113×#19212
C113×#18952
C113×#18752
C113×#18702
C113×#18522
#26147113