Finite Group Databasebeta

← C113×#24034 #43292054

Subgroups — C113×#24034 #43292054

Order 28928.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C113C211yesmaximal, characteristic
2C2×#482×C113C211yesmaximal, characteristic, complemented
3C2×#416×C113C211yesmaximal, characteristic, complemented
4C113×#2485C211yesmaximal, characteristic, complemented
5C113×#2041C211yesmaximal, characteristic, complemented
6C113×#2041C211yesmaximal, characteristic, complemented
7C113×#2034C211yesmaximal, characteristic, complemented
8C113×#2033C211yesmaximal, characteristic, complemented
9C113×#1893C211yesmaximal, characteristic, complemented
10C113×#1869C211yesmaximal, characteristic, complemented
11C113×#1865C211yesmaximal, characteristic, complemented
12C113×#1863C211yesmaximal, characteristic, complemented
13C113×#1788C211yesmaximal, characteristic, complemented
14C113×#1788C211yesmaximal, characteristic, complemented
15C113×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C23×C8×C113C2211yescharacteristic
19#550×C113—24no—
20#550×C113—24no—
21C2×#127×C113—21no—
22C2×#127×C113C2211yescharacteristic
23C2×#121×C113—21no—
24C2×#121×C113—21no—
25C2×#121×C113C2211yescharacteristic
26C2×#121×C113C2211yescharacteristic
27C2×C4×Q8×C113C2211yescharacteristic
28C2×C4×D4×C113—21no—
29C2×C4×D4×C113C2211yescharacteristic
30C2×#117×C113C2211yescharacteristic
31#482×C113—24no—
32C2×#107×C113C2211yescharacteristic
33C2×#106×C113C2211yescharacteristic
34#416×C113—24no—
35C2×#103×C113C2211yescharacteristic
36C2×#103×C113C2211yescharacteristic
37C2×#103×C113C2211yescharacteristic
38C2×#103×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×#102×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic
46C2×#102×C113C2211yescharacteristic
47C2×C22⋊C8×C113C2211yescharacteristic
48C2×C22⋊C8×C113C2211yescharacteristic
49C2×C22⋊C8×C113C2211yescharacteristic
50#397×C113—21no—
51#394×C113—21no—
52#389×C113C2211yescharacteristic
53#389×C113C2211yescharacteristic
54#388×C113—21no—
55#387×C113—21no—
56#380×C113C2211yescharacteristic
57#380×C113C2211yescharacteristic
58#380×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic
60#340×C113C2211yescharacteristic
61#336×C113C2211yescharacteristic
62#336×C113C2211yescharacteristic
63C2×#41×C113—22no—
64C2×#41×C113—22no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—22no—
70C2×#41×C113—41no—
71C2×#41×C113—41no—
72C2×#41×C113—41no—
73C2×#41×C113—41no—
74C2×#41×C113D414yes—
75C22×Q8×C113C2311yescharacteristic
76C22×D4×C113—21no—
77C22×D4×C113—21no—
78C22×D4×C113—21no—
79C22×D4×C113—21no—
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113D411yescharacteristic
83C22×D4×C113C2311yescharacteristic
84C22×D4×C113C2311yescharacteristic
85C23×C4×C113—21no—
86C23×C4×C113—21no—
87C23×C4×C113C2311yescharacteristic
88C23×C4×C113C2311yescharacteristic
89C22×C8×C113—22no—
90C22×C8×C113—41no—
91C22×C8×C113—41no—
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94C22×C8×C113C2311yescharacteristic
95C22×C8×C113C2311yescharacteristic
96#127×C113—28no—
97#127×C113—22no—
98#127×C113—22no—
99#121×C113—28no—
100#121×C113—28no—
101#121×C113—22no—
102#121×C113—22no—
103#121×C113—22no—
104#121×C113D414yes—
105C4×Q8×C113—22no—
106C4×Q8×C113—22no—
107C4×D4×C113—28no—
108C4×D4×C113—22no—
109C4×D4×C113—22no—
110#117×C113—22no—
111#117×C113—22no—
112C2×C4⋊C4×C113—21no—
113C2×C4⋊C4×C113—21no—
114C2×C4⋊C4×C113—21no—
115C2×C4⋊C4×C113D411yescharacteristic
116C2×C4⋊C4×C113C2311yescharacteristic
117C2×C4⋊C4×C113C2311yescharacteristic
118C2×C4⋊C4×C113C2311yescharacteristic
119C2×C4⋊C4×C113C2311yescharacteristic
120C2×C4⋊C4×C113C2311yescharacteristic
121C2×C22⋊C4×C113—21no—
122C2×C22⋊C4×C113—21no—
123C2×C22⋊C4×C113—21no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113D411yescharacteristic
128C2×C22⋊C4×C113D411yescharacteristic
129C2×C42×C113—21no—
130C2×C42×C113—21no—
131C2×C42×C113C2311yescharacteristic
132#107×C113—22no—
133#106×C113—22no—
134#103×C113—22no—
135#103×C113—22no—
136#103×C113—22no—
137#103×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113—41no—
143#102×C113—41no—
144#102×C113—41no—
145#102×C113—41no—
146C22⋊C8×C113—22no—
147C22⋊C8×C113—41no—
148C22⋊C8×C113—41no—
149#95×C113—21no—
150#95×C113—21no—
151#95×C113—21no—
152#95×C113—21no—
153#95×C113—21no—
154C24×C113—21no—
155C24×C113—21no—
156C24×C113C2×D411yescharacteristic
157C24×C113C2×D411yescharacteristic
158#41×C113—28no—
159#41×C113—44no—
160#41×C113—44no—
161#41×C113—44no—
162#41×C113—44no—
163#41×C113—44no—
164#41×C113—44no—
165#41×C113—44no—
166C2×Q8×C113—21no—
167C2×Q8×C113—21no—
168C2×Q8×C113—21no—
169C2×Q8×C113C2×D412yes—
170C2×Q8×C113#4112yes—
171C2×Q8×C113#4112yes—
172C2×D4×C113—24no—
173C2×D4×C113—24no—
174C2×D4×C113—22no—
175C2×D4×C113—24no—
176C2×D4×C113—24no—
177C2×D4×C113—24no—
178C2×D4×C113—24no—
179C2×D4×C113—22no—
180C2×D4×C113—21no—
181C2×D4×C113—21no—
182C2×D4×C113—21no—
183C2×D4×C113—21no—
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—41no—
191C2×D4×C113—42no—
192C2×D4×C113—42no—
193C2×D4×C113—42no—
194C2×D4×C113—42no—
195C2×D4×C113—42no—
196C2×D4×C113—42no—
197C2×D4×C113—81no—
198C2×D4×C113—81no—
199C2×D4×C113—81no—
200C2×D4×C113—81no—
201C2×D4×C113—81no—
202C2×D4×C113—81no—
203C2×D4×C113C2×D412yes—
204C2×D4×C113C2×D412yes—
205C22×C4×C113—21no—
206C22×C4×C113—21no—
207C22×C4×C113—21no—
208C22×C4×C113—21no—
209C22×C4×C113—21no—
210C22×C4×C113—24no—
211C22×C4×C113—21no—
212C22×C4×C113—24no—
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—21no—
220C22×C4×C113—21no—
221C22×C4×C113—21no—
222C22×C4×C113—21no—
223C22×C4×C113—42no—
224C22×C4×C113—42no—
225C22×C4×C113—42no—
226C22×C4×C113—42no—
227C22×C4×C113C2×D411yescharacteristic
228C22×C4×C113C2×D411yescharacteristic
229C22×C4×C113C2×D411yescharacteristic
230C22×C4×C113C2×D412yes—
231C22×C4×C113C2×D412yes—
232C22×C4×C113C2×D411yescharacteristic
233C22×C4×C113C2411yescharacteristic
234C2×C8×C113—21no—
235C2×C8×C113—21no—
236C2×C8×C113—21no—
237C2×C8×C113—21no—
238C2×C8×C113—21no—
239C2×C8×C113—21no—
240C2×C8×C113—21no—
241C2×C8×C113—21no—
242C2×C8×C113—21no—
243C2×C8×C113—21no—
244C2×C8×C113—21no—
245C2×C8×C113—21no—
246C2×C8×C113—44no—
247C4⋊C4×C113—24no—
248C4⋊C4×C113—22no—
249C4⋊C4×C113—21no—
250C4⋊C4×C113—21no—
251C4⋊C4×C113—21no—
252C4⋊C4×C113—21no—
253C4⋊C4×C113—21no—
254C4⋊C4×C113—21no—
255C4⋊C4×C113—21no—
256C4⋊C4×C113—21no—
257C4⋊C4×C113—21no—
258C4⋊C4×C113—42no—
259C4⋊C4×C113—81no—
260C4⋊C4×C113C2×D412yes—
261C22⋊C4×C113—24no—
262C22⋊C4×C113—22no—
263C22⋊C4×C113—24no—
264C22⋊C4×C113—22no—
265C22⋊C4×C113—42no—
266C22⋊C4×C113—42no—
267C22⋊C4×C113—81no—
268C22⋊C4×C113—81no—
269C42×C113—24no—
270C42×C113—21no—
271C42×C113—21no—
272C42×C113—42no—
273C23×C113—21no—
274C23×C113—21no—
275C23×C113—21no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—21no—
279C23×C113—21no—
280C23×C113—22no—
281C23×C113—22no—
282C23×C113—21no—
283C23×C113—21no—
284C23×C113—21no—
285C23×C113—21no—
286C23×C113—21no—
287C23×C113—21no—
288C23×C113—41no—
289C23×C113—41no—
290C23×C113—41no—
291C23×C113—41no—
292C23×C113—41no—
293C23×C113—41no—
294C23×C113—41no—
295C23×C113—41no—
296C23×C113—41no—
297C23×C113—41no—
298C23×C113—41no—
299C23×C113—41no—
300C23×C113#12012yes—
301C23×C113C22×D411yescharacteristic
302Q8×C113—22no—
303Q8×C113—22no—
304Q8×C113—22no—
305Q8×C113#12314yes—
306D4×C113—22no—
307D4×C113—22no—
308D4×C113—22no—
309D4×C113—22no—
310D4×C113—44no—
311D4×C113—48no—
312D4×C113—48no—
313D4×C113—48no—
314D4×C113—41no—
315D4×C113—41no—
316D4×C113—41no—
317D4×C113—41no—
318D4×C113—84no—
319D4×C113—84no—
320D4×C113—84no—
321C2×C4×C113—21no—
322C2×C4×C113—22no—
323C2×C4×C113—21no—
324C2×C4×C113—21no—
325C2×C4×C113—22no—
326C2×C4×C113—22no—
327C2×C4×C113—21no—
328C2×C4×C113—22no—
329C2×C4×C113—22no—
330C2×C4×C113—22no—
331C2×C4×C113—22no—
332C2×C4×C113—21no—
333C2×C4×C113—22no—
334C2×C4×C113—21no—
335C2×C4×C113—21no—
336C2×C4×C113—21no—
337C2×C4×C113—21no—
338C2×C4×C113—21no—
339C2×C4×C113—48no—
340C2×C4×C113—48no—
341C2×C4×C113—41no—
342C2×C4×C113—41no—
343C2×C4×C113—41no—
344C2×C4×C113—41no—
345C2×C4×C113—41no—
346C2×C4×C113—41no—
347C2×C4×C113—41no—
348C2×C4×C113—41no—
349C2×C4×C113—41no—
350C2×C4×C113—41no—
351C2×C4×C113—41no—
352C2×C4×C113—41no—
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#12012yes—
360C2×C4×C113#13512yes—
361C2×C4×C113C22×D411yescharacteristic
362C2×C4×C113C22×D411yescharacteristic
363C2×C4×C113C2×#4111yescharacteristic
364C2×C4×C113C2×#4111yescharacteristic
365C2×C4×C113H(5,𝔽2)11yescharacteristic
366C2×C4×C113H(5,𝔽2)11yescharacteristic
367C8×C113—41no—
368C8×C113—41no—
369C8×C113—41no—
370C8×C113—41no—
371C22×C113—22no—
372C22×C113—22no—
373C22×C113—22no—
374C22×C113—41no—
375C22×C113—41no—
376C22×C113—41no—
377C22×C113—41no—
378C22×C113—42no—
379C22×C113—42no—
380C22×C113—41no—
381C22×C113—41no—
382C22×C113—42no—
383C22×C113—42no—
384C22×C113—41no—
385C22×C113—42no—
386C22×C113—42no—
387C22×C113—41no—
388C22×C113—41no—
389C22×C113—41no—
390C22×C113—41no—
391C22×C113—81no—
392C22×C113—81no—
393C22×C113—81no—
394C22×C113—81no—
395C22×C113—81no—
396C22×C113—81no—
397C22×C113—81no—
398C22×C113—81no—
399C22×C113C2×#12011yescharacteristic
400C22×C113#54611yescharacteristic
401C22×C113#54611yescharacteristic
402C22×C113C2×#13511yescharacteristic
403C22×C113#57511yescharacteristic
404C22×C113#57611yescharacteristic
405C22×C113#57711yescharacteristic
406C4×C113—22no—
407C4×C113—24no—
408C4×C113—22no—
409C4×C113—41no—
410C4×C113—41no—
411C4×C113—42no—
412C4×C113—81no—
413C4×C113—81no—
414C4×C113—81no—
415C4×C113—81no—
416C4×C113C2×#12311yescharacteristic
417C4×C113#53411yescharacteristic
418C4×C113#54611yescharacteristic
419C4×C113#54611yescharacteristic
420#24034C11311yesmaximal, characteristic, direct product factor, Sylow
421C2×C113—42no—
422C2×C113—81no—
423C2×C113—82no—
424C2×C113—82no—
425C2×C113#240511yescharacteristic
426C2×C113#300211yescharacteristic
427C2×C113#301211yescharacteristic
428C2×C113#330411yescharacteristic
429C2×C113#330511yescharacteristic
430C2×C113#330911yescharacteristic
431C2×C113#331711yescharacteristic
432C2×#550C2×C11311yescharacteristic
433C2×#482C2×C11311yescharacteristic, complemented
434C2×#416C2×C11311yescharacteristic, complemented
435#2485C2×C11311yescharacteristic, complemented
436#2041C2×C11311yescharacteristic, complemented
437#2041C2×C11311yescharacteristic, complemented
438#2034C2×C11311yescharacteristic, complemented
439#2033C2×C11311yescharacteristic, complemented
440#1893C2×C11311yescharacteristic, complemented
441#1869C2×C11311yescharacteristic, complemented
442#1865C2×C11311yescharacteristic, complemented
443#1863C2×C11311yescharacteristic, complemented
444#1788C2×C11311yescharacteristic, complemented
445#1788C2×C11311yescharacteristic, complemented
446#1788C2×C11311yescharacteristic, complemented
447C113#2403411yescharacteristic, direct product factor, Sylow
448C22×#41C22×C11311yescharacteristic
449C22×#41C22×C11311yescharacteristic
450C23×C8C22×C11311yescharacteristic
451#550—24no—
452#550—24no—
453C2×#127—21no—
454C2×#127C22×C11311yescharacteristic
455C2×#121—21no—
456C2×#121—21no—
457C2×#121C22×C11311yescharacteristic
458C2×#121C22×C11311yescharacteristic
459C2×C4×Q8C22×C11311yescharacteristic
460C2×C4×D4—21no—
461C2×C4×D4C22×C11311yescharacteristic
462C2×#117C22×C11311yescharacteristic
463#482—24no—
464C2×#107C22×C11311yescharacteristic
465C2×#106C22×C11311yescharacteristic
466#416—24no—
467C2×#103C22×C11311yescharacteristic
468C2×#103C22×C11311yescharacteristic
469C2×#103C22×C11311yescharacteristic
470C2×#103C22×C11311yescharacteristic
471C2×#102C22×C11311yescharacteristic
472C2×#102C22×C11311yescharacteristic
473C2×#102C22×C11311yescharacteristic
474C2×#102C22×C11311yescharacteristic
475C2×#102C22×C11311yescharacteristic
476C2×#102C22×C11311yescharacteristic
477C2×#102C22×C11311yescharacteristic
478C2×#102C22×C11311yescharacteristic
479C2×C22⋊C8C22×C11311yescharacteristic
480C2×C22⋊C8C22×C11311yescharacteristic
481C2×C22⋊C8C22×C11311yescharacteristic
482#397—21no—
483#394—21no—
484#389C22×C11311yescharacteristic
485#389C22×C11311yescharacteristic
486#388—21no—
487#387—21no—
488#380C22×C11311yescharacteristic
489#380C22×C11311yescharacteristic
490#380C22×C11311yescharacteristic
491#340C22×C11311yescharacteristic
492#340C22×C11311yescharacteristic
493#336C22×C11311yescharacteristic
494#336C22×C11311yescharacteristic
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C11314yes—
507C22×Q8C23×C11311yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C11311yescharacteristic
515C22×D4C23×C11311yescharacteristic
516C22×D4C23×C11311yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C11311yescharacteristic
520C23×C4C23×C11311yescharacteristic
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C23×C11311yescharacteristic
525C22×C8C23×C11311yescharacteristic
526C22×C8C23×C11311yescharacteristic
527C22×C8C23×C11311yescharacteristic
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121D4×C11314yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C11311yescharacteristic
548C2×C4⋊C4C23×C11311yescharacteristic
549C2×C4⋊C4C23×C11311yescharacteristic
550C2×C4⋊C4C23×C11311yescharacteristic
551C2×C4⋊C4C23×C11311yescharacteristic
552C2×C4⋊C4C23×C11311yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C11311yescharacteristic
560C2×C22⋊C4D4×C11311yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C11311yescharacteristic
564#107—22no—
565#106—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586C24—21no—
587C24—21no—
588C24C2×D4×C11311yescharacteristic
589C24C2×D4×C11311yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C11312yes—
602C2×Q8#41×C11312yes—
603C2×Q8#41×C11312yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C11312yes—
636C2×D4C2×D4×C11312yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C11311yescharacteristic
660C22×C4C2×D4×C11311yescharacteristic
661C22×C4C2×D4×C11311yescharacteristic
662C22×C4C2×D4×C11312yes—
663C22×C4C2×D4×C11312yes—
664C22×C4C2×D4×C11311yescharacteristic
665C22×C4C24×C11311yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C11312yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#120×C11312yes—
733C23C22×D4×C11311yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#123×C11314yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#120×C11312yes—
792C2×C4#135×C11312yes—
793C2×C4C22×D4×C11311yescharacteristic
794C2×C4C22×D4×C11311yescharacteristic
795C2×C4C2×#41×C11311yescharacteristic
796C2×C4C2×#41×C11311yescharacteristic
797C2×C4H(5,𝔽2)×C11311yescharacteristic
798C2×C4H(5,𝔽2)×C11311yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#120×C11311yescharacteristic
832C22#546×C11311yescharacteristic
833C22#546×C11311yescharacteristic
834C22C2×#135×C11311yescharacteristic
835C22#575×C11311yescharacteristic
836C22#576×C11311yescharacteristic
837C22#577×C11311yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×#123×C11311yescharacteristic
849C4#534×C11311yescharacteristic
850C4#546×C11311yescharacteristic
851C4#546×C11311yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2C113×#240511yescharacteristic
857C2C113×#300211yescharacteristic
858C2C113×#301211yescharacteristic
859C2C113×#330411yescharacteristic
860C2C113×#330511yescharacteristic
861C2C113×#330911yescharacteristic
862C2C113×#331711yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC2×#550×C113C2
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
2. C2×#482×C113C2semidirect
3. C2×#416×C113C2semidirect
4. C113×#2485C2semidirect
5. C113×#2041C2semidirect
6. C113×#2041C2semidirect
7. C113×#2034C2semidirect
8. C113×#2033C2semidirect
9. C113×#1893C2semidirect
10. C113×#1869C2semidirect
11. C113×#1865C2semidirect
12. C113×#1863C2semidirect
13. C113×#1788C2semidirect
14. C113×#1788C2semidirect
15. C113×#1788C2semidirect
420. #24034C113direct (N × H)
433. C2×#482C2×C113semidirect
434. C2×#416C2×C113semidirect
435. #2485C2×C113semidirect
436. #2041C2×C113semidirect
437. #2041C2×C113semidirect
438. #2034C2×C113semidirect
439. #2033C2×C113semidirect
440. #1893C2×C113semidirect
441. #1869C2×C113semidirect
442. #1865C2×C113semidirect
443. #1863C2×C113semidirect
444. #1788C2×C113semidirect
445. #1788C2×C113semidirect
446. #1788C2×C113semidirect
447. C113#24034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#550×C1132
C2×#482×C1132
C2×#416×C1132
C113×#24852
C113×#20412
C113×#20342
C113×#20332
C113×#18932
C113×#18692
C113×#18652
C113×#18632
C113×#17882
#24034113