Finite Group Databasebeta

← C113×#24427 #43292447

Subgroups — C113×#24427 #43292447

Order 28928.

1500 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C113C211yesmaximal, characteristic
2C2×#465×C113C211yesmaximal, characteristic, complemented
3C2×#452×C113C211yesmaximal, characteristic, complemented
4C2×#452×C113C211yesmaximal, characteristic, complemented
5C2×#416×C113C211yesmaximal, characteristic, complemented
6C113×#2415C211yesmaximal, characteristic, complemented
7C113×#2041C211yesmaximal, characteristic, complemented
8C113×#2034C211yesmaximal, characteristic, complemented
9C113×#2014C211yesmaximal, characteristic, complemented
10C113×#2000C211yesmaximal, characteristic, complemented
11C113×#1878C211yesmaximal, characteristic, complemented
12C113×#1875C211yesmaximal, characteristic, complemented
13C113×#1869C211yesmaximal, characteristic, complemented
14C113×#1865C211yesmaximal, characteristic, complemented
15C113×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C22×Q16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic
20C22×SD16×C113C2211yescharacteristic
21C23×C8×C113C2211yescharacteristic
22#550×C113—24no—
23#550×C113—24no—
24C2×#127×C113—21no—
25C2×#127×C113C2211yescharacteristic
26C2×C22⋊Q8×C113C2211yescharacteristic
27C2×C22⋊Q8×C113C2211yescharacteristic
28C2×#121×C113—21no—
29C2×#121×C113—21no—
30C2×#121×C113C2211yescharacteristic
31C2×#121×C113C2211yescharacteristic
32C2×C4×Q8×C113C2211yescharacteristic
33C2×C4×D4×C113—21no—
34C2×C4×D4×C113C2211yescharacteristic
35C2×#117×C113C2211yescharacteristic
36#465×C113—24no—
37#452×C113—24no—
38#452×C113—24no—
39C2×#106×C113C2211yescharacteristic
40#416×C113—24no—
41C2×#103×C113C2211yescharacteristic
42C2×#103×C113C2211yescharacteristic
43C2×#103×C113C2211yescharacteristic
44C2×#103×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic
46C2×#102×C113C2211yescharacteristic
47C2×#102×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49C2×#102×C113C2211yescharacteristic
50C2×#102×C113C2211yescharacteristic
51C2×C22⋊C8×C113C2211yescharacteristic
52C2×C22⋊C8×C113C2211yescharacteristic
53C2×C22⋊C8×C113C2211yescharacteristic
54#397×C113—21no—
55#394×C113—21no—
56#391×C113C2211yescharacteristic
57#389×C113—21no—
58#389×C113C2211yescharacteristic
59#388×C113—21no—
60#380×C113C2211yescharacteristic
61#340×C113C2211yescharacteristic
62#340×C113C2211yescharacteristic
63#336×C113C2211yescharacteristic
64#336×C113C2211yescharacteristic
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—22no—
70C2×#41×C113—22no—
71C2×#41×C113—22no—
72C2×#41×C113—41no—
73C2×#41×C113—41no—
74C2×#41×C113—41no—
75C2×#41×C113—41no—
76C2×#41×C113D414yes—
77C22×Q8×C113C2311yescharacteristic
78C22×Q8×C113C2311yescharacteristic
79C22×D4×C113—21no—
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113—21no—
83C22×D4×C113—21no—
84C22×D4×C113—21no—
85C22×D4×C113D411yescharacteristic
86C22×D4×C113C2311yescharacteristic
87C22×D4×C113C2311yescharacteristic
88C23×C4×C113—21no—
89C23×C4×C113—21no—
90C23×C4×C113C2311yescharacteristic
91C23×C4×C113C2311yescharacteristic
92C2×Q16×C113—22no—
93C2×Q16×C113—22no—
94C2×Q16×C113—22no—
95C2×SD16×C113—22no—
96C2×SD16×C113—22no—
97C2×SD16×C113—22no—
98C2×SD16×C113—41no—
99C2×SD16×C113—41no—
100C2×SD16×C113—41no—
101C22×C8×C113—22no—
102C22×C8×C113—22no—
103C22×C8×C113—41no—
104C22×C8×C113C2311yescharacteristic
105C22×C8×C113C2311yescharacteristic
106C22×C8×C113C2311yescharacteristic
107C22×C8×C113C2311yescharacteristic
108#127×C113—28no—
109#127×C113—22no—
110#127×C113—22no—
111C22⋊Q8×C113—22no—
112C22⋊Q8×C113—22no—
113C22⋊Q8×C113—22no—
114C22⋊Q8×C113—41no—
115#121×C113—28no—
116#121×C113—28no—
117#121×C113—22no—
118#121×C113—22no—
119#121×C113—22no—
120#121×C113D414yes—
121C4×Q8×C113—22no—
122C4×Q8×C113—22no—
123C4×D4×C113—28no—
124C4×D4×C113—22no—
125C4×D4×C113—22no—
126#117×C113—22no—
127#117×C113—41no—
128C2×C4⋊C4×C113—21no—
129C2×C4⋊C4×C113—21no—
130C2×C4⋊C4×C113—21no—
131C2×C4⋊C4×C113—21no—
132C2×C4⋊C4×C113D411yescharacteristic
133C2×C4⋊C4×C113C2311yescharacteristic
134C2×C4⋊C4×C113C2311yescharacteristic
135C2×C4⋊C4×C113C2311yescharacteristic
136C2×C4⋊C4×C113C2311yescharacteristic
137C2×C22⋊C4×C113—21no—
138C2×C22⋊C4×C113—21no—
139C2×C22⋊C4×C113—21no—
140C2×C22⋊C4×C113—21no—
141C2×C22⋊C4×C113—21no—
142C2×C22⋊C4×C113—21no—
143C2×C22⋊C4×C113D411yescharacteristic
144C2×C22⋊C4×C113D411yescharacteristic
145C2×C42×C113—21no—
146C2×C42×C113—21no—
147C2×C42×C113C2311yescharacteristic
148#106×C113—22no—
149#103×C113—22no—
150#103×C113—22no—
151#103×C113—22no—
152#103×C113D414yescomplemented
153#102×C113—22no—
154#102×C113—22no—
155#102×C113—22no—
156#102×C113—22no—
157#102×C113—22no—
158#102×C113—41no—
159C22⋊C8×C113—22no—
160C22⋊C8×C113—22no—
161C22⋊C8×C113—41no—
162#95×C113—21no—
163#95×C113—21no—
164#95×C113—21no—
165#95×C113—21no—
166C24×C113—21no—
167C24×C113—21no—
168C24×C113C2×D411yescharacteristic
169C24×C113C2×D411yescharacteristic
170#41×C113—28no—
171#41×C113—44no—
172#41×C113—44no—
173#41×C113—44no—
174#41×C113—44no—
175#41×C113—44no—
176#41×C113—44no—
177#41×C113—44no—
178C2×Q8×C113—21no—
179C2×Q8×C113—21no—
180C2×Q8×C113—21no—
181C2×Q8×C113—21no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113—21no—
185C2×Q8×C113—21no—
186C2×Q8×C113—21no—
187C2×Q8×C113C2×D412yes—
188C2×Q8×C113C2×D412yes—
189C2×Q8×C113#4112yes—
190C2×D4×C113—24no—
191C2×D4×C113—24no—
192C2×D4×C113—22no—
193C2×D4×C113—24no—
194C2×D4×C113—24no—
195C2×D4×C113—24no—
196C2×D4×C113—24no—
197C2×D4×C113—22no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—21no—
202C2×D4×C113—21no—
203C2×D4×C113—21no—
204C2×D4×C113—21no—
205C2×D4×C113—21no—
206C2×D4×C113—21no—
207C2×D4×C113—21no—
208C2×D4×C113—41no—
209C2×D4×C113—42no—
210C2×D4×C113—42no—
211C2×D4×C113—42no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113—42no—
215C2×D4×C113—81no—
216C2×D4×C113—81no—
217C2×D4×C113—81no—
218C2×D4×C113—81no—
219C2×D4×C113—81no—
220C2×D4×C113—81no—
221C2×D4×C113C2×D412yes—
222C2×D4×C113C2×D412yes—
223C22×C4×C113—21no—
224C22×C4×C113—21no—
225C22×C4×C113—21no—
226C22×C4×C113—21no—
227C22×C4×C113—21no—
228C22×C4×C113—24no—
229C22×C4×C113—21no—
230C22×C4×C113—21no—
231C22×C4×C113—24no—
232C22×C4×C113—21no—
233C22×C4×C113—21no—
234C22×C4×C113—21no—
235C22×C4×C113—21no—
236C22×C4×C113—21no—
237C22×C4×C113—21no—
238C22×C4×C113—21no—
239C22×C4×C113—21no—
240C22×C4×C113—21no—
241C22×C4×C113—42no—
242C22×C4×C113—42no—
243C22×C4×C113—42no—
244C22×C4×C113—42no—
245C22×C4×C113C2×D411yescharacteristic
246C22×C4×C113C2×D411yescharacteristic
247C22×C4×C113C2×D411yescharacteristic
248C22×C4×C113C2×D412yes—
249C22×C4×C113C2×D412yes—
250C22×C4×C113C2×D411yescharacteristic
251C22×C4×C113C2411yescharacteristic
252Q16×C113—44no—
253SD16×C113—44no—
254SD16×C113—44no—
255C2×C8×C113—21no—
256C2×C8×C113—21no—
257C2×C8×C113—21no—
258C2×C8×C113—21no—
259C2×C8×C113—21no—
260C2×C8×C113—21no—
261C2×C8×C113—21no—
262C2×C8×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113—44no—
267C2×C8×C113C2×D412yes—
268C4⋊C4×C113—24no—
269C4⋊C4×C113—22no—
270C4⋊C4×C113—21no—
271C4⋊C4×C113—21no—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C4⋊C4×C113—21no—
275C4⋊C4×C113—21no—
276C4⋊C4×C113—42no—
277C4⋊C4×C113—42no—
278C4⋊C4×C113—42no—
279C4⋊C4×C113C2×D412yes—
280C4⋊C4×C113C2×D412yes—
281C22⋊C4×C113—24no—
282C22⋊C4×C113—22no—
283C22⋊C4×C113—24no—
284C22⋊C4×C113—22no—
285C22⋊C4×C113—42no—
286C22⋊C4×C113—42no—
287C22⋊C4×C113—42no—
288C22⋊C4×C113—42no—
289C42×C113—24no—
290C42×C113—21no—
291C42×C113—21no—
292C42×C113—42no—
293C23×C113—21no—
294C23×C113—21no—
295C23×C113—21no—
296C23×C113—21no—
297C23×C113—21no—
298C23×C113—21no—
299C23×C113—21no—
300C23×C113—22no—
301C23×C113—22no—
302C23×C113—21no—
303C23×C113—21no—
304C23×C113—21no—
305C23×C113—21no—
306C23×C113—21no—
307C23×C113—21no—
308C23×C113—41no—
309C23×C113—41no—
310C23×C113—41no—
311C23×C113—41no—
312C23×C113—41no—
313C23×C113—41no—
314C23×C113—41no—
315C23×C113—41no—
316C23×C113—41no—
317C23×C113—41no—
318C23×C113—41no—
319C23×C113—41no—
320C23×C113#12012yes—
321C23×C113C22×D411yescharacteristic
322Q8×C113—22no—
323Q8×C113—22no—
324Q8×C113—22no—
325Q8×C113—41no—
326Q8×C113—41no—
327Q8×C113—41no—
328Q8×C113—41no—
329Q8×C113#12114yes—
330D4×C113—22no—
331D4×C113—22no—
332D4×C113—22no—
333D4×C113—22no—
334D4×C113—44no—
335D4×C113—48no—
336D4×C113—48no—
337D4×C113—48no—
338D4×C113—41no—
339D4×C113—41no—
340D4×C113—41no—
341D4×C113—41no—
342D4×C113—84no—
343D4×C113—84no—
344D4×C113—84no—
345C2×C4×C113—21no—
346C2×C4×C113—22no—
347C2×C4×C113—21no—
348C2×C4×C113—22no—
349C2×C4×C113—21no—
350C2×C4×C113—22no—
351C2×C4×C113—21no—
352C2×C4×C113—22no—
353C2×C4×C113—22no—
354C2×C4×C113—22no—
355C2×C4×C113—22no—
356C2×C4×C113—21no—
357C2×C4×C113—22no—
358C2×C4×C113—21no—
359C2×C4×C113—22no—
360C2×C4×C113—21no—
361C2×C4×C113—21no—
362C2×C4×C113—21no—
363C2×C4×C113—21no—
364C2×C4×C113—48no—
365C2×C4×C113—48no—
366C2×C4×C113—41no—
367C2×C4×C113—41no—
368C2×C4×C113—41no—
369C2×C4×C113—41no—
370C2×C4×C113—41no—
371C2×C4×C113—41no—
372C2×C4×C113—41no—
373C2×C4×C113—41no—
374C2×C4×C113—41no—
375C2×C4×C113—41no—
376C2×C4×C113—41no—
377C2×C4×C113—41no—
378C2×C4×C113—41no—
379C2×C4×C113—41no—
380C2×C4×C113—41no—
381C2×C4×C113—41no—
382C2×C4×C113—41no—
383C2×C4×C113#12012yes—
384C2×C4×C113#13512yes—
385C2×C4×C113C22×D411yescharacteristic
386C2×C4×C113C22×D411yescharacteristic
387C2×C4×C113C22×D411yescharacteristic
388C2×C4×C113C2×#4111yescharacteristic
389C2×C4×C113H(5,𝔽2)11yescharacteristic
390C2×C4×C113H(5,𝔽2)11yescharacteristic
391C8×C113—22no—
392C8×C113—41no—
393C8×C113—41no—
394C8×C113—41no—
395C22×C113—22no—
396C22×C113—22no—
397C22×C113—22no—
398C22×C113—41no—
399C22×C113—41no—
400C22×C113—41no—
401C22×C113—41no—
402C22×C113—42no—
403C22×C113—42no—
404C22×C113—41no—
405C22×C113—41no—
406C22×C113—42no—
407C22×C113—42no—
408C22×C113—41no—
409C22×C113—42no—
410C22×C113—42no—
411C22×C113—41no—
412C22×C113—41no—
413C22×C113—41no—
414C22×C113—41no—
415C22×C113—81no—
416C22×C113—81no—
417C22×C113—81no—
418C22×C113—81no—
419C22×C113—81no—
420C22×C113—81no—
421C22×C113—81no—
422C22×C113—81no—
423C22×C113C2×#12011yescharacteristic
424C22×C113D4211yescharacteristic
425C22×C113#54611yescharacteristic
426C22×C113C2×#13511yescharacteristic
427C22×C113#57511yescharacteristic
428C22×C113#57711yescharacteristic
429C22×C113#57711yescharacteristic
430C4×C113—22no—
431C4×C113—24no—
432C4×C113—22no—
433C4×C113—41no—
434C4×C113—41no—
435C4×C113—42no—
436C4×C113—42no—
437C4×C113—81no—
438C4×C113—81no—
439C4×C113—81no—
440C4×C113C2×#12111yescharacteristic
441C4×C113#53411yescharacteristic
442C4×C113D4211yescharacteristic
443C4×C113#54611yescharacteristic
444#24427C11311yesmaximal, characteristic, direct product factor, Sylow
445C2×C113—42no—
446C2×C113—81no—
447C2×C113—82no—
448C2×C113—82no—
449C2×C113#241011yescharacteristic
450C2×C113#300211yescharacteristic
451C2×C113#300911yescharacteristic
452C2×C113#327111yescharacteristic
453C2×C113#328411yescharacteristic
454C2×C113#330411yescharacteristic
455C2×C113#331711yescharacteristic
456C2×#550C2×C11311yescharacteristic
457C2×#465C2×C11311yescharacteristic, complemented
458C2×#452C2×C11311yescharacteristic, complemented
459C2×#452C2×C11311yescharacteristic, complemented
460C2×#416C2×C11311yescharacteristic, complemented
461#2415C2×C11311yescharacteristic, complemented
462#2041C2×C11311yescharacteristic, complemented
463#2034C2×C11311yescharacteristic, complemented
464#2014C2×C11311yescharacteristic, complemented
465#2000C2×C11311yescharacteristic, complemented
466#1878C2×C11311yescharacteristic, complemented
467#1875C2×C11311yescharacteristic, complemented
468#1869C2×C11311yescharacteristic, complemented
469#1865C2×C11311yescharacteristic, complemented
470#1788C2×C11311yescharacteristic, complemented
471C113#2442711yescharacteristic, direct product factor, Sylow
472C22×#41C22×C11311yescharacteristic
473C22×#41C22×C11311yescharacteristic
474C22×Q16C22×C11311yescharacteristic
475C22×SD16C22×C11311yescharacteristic
476C22×SD16C22×C11311yescharacteristic
477C23×C8C22×C11311yescharacteristic
478#550—24no—
479#550—24no—
480C2×#127—21no—
481C2×#127C22×C11311yescharacteristic
482C2×C22⋊Q8C22×C11311yescharacteristic
483C2×C22⋊Q8C22×C11311yescharacteristic
484C2×#121—21no—
485C2×#121—21no—
486C2×#121C22×C11311yescharacteristic
487C2×#121C22×C11311yescharacteristic
488C2×C4×Q8C22×C11311yescharacteristic
489C2×C4×D4—21no—
490C2×C4×D4C22×C11311yescharacteristic
491C2×#117C22×C11311yescharacteristic
492#465—24no—
493#452—24no—
494#452—24no—
495C2×#106C22×C11311yescharacteristic
496#416—24no—
497C2×#103C22×C11311yescharacteristic
498C2×#103C22×C11311yescharacteristic
499C2×#103C22×C11311yescharacteristic
500C2×#103C22×C11311yescharacteristic
501C2×#102C22×C11311yescharacteristic
502C2×#102C22×C11311yescharacteristic
503C2×#102C22×C11311yescharacteristic
504C2×#102C22×C11311yescharacteristic
505C2×#102C22×C11311yescharacteristic
506C2×#102C22×C11311yescharacteristic
507C2×C22⋊C8C22×C11311yescharacteristic
508C2×C22⋊C8C22×C11311yescharacteristic
509C2×C22⋊C8C22×C11311yescharacteristic
510#397—21no—
511#394—21no—
512#391C22×C11311yescharacteristic
513#389—21no—
514#389C22×C11311yescharacteristic
515#388—21no—
516#380C22×C11311yescharacteristic
517#340C22×C11311yescharacteristic
518#340C22×C11311yescharacteristic
519#336C22×C11311yescharacteristic
520#336C22×C11311yescharacteristic
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41D4×C11314yes—
533C22×Q8C23×C11311yescharacteristic
534C22×Q8C23×C11311yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4D4×C11311yescharacteristic
542C22×D4C23×C11311yescharacteristic
543C22×D4C23×C11311yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C11311yescharacteristic
547C23×C4C23×C11311yescharacteristic
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8C23×C11311yescharacteristic
561C22×C8C23×C11311yescharacteristic
562C22×C8C23×C11311yescharacteristic
563C22×C8C23×C11311yescharacteristic
564#127—28no—
565#127—22no—
566#127—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571#121—28no—
572#121—28no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121D4×C11314yes—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582#117—22no—
583#117—41no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C11311yescharacteristic
589C2×C4⋊C4C23×C11311yescharacteristic
590C2×C4⋊C4C23×C11311yescharacteristic
591C2×C4⋊C4C23×C11311yescharacteristic
592C2×C4⋊C4C23×C11311yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4D4×C11311yescharacteristic
600C2×C22⋊C4D4×C11311yescharacteristic
601C2×C42—21no—
602C2×C42—21no—
603C2×C42C23×C11311yescharacteristic
604#106—22no—
605#103—22no—
606#103—22no—
607#103—22no—
608#103D4×C11314yescomplemented
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—41no—
615C22⋊C8—22no—
616C22⋊C8—22no—
617C22⋊C8—41no—
618#95—21no—
619#95—21no—
620#95—21no—
621#95—21no—
622C24—21no—
623C24—21no—
624C24C2×D4×C11311yescharacteristic
625C24C2×D4×C11311yescharacteristic
626#41—28no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C11312yes—
644C2×Q8C2×D4×C11312yes—
645C2×Q8#41×C11312yes—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—41no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C11312yes—
678C2×D4C2×D4×C11312yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4C2×D4×C11311yescharacteristic
702C22×C4C2×D4×C11311yescharacteristic
703C22×C4C2×D4×C11311yescharacteristic
704C22×C4C2×D4×C11312yes—
705C22×C4C2×D4×C11312yes—
706C22×C4C2×D4×C11311yescharacteristic
707C22×C4C24×C11311yescharacteristic
708Q16—44no—
709SD16—44no—
710SD16—44no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C11312yes—
724C4⋊C4—24no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4C2×D4×C11312yes—
736C4⋊C4C2×D4×C11312yes—
737C22⋊C4—24no—
738C22⋊C4—22no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C42—24no—
746C42—21no—
747C42—21no—
748C42—42no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—22no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23#120×C11312yes—
777C23C22×D4×C11311yescharacteristic
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8#121×C11314yes—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—44no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—84no—
799D4—84no—
800D4—84no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4#120×C11312yes—
840C2×C4#135×C11312yes—
841C2×C4C22×D4×C11311yescharacteristic
842C2×C4C22×D4×C11311yescharacteristic
843C2×C4C22×D4×C11311yescharacteristic
844C2×C4C2×#41×C11311yescharacteristic
845C2×C4H(5,𝔽2)×C11311yescharacteristic
846C2×C4H(5,𝔽2)×C11311yescharacteristic
847C8—22no—
848C8—41no—
849C8—41no—
850C8—41no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—41no—
870C22—41no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22C2×#120×C11311yescharacteristic
880C22D42×C11311yescharacteristic
881C22#546×C11311yescharacteristic
882C22C2×#135×C11311yescharacteristic
883C22#575×C11311yescharacteristic
884C22#577×C11311yescharacteristic
885C22#577×C11311yescharacteristic
886C4—22no—
887C4—24no—
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4C2×#121×C11311yescharacteristic
897C4#534×C11311yescharacteristic
898C4D42×C11311yescharacteristic
899C4#546×C11311yescharacteristic
900C2—42no—
901C2—81no—
902C2—82no—
903C2—82no—
904C2C113×#241011yescharacteristic
905C2C113×#300211yescharacteristic
906C2C113×#300911yescharacteristic
907C2C113×#327111yescharacteristic
908C2C113×#328411yescharacteristic
909C2C113×#330411yescharacteristic
910C2C113×#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×#465×C113C2semidirect
3. C2×#452×C113C2semidirect
4. C2×#452×C113C2semidirect
5. C2×#416×C113C2semidirect
6. C113×#2415C2semidirect
7. C113×#2041C2semidirect
8. C113×#2034C2semidirect
9. C113×#2014C2semidirect
10. C113×#2000C2semidirect
11. C113×#1878C2semidirect
12. C113×#1875C2semidirect
13. C113×#1869C2semidirect
14. C113×#1865C2semidirect
15. C113×#1788C2semidirect
152. #103×C113D4semidirect
444. #24427C113direct (N × H)
457. C2×#465C2×C113semidirect
458. C2×#452C2×C113semidirect
459. C2×#452C2×C113semidirect
460. C2×#416C2×C113semidirect
461. #2415C2×C113semidirect
462. #2041C2×C113semidirect
463. #2034C2×C113semidirect
464. #2014C2×C113semidirect
465. #2000C2×C113semidirect
466. #1878C2×C113semidirect
467. #1875C2×C113semidirect
468. #1869C2×C113semidirect
469. #1865C2×C113semidirect
470. #1788C2×C113semidirect
471. C113#24427direct (N × H)
608. #103D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1132
C2×#465×C1132
C2×#452×C1132
C2×#416×C1132
C113×#24152
C113×#20412
C113×#20342
C113×#20142
C113×#20002
C113×#18782
C113×#18752
C113×#18692
C113×#18652
C113×#17882
#24427113