Finite Group Databasebeta

← C113×#25102 #43293122

Subgroups — C113×#25102 #43293122

Order 28928.

1146 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C113C211yesmaximal, characteristic, complemented
2C2×#464×C113C211yesmaximal, characteristic, complemented
3C2×#452×C113C211yesmaximal, characteristic, complemented
4C2×#417×C113C211yesmaximal, characteristic, complemented
5C113×#2431C211yesmaximal, characteristic
6C113×#2360C211yesmaximal, characteristic, complemented
7C113×#2067C211yesmaximal, characteristic, complemented
8C113×#2056C211yesmaximal, characteristic, complemented
9C113×#2042C211yesmaximal, characteristic, complemented
10C113×#2014C211yesmaximal, characteristic, complemented
11C113×#1982C211yesmaximal, characteristic, complemented
12C113×#1928C211yesmaximal, characteristic, complemented
13C113×#1880C211yesmaximal, characteristic, complemented
14C113×#1874C211yesmaximal, characteristic, complemented
15C113×#1851C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×Q16×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic
20C22×M16×C113C2211yescharacteristic
21C2×#127×C113C2211yescharacteristic
22C2×#124×C113C2211yescharacteristic
23C2×C22⋊Q8×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×C4×Q8×C113C2211yescharacteristic
26C22×C4⋊C4×C113C2211yescharacteristic
27#468×C113—24no—
28#464×C113—24no—
29#452×C113—24no—
30C2×#107×C113C2211yescharacteristic
31C2×C4⋊C8×C113C2211yescharacteristic
32C2×C4⋊C8×C113C2211yescharacteristic
33#417×C113—24no—
34C2×#103×C113C2211yescharacteristic
35C2×#103×C113C2211yescharacteristic
36C2×#103×C113C2211yescharacteristic
37C2×#103×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×C22⋊C8×C113C2211yescharacteristic
45#392×C113—21no—
46#392×C113—21no—
47#391×C113C2211yescharacteristic
48#391×C113C2211yescharacteristic
49#390×C113C2211yescharacteristic
50#389×C113—21no—
51#389×C113C2211yescharacteristic
52#387×C113—21no—
53#386×C113—21no—
54#386×C113—21no—
55#385×C113—21no—
56C4×C4⋊C4×C113C2211yescharacteristic
57C4×C22⋊C4×C113—21no—
58C4×C22⋊C4×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—41no—
68C2×#41×C113—41no—
69C22×Q8×C113C2311yescharacteristic
70C22×Q8×C113C2311yescharacteristic
71C22×D4×C113—21no—
72C22×D4×C113—21no—
73C22×D4×C113—21no—
74C22×D4×C113—21no—
75C22×D4×C113C2311yescharacteristic
76C22×D4×C113C2311yescharacteristic
77C23×C4×C113—21no—
78C23×C4×C113—21no—
79C23×C4×C113C2311yescharacteristic
80C2×Q16×C113—22no—
81C2×Q16×C113—22no—
82C2×Q16×C113—41no—
83C2×SD16×C113—22no—
84C2×SD16×C113—22no—
85C2×SD16×C113—22no—
86C2×SD16×C113—22no—
87C2×SD16×C113—41no—
88C2×SD16×C113—41no—
89C2×M16×C113—22no—
90C2×M16×C113—22no—
91C2×M16×C113—41no—
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94C22×C8×C113C2311yescharacteristic
95C22×C8×C113C2311yescharacteristic
96#127×C113—22no—
97#127×C113—41no—
98#124×C113—22no—
99#124×C113—41no—
100C22⋊Q8×C113—22no—
101C22⋊Q8×C113D414yescomplemented
102#121×C113—22no—
103#121×C113—22no—
104C4×Q8×C113—22no—
105C4×Q8×C113—41no—
106C2×C4⋊C4×C113—21no—
107C2×C4⋊C4×C113—22no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113—21no—
111C2×C4⋊C4×C113—41no—
112C2×C4⋊C4×C113C2311yescharacteristic
113C2×C4⋊C4×C113C2311yescharacteristic
114C2×C4⋊C4×C113C2311yescharacteristic
115C2×C4⋊C4×C113C2311yescharacteristic
116C2×C22⋊C4×C113—21no—
117C2×C22⋊C4×C113—21no—
118C2×C22⋊C4×C113—21no—
119C2×C22⋊C4×C113—21no—
120C2×C22⋊C4×C113—21no—
121C2×C22⋊C4×C113—21no—
122C2×C22⋊C4×C113D411yescharacteristic
123C2×C22⋊C4×C113D411yescharacteristic
124C2×C42×C113—21no—
125C2×C42×C113—21no—
126C2×C42×C113C2311yescharacteristic
127C2×C42×C113C2311yescharacteristic
128#107×C113—22no—
129C4⋊C8×C113—22no—
130C4⋊C8×C113—41no—
131#103×C113—22no—
132#103×C113—22no—
133#103×C113—22no—
134#103×C113D414yescomplemented
135#102×C113—22no—
136#102×C113—22no—
137#102×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—41no—
141C22⋊C8×C113—22no—
142#95×C113—21no—
143#95×C113—21no—
144#95×C113—21no—
145#95×C113—21no—
146#95×C113—21no—
147#95×C113—21no—
148#95×C113D411yescharacteristic
149#95×C113D411yescharacteristic
150C24×C113—21no—
151C24×C113—21no—
152C24×C113C2×D411yescharacteristic
153#41×C113—28no—
154#41×C113—44no—
155#41×C113—44no—
156#41×C113—44no—
157C2×Q8×C113—21no—
158C2×Q8×C113—21no—
159C2×Q8×C113—21no—
160C2×Q8×C113—21no—
161C2×Q8×C113—21no—
162C2×Q8×C113—21no—
163C2×Q8×C113—21no—
164C2×Q8×C113—21no—
165C2×Q8×C113—21no—
166C2×Q8×C113—21no—
167C2×Q8×C113C2×D412yes—
168C2×Q8×C113C2×D412yes—
169C2×D4×C113—21no—
170C2×D4×C113—21no—
171C2×D4×C113—21no—
172C2×D4×C113—21no—
173C2×D4×C113—21no—
174C2×D4×C113—21no—
175C2×D4×C113—21no—
176C2×D4×C113—21no—
177C2×D4×C113—21no—
178C2×D4×C113—21no—
179C2×D4×C113—21no—
180C2×D4×C113—42no—
181C2×D4×C113—42no—
182C2×D4×C113—42no—
183C2×D4×C113—42no—
184C2×D4×C113—42no—
185C2×D4×C113—42no—
186C2×D4×C113—42no—
187C2×D4×C113—42no—
188C2×D4×C113—81no—
189C2×D4×C113—81no—
190C2×D4×C113—81no—
191C2×D4×C113—81no—
192C2×D4×C113#4112yes—
193C22×C4×C113—21no—
194C22×C4×C113—21no—
195C22×C4×C113—21no—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—42no—
204C22×C4×C113—42no—
205C22×C4×C113—42no—
206C22×C4×C113—42no—
207C22×C4×C113—42no—
208C22×C4×C113—81no—
209C22×C4×C113C2×D411yescharacteristic
210C22×C4×C113C2×D411yescharacteristic
211C22×C4×C113C2×D411yescharacteristic
212C22×C4×C113C2×D411yescharacteristic
213C22×C4×C113C2×D412yes—
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113#4112yes—
216C22×C4×C113C2411yescharacteristic
217Q16×C113—44no—
218SD16×C113—44no—
219SD16×C113—44no—
220M16×C113—44no—
221C2×C8×C113—21no—
222C2×C8×C113—21no—
223C2×C8×C113—21no—
224C2×C8×C113—21no—
225C2×C8×C113—21no—
226C2×C8×C113—21no—
227C2×C8×C113—21no—
228C2×C8×C113—21no—
229C2×C8×C113—21no—
230C2×C8×C113—21no—
231C2×C8×C113—21no—
232C2×C8×C113C2×D412yes—
233C4⋊C4×C113—24no—
234C4⋊C4×C113—21no—
235C4⋊C4×C113—21no—
236C4⋊C4×C113—21no—
237C4⋊C4×C113—21no—
238C4⋊C4×C113—21no—
239C4⋊C4×C113—21no—
240C4⋊C4×C113—42no—
241C4⋊C4×C113—42no—
242C4⋊C4×C113—81no—
243C4⋊C4×C113C2×D412yes—
244C4⋊C4×C113C2×D412yes—
245C22⋊C4×C113—24no—
246C22⋊C4×C113—22no—
247C22⋊C4×C113—41no—
248C22⋊C4×C113—42no—
249C22⋊C4×C113—42no—
250C22⋊C4×C113—42no—
251C22⋊C4×C113—81no—
252C22⋊C4×C113—81no—
253C42×C113—21no—
254C42×C113—21no—
255C42×C113—21no—
256C42×C113—21no—
257C42×C113—42no—
258C42×C113—81no—
259C23×C113—21no—
260C23×C113—21no—
261C23×C113—21no—
262C23×C113—21no—
263C23×C113—21no—
264C23×C113—21no—
265C23×C113—22no—
266C23×C113—41no—
267C23×C113—41no—
268C23×C113—41no—
269C23×C113—41no—
270C23×C113—41no—
271C23×C113—41no—
272C23×C113—41no—
273C23×C113—41no—
274C23×C113—41no—
275C23×C113—41no—
276C23×C113—41no—
277C23×C113—41no—
278C23×C113—41no—
279C23×C113#12112yes—
280C23×C113C22×D411yescharacteristic
281Q8×C113—22no—
282Q8×C113—22no—
283Q8×C113—22no—
284Q8×C113—22no—
285Q8×C113—41no—
286Q8×C113—41no—
287Q8×C113—41no—
288Q8×C113—41no—
289D4×C113—22no—
290D4×C113—22no—
291D4×C113—48no—
292D4×C113—41no—
293D4×C113—41no—
294D4×C113—41no—
295D4×C113—41no—
296D4×C113—41no—
297D4×C113—41no—
298D4×C113—84no—
299D4×C113—84no—
300D4×C113—84no—
301C2×C4×C113—21no—
302C2×C4×C113—21no—
303C2×C4×C113—21no—
304C2×C4×C113—21no—
305C2×C4×C113—22no—
306C2×C4×C113—22no—
307C2×C4×C113—22no—
308C2×C4×C113—22no—
309C2×C4×C113—22no—
310C2×C4×C113—22no—
311C2×C4×C113—21no—
312C2×C4×C113—21no—
313C2×C4×C113—22no—
314C2×C4×C113—22no—
315C2×C4×C113—21no—
316C2×C4×C113—21no—
317C2×C4×C113—21no—
318C2×C4×C113—21no—
319C2×C4×C113—21no—
320C2×C4×C113—21no—
321C2×C4×C113—21no—
322C2×C4×C113—48no—
323C2×C4×C113—41no—
324C2×C4×C113—41no—
325C2×C4×C113—41no—
326C2×C4×C113—41no—
327C2×C4×C113—41no—
328C2×C4×C113—41no—
329C2×C4×C113—41no—
330C2×C4×C113—41no—
331C2×C4×C113—41no—
332C2×C4×C113—41no—
333C2×C4×C113—41no—
334C2×C4×C113—41no—
335C2×C4×C113—41no—
336C2×C4×C113—41no—
337C2×C4×C113—84no—
338C2×C4×C113#12112yes—
339C2×C4×C113#13712yes—
340C2×C4×C113C22×D411yescharacteristic
341C2×C4×C113C22×D411yescharacteristic
342C2×C4×C113C2×#4111yescharacteristic
343C2×C4×C113C2×#4111yescharacteristic
344C2×C4×C113H(5,𝔽2)11yescharacteristic
345C2×C4×C113H(5,𝔽2)11yescharacteristic
346C8×C113—22no—
347C8×C113—41no—
348C8×C113—41no—
349C8×C113—41no—
350C22×C113—22no—
351C22×C113—22no—
352C22×C113—22no—
353C22×C113—41no—
354C22×C113—41no—
355C22×C113—41no—
356C22×C113—41no—
357C22×C113—42no—
358C22×C113—42no—
359C22×C113—42no—
360C22×C113—81no—
361C22×C113—81no—
362C22×C113—81no—
363C22×C113—81no—
364C22×C113—81no—
365C22×C113—81no—
366C22×C113—81no—
367C22×C113—81no—
368C22×C113—81no—
369C22×C113—81no—
370C22×C113—81no—
371C22×C113C2×#12111yescharacteristic
372C22×C113D4211yescharacteristic
373C22×C113#54611yescharacteristic
374C22×C113C2×#13711yescharacteristic
375C22×C113#57511yescharacteristic
376C22×C113#57611yescharacteristic
377C22×C113#57711yescharacteristic
378C4×C113—22no—
379C4×C113—22no—
380C4×C113—42no—
381C4×C113—42no—
382C4×C113—41no—
383C4×C113—42no—
384C4×C113—41no—
385C4×C113—42no—
386C4×C113—41no—
387C4×C113—81no—
388C4×C113—81no—
389C4×C113#52511yescharacteristic
390C4×C113#53811yescharacteristic
391C4×C113D4211yescharacteristic
392C4×C113#54611yescharacteristic
393#25102C11311yesmaximal, characteristic, direct product factor, Sylow
394C2×C113—42no—
395C2×C113—82no—
396C2×C113—161no—
397C2×C113#242411yescharacteristic
398C2×C113#303711yescharacteristic
399C2×C113#304511yescharacteristic
400C2×C113#326811yescharacteristic
401C2×C113#327811yescharacteristic
402C2×C113#331411yescharacteristic
403C2×C113#332311yescharacteristic
404C2×#468C2×C11311yescharacteristic, complemented
405C2×#464C2×C11311yescharacteristic, complemented
406C2×#452C2×C11311yescharacteristic, complemented
407C2×#417C2×C11311yescharacteristic, complemented
408#2431C2×C11311yescharacteristic
409#2360C2×C11311yescharacteristic, complemented
410#2067C2×C11311yescharacteristic, complemented
411#2056C2×C11311yescharacteristic, complemented
412#2042C2×C11311yescharacteristic, complemented
413#2014C2×C11311yescharacteristic, complemented
414#1982C2×C11311yescharacteristic, complemented
415#1928C2×C11311yescharacteristic, complemented
416#1880C2×C11311yescharacteristic, complemented
417#1874C2×C11311yescharacteristic, complemented
418#1851C2×C11311yescharacteristic, complemented
419C113#2510211yescharacteristic, direct product factor, Sylow
420C22×#41C22×C11311yescharacteristic
421C22×Q16C22×C11311yescharacteristic
422C22×SD16C22×C11311yescharacteristic
423C22×SD16C22×C11311yescharacteristic
424C22×M16C22×C11311yescharacteristic
425C2×#127C22×C11311yescharacteristic
426C2×#124C22×C11311yescharacteristic
427C2×C22⋊Q8C22×C11311yescharacteristic
428C2×#121C22×C11311yescharacteristic
429C2×C4×Q8C22×C11311yescharacteristic
430C22×C4⋊C4C22×C11311yescharacteristic
431#468—24no—
432#464—24no—
433#452—24no—
434C2×#107C22×C11311yescharacteristic
435C2×C4⋊C8C22×C11311yescharacteristic
436C2×C4⋊C8C22×C11311yescharacteristic
437#417—24no—
438C2×#103C22×C11311yescharacteristic
439C2×#103C22×C11311yescharacteristic
440C2×#103C22×C11311yescharacteristic
441C2×#103C22×C11311yescharacteristic
442C2×#102C22×C11311yescharacteristic
443C2×#102C22×C11311yescharacteristic
444C2×#102C22×C11311yescharacteristic
445C2×#102C22×C11311yescharacteristic
446C2×#102C22×C11311yescharacteristic
447C2×#102C22×C11311yescharacteristic
448C2×C22⋊C8C22×C11311yescharacteristic
449#392—21no—
450#392—21no—
451#391C22×C11311yescharacteristic
452#391C22×C11311yescharacteristic
453#390C22×C11311yescharacteristic
454#389—21no—
455#389C22×C11311yescharacteristic
456#387—21no—
457#386—21no—
458#386—21no—
459#385—21no—
460C4×C4⋊C4C22×C11311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4C22×C11311yescharacteristic
463#340C22×C11311yescharacteristic
464#340C22×C11311yescharacteristic
465#336C22×C11311yescharacteristic
466#336C22×C11311yescharacteristic
467C2×#41—22no—
468C2×#41—22no—
469C2×#41—22no—
470C2×#41—22no—
471C2×#41—41no—
472C2×#41—41no—
473C22×Q8C23×C11311yescharacteristic
474C22×Q8C23×C11311yescharacteristic
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4C23×C11311yescharacteristic
480C22×D4C23×C11311yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4C23×C11311yescharacteristic
484C2×Q16—22no—
485C2×Q16—22no—
486C2×Q16—41no—
487C2×SD16—22no—
488C2×SD16—22no—
489C2×SD16—22no—
490C2×SD16—22no—
491C2×SD16—41no—
492C2×SD16—41no—
493C2×M16—22no—
494C2×M16—22no—
495C2×M16—41no—
496C22×C8C23×C11311yescharacteristic
497C22×C8C23×C11311yescharacteristic
498C22×C8C23×C11311yescharacteristic
499C22×C8C23×C11311yescharacteristic
500#127—22no—
501#127—41no—
502#124—22no—
503#124—41no—
504C22⋊Q8—22no—
505C22⋊Q8D4×C11314yescomplemented
506#121—22no—
507#121—22no—
508C4×Q8—22no—
509C4×Q8—41no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—41no—
516C2×C4⋊C4C23×C11311yescharacteristic
517C2×C4⋊C4C23×C11311yescharacteristic
518C2×C4⋊C4C23×C11311yescharacteristic
519C2×C4⋊C4C23×C11311yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4D4×C11311yescharacteristic
527C2×C22⋊C4D4×C11311yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42C23×C11311yescharacteristic
531C2×C42C23×C11311yescharacteristic
532#107—22no—
533C4⋊C8—22no—
534C4⋊C8—41no—
535#103—22no—
536#103—22no—
537#103—22no—
538#103D4×C11314yescomplemented
539#102—22no—
540#102—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—41no—
545C22⋊C8—22no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95D4×C11311yescharacteristic
553#95D4×C11311yescharacteristic
554C24—21no—
555C24—21no—
556C24C2×D4×C11311yescharacteristic
557#41—28no—
558#41—44no—
559#41—44no—
560#41—44no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8C2×D4×C11312yes—
572C2×Q8C2×D4×C11312yes—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4#41×C11312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4C2×D4×C11311yescharacteristic
614C22×C4C2×D4×C11311yescharacteristic
615C22×C4C2×D4×C11311yescharacteristic
616C22×C4C2×D4×C11311yescharacteristic
617C22×C4C2×D4×C11312yes—
618C22×C4C2×D4×C11311yescharacteristic
619C22×C4#41×C11312yes—
620C22×C4C24×C11311yescharacteristic
621Q16—44no—
622SD16—44no—
623SD16—44no—
624M16—44no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8C2×D4×C11312yes—
637C4⋊C4—24no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C11312yes—
648C4⋊C4C2×D4×C11312yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—81no—
656C22⋊C4—81no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—42no—
662C42—81no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23#121×C11312yes—
684C23C22×D4×C11311yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—22no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4—84no—
704D4—84no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—48no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—84no—
742C2×C4#121×C11312yes—
743C2×C4#137×C11312yes—
744C2×C4C22×D4×C11311yescharacteristic
745C2×C4C22×D4×C11311yescharacteristic
746C2×C4C2×#41×C11311yescharacteristic
747C2×C4C2×#41×C11311yescharacteristic
748C2×C4H(5,𝔽2)×C11311yescharacteristic
749C2×C4H(5,𝔽2)×C11311yescharacteristic
750C8—22no—
751C8—41no—
752C8—41no—
753C8—41no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22C2×#121×C11311yescharacteristic
776C22D42×C11311yescharacteristic
777C22#546×C11311yescharacteristic
778C22C2×#137×C11311yescharacteristic
779C22#575×C11311yescharacteristic
780C22#576×C11311yescharacteristic
781C22#577×C11311yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—41no—
786C4—42no—
787C4—42no—
788C4—41no—
789C4—42no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4#525×C11311yescharacteristic
794C4#538×C11311yescharacteristic
795C4D42×C11311yescharacteristic
796C4#546×C11311yescharacteristic
797C2—42no—
798C2—82no—
799C2—161no—
800C2C113×#242411yescharacteristic
801C2C113×#303711yescharacteristic
802C2C113×#304511yescharacteristic
803C2C113×#326811yescharacteristic
804C2C113×#327811yescharacteristic
805C2C113×#331411yescharacteristic
806C2C113×#332311yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#2431C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C4×C22⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C113C2semidirect
2. C2×#464×C113C2semidirect
3. C2×#452×C113C2semidirect
4. C2×#417×C113C2semidirect
6. C113×#2360C2semidirect
7. C113×#2067C2semidirect
8. C113×#2056C2semidirect
9. C113×#2042C2semidirect
10. C113×#2014C2semidirect
11. C113×#1982C2semidirect
12. C113×#1928C2semidirect
13. C113×#1880C2semidirect
14. C113×#1874C2semidirect
15. C113×#1851C2semidirect
101. C22⋊Q8×C113D4semidirect
134. #103×C113D4semidirect
393. #25102C113direct (N × H)
404. C2×#468C2×C113semidirect
405. C2×#464C2×C113semidirect
406. C2×#452C2×C113semidirect
407. C2×#417C2×C113semidirect
409. #2360C2×C113semidirect
410. #2067C2×C113semidirect
411. #2056C2×C113semidirect
412. #2042C2×C113semidirect
413. #2014C2×C113semidirect
414. #1982C2×C113semidirect
415. #1928C2×C113semidirect
416. #1880C2×C113semidirect
417. #1874C2×C113semidirect
418. #1851C2×C113semidirect
419. C113#25102direct (N × H)
505. C22⋊Q8D4×C113semidirect
538. #103D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1132
C2×#464×C1132
C2×#452×C1132
C2×#417×C1132
C113×#24312
C113×#23602
C113×#20672
C113×#20562
C113×#20422
C113×#20142
C113×#19822
C113×#19282
C113×#18802
C113×#18742
C113×#18512
#25102113