Finite Group Databasebeta

← C113×#18263 #43286283

Subgroups — C113×#18263 #43286283

Order 28928.

948 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3535C211yesmaximal, characteristic
2C113×#3095C211yesmaximal, characteristic, complemented
3C113×#3091C211yesmaximal, characteristic, complemented
4C113×#2498C211yesmaximal, characteristic, complemented
5C113×#1618C211yesmaximal, characteristic, complemented
6C113×#1617C211yesmaximal, characteristic, complemented
7C113×#1615C211yesmaximal, characteristic, complemented
8C113×#1614C211yesmaximal, characteristic, complemented
9C113×#1612C211yesmaximal, characteristic, complemented
10C113×#1611C211yesmaximal, characteristic, complemented
11C113×#1609C211yesmaximal, characteristic, complemented
12C113×#1608C211yesmaximal, characteristic, complemented
13C113×#1504C211yesmaximal, characteristic, complemented
14C2×#328×C113C211yesmaximal, characteristic, complemented
15C113×#1468C211yesmaximal, characteristic, complemented
16#563×C113—21no—
17#562×C113—21no—
18#554×C113—21no—
19#552×C113—21no—
20#551×C113—21no—
21#551×C113—21no—
22#547×C113—21no—
23#546×C113—21no—
24#544×C113C2211yescharacteristic
25#543×C113C2211yescharacteristic
26#542×C113—21no—
27#539×C113—21no—
28#539×C113—21no—
29#539×C113C2211yescharacteristic
30#538×C113C2211yescharacteristic
31#536×C113—21no—
32#525×C113C2211yescharacteristic
33C2×#123×C113C2211yescharacteristic
34C2×C22⋊Q8×C113C2211yescharacteristic
35C2×#117×C113C2211yescharacteristic
36#485×C113—21no—
37#485×C113—21no—
38#485×C113—21no—
39#484×C113C2211yescharacteristic
40#484×C113C2211yescharacteristic
41#484×C113C2211yescharacteristic
42#483×C113C2211yescharacteristic
43#483×C113C2211yescharacteristic
44#483×C113C2211yescharacteristic
45#482×C113—21no—
46#481×C113C2211yescharacteristic
47#480×C113C2211yescharacteristic
48#428×C113—21no—
49#427×C113—21no—
50#419×C113—21no—
51#416×C113—21no—
52#407×C113C2211yescharacteristic
53C2×C22⋊C8×C113C2211yescharacteristic
54#400×C113C2211yescharacteristic
55#399×C113C2211yescharacteristic
56#398×C113C2211yescharacteristic
57#397×C113C2211yescharacteristic
58#388×C113—21no—
59#387×C113—21no—
60#386×C113—21no—
61#380×C113—21no—
62C2×#95×C113C2211yescharacteristic
63#328×C113C2211yescharacteristic
64#328×C113C2211yescharacteristic
65#328×C113C2211yescharacteristic
66#328×C113C2211yescharacteristic
67#328×C113C2211yescharacteristic
68#328×C113C2211yescharacteristic
69#327×C113C2211yescharacteristic
70#327×C113C2211yescharacteristic
71#324×C113C2211yescharacteristic
72#324×C113C2211yescharacteristic
73#323×C113C2211yescharacteristic
74#323×C113C2211yescharacteristic
75C2×#41×C113—21no—
76C2×#41×C113D411yescharacteristic
77C22×Q8×C113D411yescharacteristic
78C22×D4×C113D411yescharacteristic
79C23×C4×C113—21no—
80C23×C4×C113C2311yescharacteristic
81C2×M16×C113—21no—
82C22×C8×C113—21no—
83C4⋊Q8×C113—21no—
84C4⋊Q8×C113—21no—
85C4⋊Q8×C113—21no—
86#126×C113—21no—
87#126×C113—21no—
88#126×C113—21no—
89#126×C113—21no—
90#126×C113—21no—
91#126×C113—21no—
92#125×C113—21no—
93#125×C113—21no—
94#125×C113—21no—
95#125×C113—21no—
96#125×C113—21no—
97#124×C113—21no—
98#124×C113—21no—
99#124×C113—21no—
100#124×C113—21no—
101#123×C113—21no—
102#123×C113—21no—
103#123×C113—21no—
104#123×C113—21no—
105#123×C113—21no—
106#123×C113—21no—
107#123×C113—21no—
108#123×C113—21no—
109#123×C113—21no—
110#123×C113—21no—
111#123×C113—21no—
112#123×C113—21no—
113#123×C113—21no—
114#123×C113—21no—
115C22⋊Q8×C113—21no—
116C22⋊Q8×C113—21no—
117C22⋊Q8×C113—21no—
118C22⋊Q8×C113—21no—
119C22⋊Q8×C113—21no—
120C22⋊Q8×C113—21no—
121C22⋊Q8×C113—21no—
122C22⋊Q8×C113—21no—
123C22⋊Q8×C113—21no—
124C22⋊Q8×C113—21no—
125C22⋊Q8×C113—21no—
126C22⋊Q8×C113—21no—
127C22⋊Q8×C113—21no—
128C22⋊Q8×C113—21no—
129C22⋊Q8×C113D411yescharacteristic
130C22⋊Q8×C113D411yescharacteristic
131C22⋊Q8×C113D411yescharacteristic
132C22⋊Q8×C113C2311yescharacteristic
133C22⋊Q8×C113C2311yescharacteristic
134C22⋊Q8×C113C2311yescharacteristic
135#121×C113—21no—
136#121×C113—21no—
137#121×C113—21no—
138#121×C113—21no—
139#121×C113D411yescharacteristic
140#121×C113C2311yescharacteristic
141#120×C113—21no—
142#120×C113—21no—
143C4×Q8×C113—21no—
144C4×D4×C113—21no—
145C4×D4×C113—21no—
146C4×D4×C113—21no—
147C4×D4×C113—21no—
148C4×D4×C113—21no—
149C4×D4×C113—21no—
150C4×D4×C113—21no—
151#117×C113—21no—
152#117×C113—21no—
153#117×C113—21no—
154#117×C113—21no—
155#117×C113—21no—
156#117×C113—21no—
157#117×C113—21no—
158#117×C113D411yescharacteristic
159C2×C4⋊C4×C113—21no—
160C2×C4⋊C4×C113—21no—
161C2×C4⋊C4×C113—21no—
162C2×C4⋊C4×C113—21no—
163C2×C4⋊C4×C113D411yescharacteristic
164C2×C4⋊C4×C113D411yescharacteristic
165C2×C4⋊C4×C113C2311yescharacteristic
166C2×C4⋊C4×C113C2311yescharacteristic
167C2×C4⋊C4×C113C2311yescharacteristic
168C2×C22⋊C4×C113—21no—
169C2×C22⋊C4×C113—21no—
170C2×C22⋊C4×C113—21no—
171C2×C22⋊C4×C113—21no—
172C2×C22⋊C4×C113—21no—
173C2×C22⋊C4×C113D411yescharacteristic
174C2×C22⋊C4×C113D411yescharacteristic
175C2×C22⋊C4×C113C2311yescharacteristic
176C2×C42×C113—21no—
177#107×C113—21no—
178#107×C113—21no—
179#107×C113—21no—
180#107×C113—21no—
181#106×C113—21no—
182#106×C113—21no—
183#106×C113—21no—
184#106×C113—21no—
185#103×C113—21no—
186#103×C113—21no—
187#103×C113—21no—
188#103×C113—21no—
189#103×C113—21no—
190#103×C113—21no—
191#102×C113—21no—
192#102×C113—21no—
193C22⋊C8×C113—21no—
194C22⋊C8×C113—21no—
195C22⋊C8×C113C2311yescharacteristic
196C22⋊C8×C113C2311yescharacteristic
197C22⋊C8×C113C2311yescharacteristic
198C22⋊C8×C113C2311yescharacteristic
199#95×C113—21no—
200#95×C113—21no—
201#95×C113—21no—
202#95×C113—21no—
203#95×C113—21no—
204#95×C113C2311yescharacteristic
205#95×C113C2311yescharacteristic
206C24×C113C2×D411yescharacteristic
207C24×C113C2×D411yescharacteristic
208#41×C113—42no—
209#41×C113—82no—
210C2×Q8×C113—21no—
211C2×Q8×C113—21no—
212C2×Q8×C113—21no—
213C2×Q8×C113—42no—
214C2×Q8×C113C2×D411yescharacteristic
215C2×Q8×C113C2×D411yescharacteristic
216C2×Q8×C113C2×D411yescharacteristic
217C2×D4×C113—21no—
218C2×D4×C113—21no—
219C2×D4×C113—21no—
220C2×D4×C113—21no—
221C2×D4×C113—21no—
222C2×D4×C113—21no—
223C2×D4×C113—21no—
224C2×D4×C113—42no—
225C2×D4×C113C2×D411yescharacteristic
226C22×C4×C113—21no—
227C22×C4×C113—21no—
228C22×C4×C113—21no—
229C22×C4×C113—21no—
230C22×C4×C113—21no—
231C22×C4×C113—21no—
232C22×C4×C113—21no—
233C22×C4×C113—21no—
234C22×C4×C113—21no—
235C22×C4×C113—21no—
236C22×C4×C113—21no—
237C22×C4×C113—42no—
238C22×C4×C113—42no—
239C22×C4×C113—42no—
240C22×C4×C113—81no—
241C22×C4×C113C2×D411yescharacteristic
242C22×C4×C113C2×D411yescharacteristic
243C22×C4×C113C2×D411yescharacteristic
244C22×C4×C113C2×D411yescharacteristic
245C22×C4×C113C2×D411yescharacteristic
246C22×C4×C113C2×D411yescharacteristic
247C22×C4×C113C2×D411yescharacteristic
248C22×C4×C113C2×D411yescharacteristic
249C22×C4×C113C2411yescharacteristic
250M16×C113—42no—
251C2×C8×C113—21no—
252C2×C8×C113—21no—
253C2×C8×C113—21no—
254C2×C8×C113—21no—
255C2×C8×C113—42no—
256C4⋊C4×C113—21no—
257C4⋊C4×C113—21no—
258C4⋊C4×C113—21no—
259C4⋊C4×C113—21no—
260C4⋊C4×C113—21no—
261C4⋊C4×C113—21no—
262C4⋊C4×C113—21no—
263C4⋊C4×C113—21no—
264C4⋊C4×C113—21no—
265C4⋊C4×C113—21no—
266C4⋊C4×C113—21no—
267C4⋊C4×C113—21no—
268C4⋊C4×C113—21no—
269C4⋊C4×C113—21no—
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—21no—
277C4⋊C4×C113—21no—
278C4⋊C4×C113—21no—
279C4⋊C4×C113—21no—
280C4⋊C4×C113—21no—
281C4⋊C4×C113—21no—
282C4⋊C4×C113—21no—
283C4⋊C4×C113—42no—
284C4⋊C4×C113—81no—
285C4⋊C4×C113C2×D411yescharacteristic
286C4⋊C4×C113C2×D411yescharacteristic
287C4⋊C4×C113C2×D411yescharacteristic
288C4⋊C4×C113C2×D411yescharacteristic
289C22⋊C4×C113—21no—
290C22⋊C4×C113—21no—
291C22⋊C4×C113—21no—
292C22⋊C4×C113—21no—
293C22⋊C4×C113—21no—
294C22⋊C4×C113—21no—
295C22⋊C4×C113—21no—
296C22⋊C4×C113—21no—
297C22⋊C4×C113—21no—
298C22⋊C4×C113—21no—
299C22⋊C4×C113—21no—
300C22⋊C4×C113—21no—
301C22⋊C4×C113—21no—
302C22⋊C4×C113—21no—
303C22⋊C4×C113—21no—
304C22⋊C4×C113—21no—
305C22⋊C4×C113—21no—
306C22⋊C4×C113—21no—
307C22⋊C4×C113—21no—
308C22⋊C4×C113—21no—
309C22⋊C4×C113—21no—
310C22⋊C4×C113—21no—
311C22⋊C4×C113—21no—
312C22⋊C4×C113—42no—
313C22⋊C4×C113—41no—
314C22⋊C4×C113—41no—
315C22⋊C4×C113—81no—
316C42×C113—21no—
317C42×C113—21no—
318C42×C113—21no—
319C42×C113—21no—
320C42×C113—21no—
321C42×C113—41no—
322C42×C113—41no—
323C23×C113—21no—
324C23×C113—21no—
325C23×C113—22no—
326C23×C113—21no—
327C23×C113—21no—
328C23×C113—21no—
329C23×C113—21no—
330C23×C113—41no—
331C23×C113—41no—
332C23×C113—41no—
333C23×C113#12011yescharacteristic
334C23×C113#12011yescharacteristic
335C23×C113C22×D411yescharacteristic
336Q8×C113—41no—
337Q8×C113—41no—
338Q8×C113—41no—
339Q8×C113—81no—
340Q8×C113—81no—
341Q8×C113—81no—
342D4×C113—41no—
343D4×C113—41no—
344D4×C113—41no—
345D4×C113—42no—
346D4×C113—42no—
347D4×C113—81no—
348D4×C113—81no—
349D4×C113—81no—
350D4×C113—81no—
351C2×C4×C113—22no—
352C2×C4×C113—22no—
353C2×C4×C113—22no—
354C2×C4×C113—21no—
355C2×C4×C113—21no—
356C2×C4×C113—21no—
357C2×C4×C113—21no—
358C2×C4×C113—21no—
359C2×C4×C113—21no—
360C2×C4×C113—21no—
361C2×C4×C113—21no—
362C2×C4×C113—21no—
363C2×C4×C113—21no—
364C2×C4×C113—21no—
365C2×C4×C113—21no—
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—42no—
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—41no—
384C2×C4×C113—81no—
385C2×C4×C113—81no—
386C2×C4×C113—81no—
387C2×C4×C113—81no—
388C2×C4×C113—81no—
389C2×C4×C113—81no—
390C2×C4×C113—84no—
391C2×C4×C113#12011yescharacteristic
392C2×C4×C113#12011yescharacteristic
393C2×C4×C113C22×D411yescharacteristic
394C2×C4×C113C22×D411yescharacteristic
395C8×C113—41no—
396C8×C113—41no—
397C8×C113—41no—
398C8×C113—41no—
399C22×C113—21no—
400C22×C113—21no—
401C22×C113—21no—
402C22×C113—21no—
403C22×C113—21no—
404C22×C113—21no—
405C22×C113—21no—
406C22×C113—42no—
407C22×C113—42no—
408C22×C113—41no—
409C22×C113—41no—
410C22×C113—41no—
411C22×C113—41no—
412C22×C113—41no—
413C22×C113—41no—
414C22×C113—81no—
415C22×C113—81no—
416C22×C113#45812yes—
417C22×C113C2×#12011yescharacteristic
418C22×C113#57711yescharacteristic
419C22×C113#57811yescharacteristic
420C4×C113—21no—
421C4×C113—21no—
422C4×C113—21no—
423C4×C113—21no—
424C4×C113—42no—
425C4×C113—41no—
426C4×C113—41no—
427C4×C113—41no—
428C4×C113—41no—
429C4×C113—41no—
430C4×C113—41no—
431C4×C113—41no—
432C4×C113—41no—
433C4×C113—41no—
434C4×C113—41no—
435C4×C113—81no—
436C4×C113—81no—
437C4×C113—81no—
438#18263C11311yesmaximal, characteristic, direct product factor, Sylow
439C2×C113—21no—
440C2×C113—21no—
441C2×C113—22no—
442C2×C113—41no—
443C2×C113—81no—
444C2×C113—81no—
445C2×C113#301311yescharacteristic
446C2×C113#301811yescharacteristic
447C2×C113C2×#45811yescharacteristic
448#3535C2×C11311yescharacteristic
449#3095C2×C11311yescharacteristic, complemented
450#3091C2×C11311yescharacteristic, complemented
451#2498C2×C11311yescharacteristic, complemented
452#1618C2×C11311yescharacteristic, complemented
453#1617C2×C11311yescharacteristic, complemented
454#1615C2×C11311yescharacteristic, complemented
455#1614C2×C11311yescharacteristic, complemented
456#1612C2×C11311yescharacteristic, complemented
457#1611C2×C11311yescharacteristic, complemented
458#1609C2×C11311yescharacteristic, complemented
459#1608C2×C11311yescharacteristic, complemented
460#1504C2×C11311yescharacteristic, complemented
461C2×#328C2×C11311yescharacteristic, complemented
462#1468C2×C11311yescharacteristic, complemented
463C113#1826311yescharacteristic, direct product factor, Sylow
464#563—21no—
465#562—21no—
466#554—21no—
467#552—21no—
468#551—21no—
469#551—21no—
470#547—21no—
471#546—21no—
472#544C22×C11311yescharacteristic
473#543C22×C11311yescharacteristic
474#542—21no—
475#539—21no—
476#539—21no—
477#539C22×C11311yescharacteristic
478#538C22×C11311yescharacteristic
479#536—21no—
480#525C22×C11311yescharacteristic
481C2×#123C22×C11311yescharacteristic
482C2×C22⋊Q8C22×C11311yescharacteristic
483C2×#117C22×C11311yescharacteristic
484#485—21no—
485#485—21no—
486#485—21no—
487#484C22×C11311yescharacteristic
488#484C22×C11311yescharacteristic
489#484C22×C11311yescharacteristic
490#483C22×C11311yescharacteristic
491#483C22×C11311yescharacteristic
492#483C22×C11311yescharacteristic
493#482—21no—
494#481C22×C11311yescharacteristic
495#480C22×C11311yescharacteristic
496#428—21no—
497#427—21no—
498#419—21no—
499#416—21no—
500#407C22×C11311yescharacteristic
501C2×C22⋊C8C22×C11311yescharacteristic
502#400C22×C11311yescharacteristic
503#399C22×C11311yescharacteristic
504#398C22×C11311yescharacteristic
505#397C22×C11311yescharacteristic
506#388—21no—
507#387—21no—
508#386—21no—
509#380—21no—
510C2×#95C22×C11311yescharacteristic
511#328C22×C11311yescharacteristic
512#328C22×C11311yescharacteristic
513#328C22×C11311yescharacteristic
514#328C22×C11311yescharacteristic
515#328C22×C11311yescharacteristic
516#328C22×C11311yescharacteristic
517#327C22×C11311yescharacteristic
518#327C22×C11311yescharacteristic
519#324C22×C11311yescharacteristic
520#324C22×C11311yescharacteristic
521#323C22×C11311yescharacteristic
522#323C22×C11311yescharacteristic
523C2×#41—21no—
524C2×#41D4×C11311yescharacteristic
525C22×Q8D4×C11311yescharacteristic
526C22×D4D4×C11311yescharacteristic
527C23×C4—21no—
528C23×C4C23×C11311yescharacteristic
529C2×M16—21no—
530C22×C8—21no—
531C4⋊Q8—21no—
532C4⋊Q8—21no—
533C4⋊Q8—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#126—21no—
539#126—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125—21no—
544#125—21no—
545#124—21no—
546#124—21no—
547#124—21no—
548#124—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C11311yescharacteristic
578C22⋊Q8D4×C11311yescharacteristic
579C22⋊Q8D4×C11311yescharacteristic
580C22⋊Q8C23×C11311yescharacteristic
581C22⋊Q8C23×C11311yescharacteristic
582C22⋊Q8C23×C11311yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121D4×C11311yescharacteristic
588#121C23×C11311yescharacteristic
589#120—21no—
590#120—21no—
591C4×Q8—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117—21no—
605#117—21no—
606#117D4×C11311yescharacteristic
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4D4×C11311yescharacteristic
612C2×C4⋊C4D4×C11311yescharacteristic
613C2×C4⋊C4C23×C11311yescharacteristic
614C2×C4⋊C4C23×C11311yescharacteristic
615C2×C4⋊C4C23×C11311yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4D4×C11311yescharacteristic
622C2×C22⋊C4D4×C11311yescharacteristic
623C2×C22⋊C4C23×C11311yescharacteristic
624C2×C42—21no—
625#107—21no—
626#107—21no—
627#107—21no—
628#107—21no—
629#106—21no—
630#106—21no—
631#106—21no—
632#106—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#103—21no—
637#103—21no—
638#103—21no—
639#102—21no—
640#102—21no—
641C22⋊C8—21no—
642C22⋊C8—21no—
643C22⋊C8C23×C11311yescharacteristic
644C22⋊C8C23×C11311yescharacteristic
645C22⋊C8C23×C11311yescharacteristic
646C22⋊C8C23×C11311yescharacteristic
647#95—21no—
648#95—21no—
649#95—21no—
650#95—21no—
651#95—21no—
652#95C23×C11311yescharacteristic
653#95C23×C11311yescharacteristic
654C24C2×D4×C11311yescharacteristic
655C24C2×D4×C11311yescharacteristic
656#41—42no—
657#41—82no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—42no—
662C2×Q8C2×D4×C11311yescharacteristic
663C2×Q8C2×D4×C11311yescharacteristic
664C2×Q8C2×D4×C11311yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—42no—
673C2×D4C2×D4×C11311yescharacteristic
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—81no—
689C22×C4C2×D4×C11311yescharacteristic
690C22×C4C2×D4×C11311yescharacteristic
691C22×C4C2×D4×C11311yescharacteristic
692C22×C4C2×D4×C11311yescharacteristic
693C22×C4C2×D4×C11311yescharacteristic
694C22×C4C2×D4×C11311yescharacteristic
695C22×C4C2×D4×C11311yescharacteristic
696C22×C4C2×D4×C11311yescharacteristic
697C22×C4C24×C11311yescharacteristic
698M16—42no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—42no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—42no—
732C4⋊C4—81no—
733C4⋊C4C2×D4×C11311yescharacteristic
734C4⋊C4C2×D4×C11311yescharacteristic
735C4⋊C4C2×D4×C11311yescharacteristic
736C4⋊C4C2×D4×C11311yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—42no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C22⋊C4—81no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42—41no—
770C42—41no—
771C23—21no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23#120×C11311yescharacteristic
782C23#120×C11311yescharacteristic
783C23C22×D4×C11311yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—81no—
788Q8—81no—
789Q8—81no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—42no—
794D4—42no—
795D4—81no—
796D4—81no—
797D4—81no—
798D4—81no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
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—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—84no—
839C2×C4#120×C11311yescharacteristic
840C2×C4#120×C11311yescharacteristic
841C2×C4C22×D4×C11311yescharacteristic
842C2×C4C22×D4×C11311yescharacteristic
843C8—41no—
844C8—41no—
845C8—41no—
846C8—41no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—42no—
855C22—42no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—81no—
863C22—81no—
864C22#458×C11312yes—
865C22C2×#120×C11311yescharacteristic
866C22#577×C11311yescharacteristic
867C22#578×C11311yescharacteristic
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C2—21no—
887C2—21no—
888C2—22no—
889C2—41no—
890C2—81no—
891C2—81no—
892C2C113×#301311yescharacteristic
893C2C113×#301811yescharacteristic
894C2C2×#458×C11311yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#3535C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#3095C2semidirect
3. C113×#3091C2semidirect
4. C113×#2498C2semidirect
5. C113×#1618C2semidirect
6. C113×#1617C2semidirect
7. C113×#1615C2semidirect
8. C113×#1614C2semidirect
9. C113×#1612C2semidirect
10. C113×#1611C2semidirect
11. C113×#1609C2semidirect
12. C113×#1608C2semidirect
13. C113×#1504C2semidirect
14. C2×#328×C113C2semidirect
15. C113×#1468C2semidirect
438. #18263C113direct (N × H)
449. #3095C2×C113semidirect
450. #3091C2×C113semidirect
451. #2498C2×C113semidirect
452. #1618C2×C113semidirect
453. #1617C2×C113semidirect
454. #1615C2×C113semidirect
455. #1614C2×C113semidirect
456. #1612C2×C113semidirect
457. #1611C2×C113semidirect
458. #1609C2×C113semidirect
459. #1608C2×C113semidirect
460. #1504C2×C113semidirect
461. C2×#328C2×C113semidirect
462. #1468C2×C113semidirect
463. C113#18263direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35352
C113×#30952
C113×#30912
C113×#24982
C113×#16182
C113×#16172
C113×#16152
C113×#16142
C113×#16122
C113×#16112
C113×#16092
C113×#16082
C113×#15042
C2×#328×C1132
C113×#14682
#18263113