Finite Group Databasebeta

← C113×#25585 #43293605

Subgroups — C113×#25585 #43293605

Order 28928.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3505C211yesmaximal, characteristic, complemented
2C113×#2435C211yesmaximal, characteristic, complemented
3C113×#2433C211yesmaximal, characteristic, complemented
4C113×#2408C211yesmaximal, characteristic, complemented
5C113×#2021C214yesmaximal, complemented
6C113×#1996C211yesmaximal, characteristic, complemented
7C113×#1964C211yesmaximal, characteristic, complemented
8C113×#1889C214yesmaximal, complemented
9C4×#99×C113C211yesmaximal, characteristic, complemented
10C23×D4×C113C2211yescharacteristic
11#553×C113—21no—
12#553×C113—22no—
13#552×C113—21no—
14#551×C113—22no—
15#548×C113—21no—
16#546×C113—21no—
17#539×C113—21no—
18#538×C113—21no—
19#534×C113C2212yes—
20C2×#127×C113—21no—
21#529×C113—21no—
22C2×#124×C113—21no—
23#525×C113—21no—
24C2×C22⋊Q8×C113C2211yescharacteristic
25C2×#121×C113—21no—
26C2×#121×C113C2211yescharacteristic
27C2×#120×C113C2214yes—
28C2×#120×C113C2212yes—
29#518×C113C2212yes—
30C2×C4×D4×C113C2211yescharacteristic
31C2×#99×C113C2212yes—
32C2×#99×C113C2214yes—
33#394×C113—21no—
34#394×C113—22no—
35#392×C113—21no—
36#392×C113—22no—
37#390×C113—21no—
38#390×C113—21no—
39#390×C113—21no—
40#380×C113C2211yescharacteristic
41#379×C113C2214yes—
42#379×C113C2212yes—
43C4×C22⋊C4×C113C2211yescharacteristic
44C4×C22⋊C4×C113C2211yescharacteristic
45#342×C113C2214yes—
46#342×C113C2212yes—
47C25×C113C2312yes—
48C2×#41×C113—21no—
49C22×Q8×C113D411yescharacteristic, complemented
50C22×D4×C113—22no—
51C22×D4×C113—24no—
52C22×D4×C113—21no—
53C22×D4×C113—21no—
54C22×D4×C113—21no—
55C22×D4×C113—21no—
56C22×D4×C113—21no—
57C22×D4×C113—21no—
58C22×D4×C113—44no—
59C22×D4×C113D411yescharacteristic, complemented
60C22×D4×C113C2311yescharacteristic
61C22×D4×C113C2312yes—
62C23×C4×C113D411yescharacteristic, complemented
63C23×C4×C113C2311yescharacteristic
64#127×C113—44no—
65#126×C113—22no—
66#126×C113—22no—
67#126×C113—22no—
68#125×C113—21no—
69#125×C113—22no—
70#124×C113—21no—
71#124×C113—22no—
72#124×C113—44no—
73#123×C113—22no—
74#123×C113—22no—
75#123×C113—22no—
76#123×C113—22no—
77#123×C113—22no—
78C22⋊Q8×C113—21no—
79C22⋊Q8×C113—22no—
80C22⋊Q8×C113—21no—
81C22⋊Q8×C113—21no—
82C22⋊Q8×C113—21no—
83C22⋊Q8×C113—21no—
84#121×C113—21no—
85#121×C113—22no—
86#121×C113—21no—
87#121×C113—21no—
88#121×C113—21no—
89#121×C113—21no—
90#121×C113—22no—
91#121×C113—22no—
92#121×C113—44no—
93#120×C113—22no—
94#120×C113—22no—
95#120×C113—28no—
96#120×C113—44no—
97#120×C113—44no—
98C4×Q8×C113—21no—
99C4×D4×C113—22no—
100C4×D4×C113—21no—
101C4×D4×C113—21no—
102C4×D4×C113—21no—
103C4×D4×C113—21no—
104C4×D4×C113—21no—
105C4×D4×C113—22no—
106C4×D4×C113—22no—
107C4×D4×C113—22no—
108C4×D4×C113—22no—
109#117×C113—21no—
110#117×C113—22no—
111#117×C113—22no—
112C2×C4⋊C4×C113—21no—
113C2×C4⋊C4×C113D411yescharacteristic, complemented
114C2×C4⋊C4×C113D411yescharacteristic, complemented
115C2×C4⋊C4×C113D411yescharacteristic, complemented
116C2×C4⋊C4×C113D412yescomplemented
117C2×C22⋊C4×C113—22no—
118C2×C22⋊C4×C113—24no—
119C2×C22⋊C4×C113—22no—
120C2×C22⋊C4×C113—22no—
121C2×C22⋊C4×C113—24no—
122C2×C22⋊C4×C113—22no—
123C2×C22⋊C4×C113—24no—
124C2×C22⋊C4×C113D411yescharacteristic, complemented
125C2×C22⋊C4×C113D412yescomplemented
126C2×C22⋊C4×C113C2312yes—
127C2×C22⋊C4×C113C2312yes—
128C2×C22⋊C4×C113C2311yescharacteristic
129C2×C22⋊C4×C113C2312yes—
130C2×C22⋊C4×C113C2312yes—
131C2×C42×C113—21no—
132C2×C42×C113—21no—
133C2×C42×C113D411yescharacteristic, complemented
134#99×C113—24no—
135#99×C113—44no—
136#95×C113—21no—
137#95×C113—21no—
138#95×C113—21no—
139C24×C113—22no—
140C24×C113—22no—
141C24×C113—22no—
142C24×C113—24no—
143C24×C113—24no—
144C24×C113—44no—
145C24×C113—82no—
146C24×C113C2×D412yes—
147C24×C113C2×D411yescharacteristic
148C24×C113C2411yescharacteristic
149#41×C113—82no—
150C2×Q8×C113—21no—
151C2×Q8×C113—21no—
152C2×Q8×C113—42no—
153C2×D4×C113—24no—
154C2×D4×C113—24no—
155C2×D4×C113—24no—
156C2×D4×C113—21no—
157C2×D4×C113—22no—
158C2×D4×C113—21no—
159C2×D4×C113—22no—
160C2×D4×C113—22no—
161C2×D4×C113—24no—
162C2×D4×C113—24no—
163C2×D4×C113—22no—
164C2×D4×C113—22no—
165C2×D4×C113—22no—
166C2×D4×C113—21no—
167C2×D4×C113—21no—
168C2×D4×C113—42no—
169C2×D4×C113—42no—
170C2×D4×C113—42no—
171C2×D4×C113—42no—
172C2×D4×C113—48no—
173C2×D4×C113—44no—
174C2×D4×C113—44no—
175C2×D4×C113—44no—
176C2×D4×C113—44no—
177C2×D4×C113—44no—
178C2×D4×C113—48no—
179C2×D4×C113—41no—
180C2×D4×C113—41no—
181C2×D4×C113—41no—
182C2×D4×C113—41no—
183C2×D4×C113—84no—
184C2×D4×C113—82no—
185C22×C4×C113—22no—
186C22×C4×C113—22no—
187C22×C4×C113—22no—
188C22×C4×C113—21no—
189C22×C4×C113—21no—
190C22×C4×C113—22no—
191C22×C4×C113—22no—
192C22×C4×C113—42no—
193C22×C4×C113—42no—
194C22×C4×C113C2×D411yescharacteristic
195C22×C4×C113C2×D412yes—
196C22×C4×C113C2×D411yescharacteristic
197C22×C4×C113C2×D411yescharacteristic
198C22×C4×C113C2×D411yescharacteristic
199C22×C4×C113C2×D411yescharacteristic
200C22×C4×C113C2×D412yes—
201C22×C4×C113C2×D411yescharacteristic
202C22×C4×C113C2×D412yes—
203C22×C4×C113C2×D411yescharacteristic
204C22×C4×C113C2×D411yescharacteristic
205C22×C4×C113C2×D411yescharacteristic
206C4⋊C4×C113—22no—
207C4⋊C4×C113—22no—
208C4⋊C4×C113—22no—
209C4⋊C4×C113—22no—
210C4⋊C4×C113—21no—
211C4⋊C4×C113—22no—
212C4⋊C4×C113—21no—
213C4⋊C4×C113—21no—
214C4⋊C4×C113—21no—
215C4⋊C4×C113—21no—
216C4⋊C4×C113—22no—
217C4⋊C4×C113—21no—
218C4⋊C4×C113—42no—
219C22⋊C4×C113—22no—
220C22⋊C4×C113—22no—
221C22⋊C4×C113—22no—
222C22⋊C4×C113—22no—
223C22⋊C4×C113—22no—
224C22⋊C4×C113—22no—
225C22⋊C4×C113—21no—
226C22⋊C4×C113—22no—
227C22⋊C4×C113—21no—
228C22⋊C4×C113—22no—
229C22⋊C4×C113—22no—
230C22⋊C4×C113—22no—
231C22⋊C4×C113—21no—
232C22⋊C4×C113—21no—
233C22⋊C4×C113—22no—
234C22⋊C4×C113—22no—
235C22⋊C4×C113—22no—
236C22⋊C4×C113—24no—
237C22⋊C4×C113—48no—
238C22⋊C4×C113—44no—
239C22⋊C4×C113—44no—
240C22⋊C4×C113—48no—
241C22⋊C4×C113—84no—
242C22⋊C4×C113—82no—
243C22⋊C4×C113#4114yescomplemented
244C42×C113—22no—
245C42×C113—22no—
246C42×C113—21no—
247C42×C113—21no—
248C42×C113—42no—
249C42×C113—42no—
250C23×C113—24no—
251C23×C113—24no—
252C23×C113—24no—
253C23×C113—21no—
254C23×C113—22no—
255C23×C113—21no—
256C23×C113—21no—
257C23×C113—24no—
258C23×C113—41no—
259C23×C113—41no—
260C23×C113—41no—
261C23×C113—41no—
262C23×C113—44no—
263C23×C113—42no—
264C23×C113—42no—
265C23×C113—42no—
266C23×C113—42no—
267C23×C113—42no—
268C23×C113—44no—
269C23×C113—42no—
270C23×C113—42no—
271C23×C113—42no—
272C23×C113—42no—
273C23×C113—42no—
274C23×C113—44no—
275C23×C113—44no—
276C23×C113—88no—
277C23×C113—88no—
278C23×C113C22×D411yescharacteristic
279C23×C113C22×D411yescharacteristic
280C23×C113C22×D411yescharacteristic
281C23×C113C2×#4112yes—
282C23×C113H(5,𝔽2)12yes—
283Q8×C113—42no—
284Q8×C113—81no—
285D4×C113—44no—
286D4×C113—44no—
287D4×C113—44no—
288D4×C113—42no—
289D4×C113—42no—
290D4×C113—42no—
291D4×C113—42no—
292D4×C113—44no—
293D4×C113—44no—
294D4×C113—42no—
295D4×C113—81no—
296D4×C113—82no—
297D4×C113—82no—
298D4×C113—816no—
299D4×C113—88no—
300C2×C4×C113—22no—
301C2×C4×C113—22no—
302C2×C4×C113—22no—
303C2×C4×C113—21no—
304C2×C4×C113—22no—
305C2×C4×C113—21no—
306C2×C4×C113—21no—
307C2×C4×C113—22no—
308C2×C4×C113—22no—
309C2×C4×C113—21no—
310C2×C4×C113—21no—
311C2×C4×C113—24no—
312C2×C4×C113—24no—
313C2×C4×C113—41no—
314C2×C4×C113—41no—
315C2×C4×C113—41no—
316C2×C4×C113—42no—
317C2×C4×C113—42no—
318C2×C4×C113—42no—
319C2×C4×C113—41no—
320C2×C4×C113—42no—
321C2×C4×C113—41no—
322C2×C4×C113—42no—
323C2×C4×C113—42no—
324C2×C4×C113—42no—
325C2×C4×C113—42no—
326C2×C4×C113—42no—
327C2×C4×C113—42no—
328C2×C4×C113—42no—
329C2×C4×C113—81no—
330C2×C4×C113—82no—
331C2×C4×C113—82no—
332C2×C4×C113#12011yescharacteristic
333C2×C4×C113#12011yescharacteristic
334C2×C4×C113#12011yescharacteristic
335C2×C4×C113#12011yescharacteristic
336C22×C113—21no—
337C22×C113—21no—
338C22×C113—21no—
339C22×C113—21no—
340C22×C113—21no—
341C22×C113—21no—
342C22×C113—42no—
343C22×C113—42no—
344C22×C113—42no—
345C22×C113—48no—
346C22×C113—44no—
347C22×C113—48no—
348C22×C113—44no—
349C22×C113—41no—
350C22×C113—42no—
351C22×C113—41no—
352C22×C113—42no—
353C22×C113—44no—
354C22×C113—42no—
355C22×C113—41no—
356C22×C113—84no—
357C22×C113—81no—
358C22×C113—84no—
359C22×C113—82no—
360C22×C113—84no—
361C22×C113—82no—
362C22×C113—82no—
363C22×C113—82no—
364C22×C113C2×#12011yescharacteristic
365C22×C113#53211yescharacteristic
366C22×C113#53511yescharacteristic
367C22×C113#54612yes—
368C22×C113#55012yes—
369C4×C113—21no—
370C4×C113—21no—
371C4×C113—21no—
372C4×C113—44no—
373C4×C113—41no—
374C4×C113—42no—
375C4×C113—41no—
376C4×C113—42no—
377C4×C113—41no—
378C4×C113—42no—
379C4×C113—82no—
380C4×C113—82no—
381C4×C113B(4,𝔽2)12yes—
382#25585C11311yesmaximal, characteristic, direct product factor, Sylow
383C2×C113—22no—
384C2×C113—21no—
385C2×C113—22no—
386C2×C113—21no—
387C2×C113—84no—
388C2×C113—81no—
389C2×C113—82no—
390C2×C113#243111yescharacteristic
391C2×C113C2×B(4,𝔽2)11yescharacteristic
392C2×C113#302711yescharacteristic
393#3505C2×C11311yescharacteristic, complemented
394#2435C2×C11311yescharacteristic, complemented
395#2433C2×C11311yescharacteristic, complemented
396#2408C2×C11311yescharacteristic, complemented
397#2021C2×C11314yescomplemented
398#1996C2×C11311yescharacteristic, complemented
399#1964C2×C11311yescharacteristic, complemented
400#1889C2×C11314yescomplemented
401C4×#99C2×C11311yescharacteristic, complemented
402C113#2558511yescharacteristic, direct product factor, Sylow
403C23×D4C22×C11311yescharacteristic
404#553—21no—
405#553—22no—
406#552—21no—
407#551—22no—
408#548—21no—
409#546—21no—
410#539—21no—
411#538—21no—
412#534C22×C11312yes—
413C2×#127—21no—
414#529—21no—
415C2×#124—21no—
416#525—21no—
417C2×C22⋊Q8C22×C11311yescharacteristic
418C2×#121—21no—
419C2×#121C22×C11311yescharacteristic
420C2×#120C22×C11314yes—
421C2×#120C22×C11312yes—
422#518C22×C11312yes—
423C2×C4×D4C22×C11311yescharacteristic
424C2×#99C22×C11312yes—
425C2×#99C22×C11314yes—
426#394—21no—
427#394—22no—
428#392—21no—
429#392—22no—
430#390—21no—
431#390—21no—
432#390—21no—
433#380C22×C11311yescharacteristic
434#379C22×C11312yes—
435#379C22×C11314yes—
436C4×C22⋊C4C22×C11311yescharacteristic
437C4×C22⋊C4C22×C11311yescharacteristic
438#342C22×C11312yes—
439#342C22×C11314yes—
440C25C23×C11312yes—
441C2×#41—21no—
442C22×Q8D4×C11311yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C11311yescharacteristic, complemented
453C22×D4C23×C11311yescharacteristic
454C22×D4C23×C11312yes—
455C23×C4D4×C11311yescharacteristic, complemented
456C23×C4C23×C11311yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C11311yescharacteristic, complemented
507C2×C4⋊C4D4×C11311yescharacteristic, complemented
508C2×C4⋊C4D4×C11311yescharacteristic, complemented
509C2×C4⋊C4D4×C11312yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C11311yescharacteristic, complemented
518C2×C22⋊C4D4×C11312yescomplemented
519C2×C22⋊C4C23×C11312yes—
520C2×C22⋊C4C23×C11312yes—
521C2×C22⋊C4C23×C11311yescharacteristic
522C2×C22⋊C4C23×C11312yes—
523C2×C22⋊C4C23×C11312yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C11311yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C11312yes—
540C24C2×D4×C11311yescharacteristic
541C24C24×C11311yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C11311yescharacteristic
588C22×C4C2×D4×C11312yes—
589C22×C4C2×D4×C11311yescharacteristic
590C22×C4C2×D4×C11311yescharacteristic
591C22×C4C2×D4×C11311yescharacteristic
592C22×C4C2×D4×C11311yescharacteristic
593C22×C4C2×D4×C11312yes—
594C22×C4C2×D4×C11311yescharacteristic
595C22×C4C2×D4×C11312yes—
596C22×C4C2×D4×C11311yescharacteristic
597C22×C4C2×D4×C11311yescharacteristic
598C22×C4C2×D4×C11311yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C11314yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C11311yescharacteristic
672C23C22×D4×C11311yescharacteristic
673C23C22×D4×C11311yescharacteristic
674C23C2×#41×C11312yes—
675C23H(5,𝔽2)×C11312yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C11311yescharacteristic
726C2×C4#120×C11311yescharacteristic
727C2×C4#120×C11311yescharacteristic
728C2×C4#120×C11311yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—41no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C11311yescharacteristic
758C22#532×C11311yescharacteristic
759C22#535×C11311yescharacteristic
760C22#546×C11312yes—
761C22#550×C11312yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4B(4,𝔽2)×C11312yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C113×#243111yescharacteristic
783C2C2×B(4,𝔽2)×C11311yescharacteristic
784C2C113×#302711yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC24C24×C113
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3505C2semidirect
2. C113×#2435C2semidirect
3. C113×#2433C2semidirect
4. C113×#2408C2semidirect
5. C113×#2021C2semidirect
6. C113×#1996C2semidirect
7. C113×#1964C2semidirect
8. C113×#1889C2semidirect
9. C4×#99×C113C2semidirect
49. C22×Q8×C113D4semidirect
59. C22×D4×C113D4semidirect
62. C23×C4×C113D4semidirect
113. C2×C4⋊C4×C113D4semidirect
114. C2×C4⋊C4×C113D4semidirect
115. C2×C4⋊C4×C113D4semidirect
116. C2×C4⋊C4×C113D4semidirect
124. C2×C22⋊C4×C113D4semidirect
125. C2×C22⋊C4×C113D4semidirect
133. C2×C42×C113D4semidirect
243. C22⋊C4×C113#41semidirect
382. #25585C113direct (N × H)
393. #3505C2×C113semidirect
394. #2435C2×C113semidirect
395. #2433C2×C113semidirect
396. #2408C2×C113semidirect
397. #2021C2×C113semidirect
398. #1996C2×C113semidirect
399. #1964C2×C113semidirect
400. #1889C2×C113semidirect
401. C4×#99C2×C113semidirect
402. C113#25585direct (N × H)
442. C22×Q8D4×C113semidirect
452. C22×D4D4×C113semidirect
455. C23×C4D4×C113semidirect
506. C2×C4⋊C4D4×C113semidirect
507. C2×C4⋊C4D4×C113semidirect
508. C2×C4⋊C4D4×C113semidirect
509. C2×C4⋊C4D4×C113semidirect
517. C2×C22⋊C4D4×C113semidirect
518. C2×C22⋊C4D4×C113semidirect
526. C2×C42D4×C113semidirect
636. C22⋊C4#41×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35052
C113×#24352
C113×#24332
C113×#24082
C113×#20212
C113×#19962
C113×#19642
C113×#18892
C4×#99×C1132
#25585113