Finite Group Databasebeta

← C113×#23955 #43291975

Subgroups — C113×#23955 #43291975

Order 28928.

1234 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3494C211yesmaximal, characteristic
2C113×#3004C211yesmaximal, characteristic, complemented
3C2×#419×C113C211yesmaximal, characteristic, complemented
4C113×#2436C211yesmaximal, characteristic, complemented
5C113×#2028C212yesmaximal, complemented
6C113×#2004C212yesmaximal, complemented
7C113×#1900C211yesmaximal, characteristic, complemented
8C113×#1885C212yesmaximal, complemented
9C113×#1882C212yesmaximal, complemented
10C113×#1871C211yesmaximal, characteristic, complemented
11C113×#1826C211yesmaximal, characteristic, complemented
12C23×Q8×C113C2211yescharacteristic
13C2×#137×C113C2212yes—
14C22×M16×C113C2211yescharacteristic
15#555×C113—21no—
16#553×C113—21no—
17#553×C113—21no—
18#551×C113—22no—
19#547×C113—21no—
20#546×C113—22no—
21#544×C113C2211yescharacteristic
22#542×C113—21no—
23#540×C113—21no—
24#535×C113C2211yescharacteristic
25#532×C113—21no—
26#529×C113—21no—
27C2×#124×C113C2212yes—
28#525×C113C2211yescharacteristic
29C2×#121×C113C2211yescharacteristic
30#520×C113C2211yescharacteristic
31#518×C113C2211yescharacteristic
32C2×#117×C113C2211yescharacteristic
33#451×C113—21no—
34#451×C113—21no—
35#448×C113—21no—
36#448×C113—21no—
37C2×#104×C113C2212yes—
38#419×C113—21no—
39#419×C113—21no—
40#419×C113C2212yes—
41#419×C113C2212yes—
42#419×C113C2212yes—
43C2×#103×C113—21no—
44C2×#103×C113—21no—
45C2×#100×C113C2212yes—
46#407×C113C2211yescharacteristic
47#393×C113—22no—
48#391×C113C2212yes—
49#386×C113—22no—
50C4×C22⋊C4×C113C2211yescharacteristic
51#343×C113C2212yes—
52#339×C113C2212yes—
53#339×C113C2212yes—
54#339×C113C2212yes—
55C2×#41×C113—22no—
56C2×#41×C113C2311yescharacteristic
57C22×Q8×C113—21no—
58C22×Q8×C113—24no—
59C22×Q8×C113—21no—
60C22×Q8×C113—21no—
61C22×Q8×C113—21no—
62C22×Q8×C113—21no—
63C22×Q8×C113—42no—
64C22×Q8×C113C2312yes—
65C22×D4×C113D412yes—
66C22×D4×C113C2311yescharacteristic
67C23×C4×C113—21no—
68C23×C4×C113C2311yescharacteristic
69#137×C113—24no—
70#137×C113—42no—
71C2×Q16×C113—22no—
72C2×SD16×C113—22no—
73C2×M16×C113—21no—
74C2×M16×C113—42no—
75C2×M16×C113C2312yes—
76C2×M16×C113C2312yes—
77C22×C8×C113—21no—
78C4⋊Q8×C113—21no—
79C4⋊Q8×C113—21no—
80#127×C113—21no—
81#126×C113—22no—
82#126×C113—22no—
83#125×C113—21no—
84#125×C113—21no—
85#124×C113—22no—
86#124×C113—22no—
87#124×C113—21no—
88#124×C113—24no—
89#124×C113—42no—
90#123×C113—22no—
91#123×C113—22no—
92#123×C113—22no—
93#123×C113—22no—
94#123×C113—21no—
95C22⋊Q8×C113—22no—
96C22⋊Q8×C113—22no—
97C22⋊Q8×C113D411yescharacteristic
98C22⋊Q8×C113D411yescharacteristic
99#121×C113—22no—
100#121×C113—22no—
101#121×C113—22no—
102#121×C113—21no—
103#121×C113—21no—
104#121×C113—21no—
105#121×C113—21no—
106#121×C113—21no—
107#121×C113—21no—
108#121×C113D411yescharacteristic
109#121×C113D411yescharacteristic
110#120×C113—21no—
111#120×C113—22no—
112C4×Q8×C113—21no—
113C4×D4×C113—22no—
114C4×D4×C113—22no—
115C4×D4×C113—21no—
116C4×D4×C113—22no—
117C4×D4×C113—21no—
118C4×D4×C113—21no—
119C4×D4×C113—21no—
120C4×D4×C113—21no—
121C4×D4×C113—21no—
122C4×D4×C113—21no—
123#117×C113—22no—
124#117×C113—21no—
125#117×C113—21no—
126#117×C113—21no—
127#117×C113D411yescharacteristic
128#117×C113D411yescharacteristic
129#117×C113C2311yescharacteristic
130#117×C113C2311yescharacteristic
131#117×C113C2311yescharacteristic
132C2×C4⋊C4×C113—21no—
133C2×C4⋊C4×C113D411yescharacteristic
134C2×C4⋊C4×C113D411yescharacteristic
135C2×C4⋊C4×C113C2311yescharacteristic
136C2×C22⋊C4×C113—21no—
137C2×C22⋊C4×C113—22no—
138C2×C22⋊C4×C113—24no—
139C2×C22⋊C4×C113—21no—
140C2×C22⋊C4×C113D412yes—
141C2×C42×C113—21no—
142C2×C42×C113C2312yes—
143#104×C113—42no—
144#103×C113—22no—
145#103×C113—22no—
146#103×C113—22no—
147#103×C113—22no—
148#103×C113—22no—
149#103×C113—22no—
150#100×C113—42no—
151C22⋊C8×C113—21no—
152C22⋊C8×C113—21no—
153#95×C113—21no—
154#95×C113—24no—
155C24×C113C2×D411yescharacteristic
156C24×C113C2×D412yes—
157#41×C113—22no—
158#41×C113—22no—
159#41×C113—84no—
160C2×Q8×C113—22no—
161C2×Q8×C113—22no—
162C2×Q8×C113—24no—
163C2×Q8×C113—24no—
164C2×Q8×C113—22no—
165C2×Q8×C113—22no—
166C2×Q8×C113—22no—
167C2×Q8×C113—22no—
168C2×Q8×C113—44no—
169C2×Q8×C113—44no—
170C2×Q8×C113—44no—
171C2×Q8×C113—42no—
172C2×Q8×C113—42no—
173C2×Q8×C113—41no—
174C2×Q8×C113—41no—
175C2×Q8×C113C2×D411yescharacteristic
176C2×Q8×C113#4114yescomplemented
177C2×D4×C113—21no—
178C2×D4×C113—22no—
179C2×D4×C113—21no—
180C2×D4×C113—22no—
181C2×D4×C113—22no—
182C2×D4×C113—21no—
183C2×D4×C113—22no—
184C2×D4×C113—21no—
185C2×D4×C113—21no—
186C2×D4×C113—22no—
187C2×D4×C113—22no—
188C2×D4×C113—44no—
189C2×D4×C113C2×D411yescharacteristic
190C22×C4×C113—22no—
191C22×C4×C113—22no—
192C22×C4×C113—21no—
193C22×C4×C113—22no—
194C22×C4×C113—22no—
195C22×C4×C113—22no—
196C22×C4×C113—22no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—22no—
200C22×C4×C113—44no—
201C22×C4×C113—41no—
202C22×C4×C113—41no—
203C22×C4×C113C2×D411yescharacteristic
204C22×C4×C113C2×D411yescharacteristic
205C22×C4×C113C2×D411yescharacteristic
206C22×C4×C113C2×D411yescharacteristic
207C22×C4×C113C2×D411yescharacteristic
208C22×C4×C113C2×D412yes—
209C22×C4×C113C2411yescharacteristic
210Q16×C113—44no—
211SD16×C113—44no—
212M16×C113—22no—
213M16×C113—22no—
214M16×C113—22no—
215M16×C113—22no—
216M16×C113—42no—
217C2×C8×C113—22no—
218C2×C8×C113—22no—
219C2×C8×C113—42no—
220C4⋊C4×C113—22no—
221C4⋊C4×C113—22no—
222C4⋊C4×C113—22no—
223C4⋊C4×C113—22no—
224C4⋊C4×C113—21no—
225C4⋊C4×C113—21no—
226C4⋊C4×C113—21no—
227C4⋊C4×C113—21no—
228C4⋊C4×C113—21no—
229C4⋊C4×C113—21no—
230C4⋊C4×C113C2×D411yescharacteristic
231C4⋊C4×C113C2×D411yescharacteristic
232C4⋊C4×C113C2×D411yescharacteristic
233C4⋊C4×C113C2×D411yescharacteristic
234C4⋊C4×C113C2×D411yescharacteristic
235C4⋊C4×C113C2×D411yescharacteristic
236C22⋊C4×C113—22no—
237C22⋊C4×C113—22no—
238C22⋊C4×C113—22no—
239C22⋊C4×C113—22no—
240C22⋊C4×C113—22no—
241C22⋊C4×C113—21no—
242C22⋊C4×C113—21no—
243C22⋊C4×C113—21no—
244C22⋊C4×C113—21no—
245C22⋊C4×C113—21no—
246C22⋊C4×C113—21no—
247C22⋊C4×C113—21no—
248C22⋊C4×C113—22no—
249C22⋊C4×C113—22no—
250C22⋊C4×C113—21no—
251C22⋊C4×C113—21no—
252C22⋊C4×C113—48no—
253C22⋊C4×C113—42no—
254C42×C113—22no—
255C42×C113—21no—
256C42×C113—21no—
257C42×C113—21no—
258C42×C113—21no—
259C42×C113—21no—
260C42×C113—22no—
261C42×C113—22no—
262C23×C113—22no—
263C23×C113—22no—
264C23×C113—22no—
265C23×C113—21no—
266C23×C113—24no—
267C23×C113—41no—
268C23×C113—42no—
269C23×C113—42no—
270C23×C113#12011yescharacteristic
271C23×C113#12011yescharacteristic
272C23×C113C22×D411yescharacteristic
273Q8×C113—24no—
274Q8×C113—24no—
275Q8×C113—22no—
276Q8×C113—44no—
277Q8×C113—44no—
278Q8×C113—42no—
279Q8×C113—42no—
280Q8×C113—82no—
281D4×C113—22no—
282D4×C113—42no—
283D4×C113—44no—
284D4×C113—42no—
285D4×C113—41no—
286D4×C113—41no—
287D4×C113—42no—
288D4×C113—81no—
289D4×C113—82no—
290D4×C113—82no—
291D4×C113—82no—
292C2×C4×C113—22no—
293C2×C4×C113—21no—
294C2×C4×C113—21no—
295C2×C4×C113—21no—
296C2×C4×C113—21no—
297C2×C4×C113—22no—
298C2×C4×C113—22no—
299C2×C4×C113—21no—
300C2×C4×C113—21no—
301C2×C4×C113—21no—
302C2×C4×C113—21no—
303C2×C4×C113—21no—
304C2×C4×C113—21no—
305C2×C4×C113—21no—
306C2×C4×C113—22no—
307C2×C4×C113—24no—
308C2×C4×C113—44no—
309C2×C4×C113—44no—
310C2×C4×C113—42no—
311C2×C4×C113—42no—
312C2×C4×C113—42no—
313C2×C4×C113—41no—
314C2×C4×C113—41no—
315C2×C4×C113—42no—
316C2×C4×C113—42no—
317C2×C4×C113—42no—
318C2×C4×C113—42no—
319C2×C4×C113—81no—
320C2×C4×C113—82no—
321C2×C4×C113—82no—
322C2×C4×C113—82no—
323C2×C4×C113#12011yescharacteristic
324C2×C4×C113#12011yescharacteristic
325C2×C4×C113C22×D411yescharacteristic
326C2×C4×C113C22×D411yescharacteristic
327C2×C4×C113C2×#4112yes—
328C2×C4×C113H(5,𝔽2)12yes—
329C8×C113—42no—
330C8×C113—42no—
331C22×C113—21no—
332C22×C113—21no—
333C22×C113—21no—
334C22×C113—21no—
335C22×C113—21no—
336C22×C113—21no—
337C22×C113—21no—
338C22×C113—44no—
339C22×C113—41no—
340C22×C113—42no—
341C22×C113—41no—
342C22×C113—42no—
343C22×C113—42no—
344C22×C113—41no—
345C22×C113—84no—
346C22×C113#45512yes—
347C22×C113C2×#12011yescharacteristic
348C22×C113#54612yes—
349C4×C113—21no—
350C4×C113—21no—
351C4×C113—44no—
352C4×C113—41no—
353C4×C113—41no—
354C4×C113—41no—
355C4×C113—42no—
356C4×C113—41no—
357C4×C113—41no—
358C4×C113—41no—
359C4×C113—41no—
360C4×C113—82no—
361C4×C113#52511yescharacteristic
362C4×C113#53511yescharacteristic
363C4×C113#54612yes—
364#23955C11311yesmaximal, characteristic, direct product factor, Sylow
365C2×C113—22no—
366C2×C113—22no—
367C2×C113—41no—
368C2×C113—81no—
369C2×C113—82no—
370C2×C113#240411yescharacteristic
371C2×C113C2×#45511yescharacteristic
372C2×C113#302211yescharacteristic
373#3494C2×C11311yescharacteristic
374#3004C2×C11311yescharacteristic, complemented
375C2×#419C2×C11311yescharacteristic, complemented
376#2436C2×C11311yescharacteristic, complemented
377#2028C2×C11312yescomplemented
378#2004C2×C11312yescomplemented
379#1900C2×C11311yescharacteristic, complemented
380#1885C2×C11312yescomplemented
381#1882C2×C11312yescomplemented
382#1871C2×C11311yescharacteristic, complemented
383#1826C2×C11311yescharacteristic, complemented
384C113#2395511yescharacteristic, direct product factor, Sylow
385C23×Q8C22×C11311yescharacteristic
386C2×#137C22×C11312yes—
387C22×M16C22×C11311yescharacteristic
388#555—21no—
389#553—21no—
390#553—21no—
391#551—22no—
392#547—21no—
393#546—22no—
394#544C22×C11311yescharacteristic
395#542—21no—
396#540—21no—
397#535C22×C11311yescharacteristic
398#532—21no—
399#529—21no—
400C2×#124C22×C11312yes—
401#525C22×C11311yescharacteristic
402C2×#121C22×C11311yescharacteristic
403#520C22×C11311yescharacteristic
404#518C22×C11311yescharacteristic
405C2×#117C22×C11311yescharacteristic
406#451—21no—
407#451—21no—
408#448—21no—
409#448—21no—
410C2×#104C22×C11312yes—
411#419—21no—
412#419—21no—
413#419C22×C11312yes—
414#419C22×C11312yes—
415#419C22×C11312yes—
416C2×#103—21no—
417C2×#103—21no—
418C2×#100C22×C11312yes—
419#407C22×C11311yescharacteristic
420#393—22no—
421#391C22×C11312yes—
422#386—22no—
423C4×C22⋊C4C22×C11311yescharacteristic
424#343C22×C11312yes—
425#339C22×C11312yes—
426#339C22×C11312yes—
427#339C22×C11312yes—
428C2×#41—22no—
429C2×#41C23×C11311yescharacteristic
430C22×Q8—21no—
431C22×Q8—24no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—21no—
435C22×Q8—21no—
436C22×Q8—42no—
437C22×Q8C23×C11312yes—
438C22×D4D4×C11312yes—
439C22×D4C23×C11311yescharacteristic
440C23×C4—21no—
441C23×C4C23×C11311yescharacteristic
442#137—24no—
443#137—42no—
444C2×Q16—22no—
445C2×SD16—22no—
446C2×M16—21no—
447C2×M16—42no—
448C2×M16C23×C11312yes—
449C2×M16C23×C11312yes—
450C22×C8—21no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453#127—21no—
454#126—22no—
455#126—22no—
456#125—21no—
457#125—21no—
458#124—22no—
459#124—22no—
460#124—21no—
461#124—24no—
462#124—42no—
463#123—22no—
464#123—22no—
465#123—22no—
466#123—22no—
467#123—21no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8D4×C11311yescharacteristic
471C22⋊Q8D4×C11311yescharacteristic
472#121—22no—
473#121—22no—
474#121—22no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121D4×C11311yescharacteristic
482#121D4×C11311yescharacteristic
483#120—21no—
484#120—22no—
485C4×Q8—21no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—21no—
489C4×D4—22no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496#117—22no—
497#117—21no—
498#117—21no—
499#117—21no—
500#117D4×C11311yescharacteristic
501#117D4×C11311yescharacteristic
502#117C23×C11311yescharacteristic
503#117C23×C11311yescharacteristic
504#117C23×C11311yescharacteristic
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C11311yescharacteristic
507C2×C4⋊C4D4×C11311yescharacteristic
508C2×C4⋊C4C23×C11311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4D4×C11312yes—
514C2×C42—21no—
515C2×C42C23×C11312yes—
516#104—42no—
517#103—22no—
518#103—22no—
519#103—22no—
520#103—22no—
521#103—22no—
522#103—22no—
523#100—42no—
524C22⋊C8—21no—
525C22⋊C8—21no—
526#95—21no—
527#95—24no—
528C24C2×D4×C11311yescharacteristic
529C24C2×D4×C11312yes—
530#41—22no—
531#41—22no—
532#41—84no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—24no—
536C2×Q8—24no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—44no—
542C2×Q8—44no—
543C2×Q8—44no—
544C2×Q8—42no—
545C2×Q8—42no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8C2×D4×C11311yescharacteristic
549C2×Q8#41×C11314yescomplemented
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—44no—
562C2×D4C2×D4×C11311yescharacteristic
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—44no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4C2×D4×C11311yescharacteristic
577C22×C4C2×D4×C11311yescharacteristic
578C22×C4C2×D4×C11311yescharacteristic
579C22×C4C2×D4×C11311yescharacteristic
580C22×C4C2×D4×C11311yescharacteristic
581C22×C4C2×D4×C11312yes—
582C22×C4C24×C11311yescharacteristic
583Q16—44no—
584SD16—44no—
585M16—22no—
586M16—22no—
587M16—22no—
588M16—22no—
589M16—42no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—42no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4C2×D4×C11311yescharacteristic
604C4⋊C4C2×D4×C11311yescharacteristic
605C4⋊C4C2×D4×C11311yescharacteristic
606C4⋊C4C2×D4×C11311yescharacteristic
607C4⋊C4C2×D4×C11311yescharacteristic
608C4⋊C4C2×D4×C11311yescharacteristic
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—48no—
626C22⋊C4—42no—
627C42—22no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—22no—
634C42—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—24no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23#120×C11311yescharacteristic
644C23#120×C11311yescharacteristic
645C23C22×D4×C11311yescharacteristic
646Q8—24no—
647Q8—24no—
648Q8—22no—
649Q8—44no—
650Q8—44no—
651Q8—42no—
652Q8—42no—
653Q8—82no—
654D4—22no—
655D4—42no—
656D4—44no—
657D4—42no—
658D4—41no—
659D4—41no—
660D4—42no—
661D4—82no—
662D4—81no—
663D4—82no—
664D4—82no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—81no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4—82no—
696C2×C4#120×C11311yescharacteristic
697C2×C4#120×C11311yescharacteristic
698C2×C4C22×D4×C11311yescharacteristic
699C2×C4C22×D4×C11311yescharacteristic
700C2×C4C2×#41×C11312yes—
701C2×C4H(5,𝔽2)×C11312yes—
702C8—42no—
703C8—42no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—44no—
712C22—41no—
713C22—42no—
714C22—41no—
715C22—42no—
716C22—42no—
717C22—41no—
718C22—84no—
719C22#455×C11312yes—
720C22C2×#120×C11311yescharacteristic
721C22#546×C11312yes—
722C4—21no—
723C4—21no—
724C4—44no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—82no—
734C4#525×C11311yescharacteristic
735C4#535×C11311yescharacteristic
736C4#546×C11312yes—
737C2—22no—
738C2—22no—
739C2—41no—
740C2—82no—
741C2—81no—
742C2C113×#240411yescharacteristic
743C2C2×#455×C11311yescharacteristic
744C2C113×#302211yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#3494C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#3004C2semidirect
3. C2×#419×C113C2semidirect
4. C113×#2436C2semidirect
5. C113×#2028C2semidirect
6. C113×#2004C2semidirect
7. C113×#1900C2semidirect
8. C113×#1885C2semidirect
9. C113×#1882C2semidirect
10. C113×#1871C2semidirect
11. C113×#1826C2semidirect
176. C2×Q8×C113#41semidirect
364. #23955C113direct (N × H)
374. #3004C2×C113semidirect
375. C2×#419C2×C113semidirect
376. #2436C2×C113semidirect
377. #2028C2×C113semidirect
378. #2004C2×C113semidirect
379. #1900C2×C113semidirect
380. #1885C2×C113semidirect
381. #1882C2×C113semidirect
382. #1871C2×C113semidirect
383. #1826C2×C113semidirect
384. C113#23955direct (N × H)
549. C2×Q8#41×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34942
C113×#30042
C2×#419×C1132
C113×#24362
C113×#20282
C113×#20042
C113×#19002
C113×#18852
C113×#18822
C113×#18712
C113×#18262
#23955113