Finite Group Databasebeta

← C113×#18415 #43286435

Subgroups — C113×#18415 #43286435

Order 28928.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3534C211yesmaximal, characteristic
2C113×#3196C211yesmaximal, characteristic, complemented
3C113×#3187C211yesmaximal, characteristic, complemented
4C113×#2663C211yesmaximal, characteristic, complemented
5C113×#1618C211yesmaximal, characteristic, complemented
6C113×#1616C211yesmaximal, characteristic, complemented
7C113×#1615C211yesmaximal, characteristic, complemented
8C113×#1613C211yesmaximal, characteristic, complemented
9C113×#1606C211yesmaximal, characteristic, complemented
10C113×#1604C211yesmaximal, characteristic, complemented
11C113×#1603C211yesmaximal, characteristic, complemented
12C113×#1601C211yesmaximal, characteristic, complemented
13C113×#1507C211yesmaximal, characteristic, complemented
14C113×#1501C211yesmaximal, characteristic, complemented
15C113×#1468C211yesmaximal, characteristic, complemented
16#562×C113—21no—
17#560×C113—21no—
18#553×C113—21no—
19#551×C113—21no—
20#546×C113—21no—
21#546×C113—21no—
22#546×C113—21no—
23D42×C113—21no—
24#540×C113—21no—
25#539×C113—21no—
26#539×C113C2211yescharacteristic
27#538×C113—21no—
28#538×C113C2211yescharacteristic
29#537×C113C2211yescharacteristic
30#534×C113—21no—
31#534×C113C2211yescharacteristic
32#525×C113C2211yescharacteristic
33C2×#123×C113C2211yescharacteristic
34C2×C22⋊Q8×C113C2211yescharacteristic, complemented
35C2×#121×C113C2211yescharacteristic
36#485×C113—21no—
37#484×C113C2211yescharacteristic, complemented
38#483×C113—21no—
39#481×C113C2211yescharacteristic
40#481×C113C2211yescharacteristic, complemented
41#481×C113C2211yescharacteristic, complemented
42#470×C113—21no—
43#468×C113—21no—
44#465×C113—21no—
45#465×C113—21no—
46#452×C113—21no—
47#451×C113C2211yescharacteristic, complemented
48#450×C113—21no—
49#448×C113C2211yescharacteristic
50#448×C113C2211yescharacteristic, complemented
51#448×C113C2211yescharacteristic, complemented
52#407×C113C2211yescharacteristic, complemented
53C2×C22⋊C8×C113C2211yescharacteristic, complemented
54#400×C113C2211yescharacteristic, complemented
55#399×C113C2211yescharacteristic, complemented
56#397×C113—21no—
57#395×C113C2211yescharacteristic, complemented
58#394×C113—21no—
59#393×C113C2211yescharacteristic, complemented
60#389×C113—21no—
61#388×C113—21no—
62C4×C22⋊C4×C113C2211yescharacteristic, complemented
63#328×C113C2211yescharacteristic, complemented
64#328×C113C2211yescharacteristic, complemented
65#327×C113C2211yescharacteristic
66#327×C113C2211yescharacteristic
67#327×C113C2211yescharacteristic, complemented
68#327×C113C2211yescharacteristic, complemented
69#327×C113C2211yescharacteristic, complemented
70#327×C113C2211yescharacteristic, complemented
71#324×C113C2211yescharacteristic, complemented
72#324×C113C2211yescharacteristic, complemented
73#323×C113C2211yescharacteristic, complemented
74#323×C113C2211yescharacteristic, complemented
75C2×#41×C113—21no—
76C2×#41×C113D411yescharacteristic
77C22×Q8×C113C2311yescharacteristic
78C22×D4×C113—21no—
79C22×D4×C113—21no—
80C22×D4×C113—21no—
81C22×D4×C113D411yescharacteristic
82C22×D4×C113D411yescharacteristic
83C23×C4×C113C2311yescharacteristic
84C2×Q16×C113—21no—
85C2×SD16×C113—21no—
86C2×SD16×C113—21no—
87C2×SD16×C113—21no—
88C2×M16×C113—21no—
89C22×C8×C113—21no—
90#127×C113—21no—
91#126×C113—21no—
92#126×C113—21no—
93#126×C113—21no—
94#126×C113—21no—
95#125×C113—21no—
96#125×C113—21no—
97#124×C113—21no—
98#124×C113—21no—
99#124×C113—21no—
100#123×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—
114C22⋊Q8×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×C113D411yescharacteristic
124C22⋊Q8×C113C2311yescharacteristic
125#121×C113—21no—
126#121×C113—21no—
127#121×C113—21no—
128#121×C113—21no—
129#121×C113—21no—
130#121×C113—21no—
131#121×C113—21no—
132#121×C113—21no—
133#121×C113—21no—
134#121×C113—21no—
135#121×C113—21no—
136#121×C113—21no—
137#121×C113—21no—
138#121×C113—21no—
139#121×C113—21no—
140#121×C113D411yescharacteristic
141#121×C113D411yescharacteristic
142#121×C113D411yescharacteristic
143#121×C113C2311yescharacteristic
144#121×C113C2311yescharacteristic
145#121×C113C2311yescharacteristic
146#120×C113—21no—
147#120×C113—21no—
148#120×C113—21no—
149#120×C113—21no—
150#120×C113—21no—
151#120×C113—21no—
152#120×C113—21no—
153#120×C113—21no—
154C4×D4×C113—21no—
155C4×D4×C113—21no—
156C4×D4×C113—21no—
157C4×D4×C113—21no—
158C4×D4×C113—21no—
159C4×D4×C113—21no—
160C4×D4×C113—21no—
161C4×D4×C113—21no—
162#117×C113—21no—
163#117×C113D411yescharacteristic
164C2×C4⋊C4×C113—21no—
165C2×C4⋊C4×C113—21no—
166C2×C4⋊C4×C113—21no—
167C2×C4⋊C4×C113D411yescharacteristic
168C2×C4⋊C4×C113D411yescharacteristic
169C2×C4⋊C4×C113C2311yescharacteristic
170C2×C4⋊C4×C113C2311yescharacteristic
171C2×C22⋊C4×C113—21no—
172C2×C22⋊C4×C113—21no—
173C2×C22⋊C4×C113—21no—
174C2×C22⋊C4×C113—21no—
175C2×C22⋊C4×C113—21no—
176C2×C22⋊C4×C113—21no—
177C2×C22⋊C4×C113—21no—
178C2×C22⋊C4×C113D411yescharacteristic
179C2×C22⋊C4×C113D411yescharacteristic
180C2×C22⋊C4×C113C2311yescharacteristic
181C2×C42×C113—21no—
182#107×C113—21no—
183#106×C113—21no—
184#106×C113—21no—
185#106×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—
193#102×C113—21no—
194C22⋊C8×C113—21no—
195C22⋊C8×C113—21no—
196C22⋊C8×C113C2311yescharacteristic
197C22⋊C8×C113C2311yescharacteristic
198C22⋊C8×C113C2311yescharacteristic
199C22⋊C8×C113C2311yescharacteristic
200#95×C113—21no—
201#95×C113—21no—
202#95×C113—21no—
203#95×C113—21no—
204#95×C113C2311yescharacteristic
205#95×C113C2311yescharacteristic
206C24×C113—21no—
207C24×C113—21no—
208C24×C113C2×D411yescharacteristic
209C24×C113C2×D411yescharacteristic
210#41×C113—81no—
211#41×C113—81no—
212#41×C113—81no—
213C2×Q8×C113—21no—
214C2×Q8×C113—21no—
215C2×Q8×C113—21no—
216C2×Q8×C113—81no—
217C2×Q8×C113C2×D411yescharacteristic
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—21no—
225C2×D4×C113—21no—
226C2×D4×C113—21no—
227C2×D4×C113—21no—
228C2×D4×C113—21no—
229C2×D4×C113—21no—
230C2×D4×C113—21no—
231C2×D4×C113—21no—
232C2×D4×C113—21no—
233C2×D4×C113—21no—
234C2×D4×C113—21no—
235C2×D4×C113—81no—
236C2×D4×C113—81no—
237C2×D4×C113—81no—
238C2×D4×C113—81no—
239C2×D4×C113—81no—
240C2×D4×C113—81no—
241C2×D4×C113—82no—
242C2×D4×C113C2×D411yescharacteristic
243C2×D4×C113C2×D411yescharacteristic
244C2×D4×C113C2×D411yescharacteristic
245C22×C4×C113—21no—
246C22×C4×C113—21no—
247C22×C4×C113—21no—
248C22×C4×C113—21no—
249C22×C4×C113—21no—
250C22×C4×C113—21no—
251C22×C4×C113—21no—
252C22×C4×C113—21no—
253C22×C4×C113—21no—
254C22×C4×C113—21no—
255C22×C4×C113—21no—
256C22×C4×C113—81no—
257C22×C4×C113C2×D411yescharacteristic
258C22×C4×C113C2×D411yescharacteristic
259C22×C4×C113C2×D411yescharacteristic
260C22×C4×C113C2×D411yescharacteristic
261C22×C4×C113C2×D411yescharacteristic
262C22×C4×C113C2×D411yescharacteristic
263C22×C4×C113C2×D411yescharacteristic
264C22×C4×C113C2×D411yescharacteristic
265C22×C4×C113C2411yescharacteristic
266Q16×C113—81no—
267SD16×C113—81no—
268SD16×C113—81no—
269SD16×C113—81no—
270M16×C113—81no—
271C2×C8×C113—21no—
272C2×C8×C113—21no—
273C2×C8×C113—21no—
274C2×C8×C113—21no—
275C2×C8×C113—81no—
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—21no—
284C4⋊C4×C113—21no—
285C4⋊C4×C113—21no—
286C4⋊C4×C113—21no—
287C4⋊C4×C113—21no—
288C4⋊C4×C113—21no—
289C4⋊C4×C113—21no—
290C4⋊C4×C113—21no—
291C4⋊C4×C113—42no—
292C4⋊C4×C113—41no—
293C4⋊C4×C113—41no—
294C4⋊C4×C113—81no—
295C4⋊C4×C113C2×D411yescharacteristic
296C4⋊C4×C113C2×D411yescharacteristic
297C4⋊C4×C113C2×D411yescharacteristic
298C4⋊C4×C113C2×D411yescharacteristic
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—21no—
313C22⋊C4×C113—21no—
314C22⋊C4×C113—21no—
315C22⋊C4×C113—21no—
316C22⋊C4×C113—21no—
317C22⋊C4×C113—21no—
318C22⋊C4×C113—21no—
319C22⋊C4×C113—21no—
320C22⋊C4×C113—21no—
321C22⋊C4×C113—21no—
322C22⋊C4×C113—21no—
323C22⋊C4×C113—21no—
324C22⋊C4×C113—42no—
325C22⋊C4×C113—42no—
326C22⋊C4×C113—41no—
327C22⋊C4×C113—41no—
328C22⋊C4×C113—81no—
329C42×C113—21no—
330C42×C113—21no—
331C42×C113—21no—
332C42×C113—81no—
333C23×C113—21no—
334C23×C113—21no—
335C23×C113—21no—
336C23×C113—21no—
337C23×C113—21no—
338C23×C113—21no—
339C23×C113—21no—
340C23×C113—21no—
341C23×C113—41no—
342C23×C113—41no—
343C23×C113—42no—
344C23×C113—41no—
345C23×C113—41no—
346C23×C113—81no—
347C23×C113—81no—
348C23×C113—81no—
349C23×C113—81no—
350C23×C113—81no—
351C23×C113#12011yescharacteristic
352C23×C113#12011yescharacteristic
353C23×C113C22×D411yescharacteristic
354Q8×C113—41no—
355Q8×C113—41no—
356Q8×C113—41no—
357Q8×C113—41no—
358Q8×C113—41no—
359Q8×C113—81no—
360D4×C113—41no—
361D4×C113—41no—
362D4×C113—41no—
363D4×C113—42no—
364D4×C113—42no—
365D4×C113—41no—
366D4×C113—41no—
367D4×C113—41no—
368D4×C113—41no—
369D4×C113—41no—
370D4×C113—41no—
371D4×C113—81no—
372D4×C113—81no—
373D4×C113—81no—
374D4×C113—81no—
375D4×C113—81no—
376D4×C113—81no—
377D4×C113—81no—
378D4×C113—81no—
379D4×C113—81no—
380D4×C113—81no—
381D4×C113—81no—
382D4×C113—81no—
383C2×C4×C113—22no—
384C2×C4×C113—21no—
385C2×C4×C113—21no—
386C2×C4×C113—21no—
387C2×C4×C113—21no—
388C2×C4×C113—21no—
389C2×C4×C113—21no—
390C2×C4×C113—21no—
391C2×C4×C113—21no—
392C2×C4×C113—21no—
393C2×C4×C113—21no—
394C2×C4×C113—41no—
395C2×C4×C113—41no—
396C2×C4×C113—41no—
397C2×C4×C113—41no—
398C2×C4×C113—41no—
399C2×C4×C113—41no—
400C2×C4×C113—41no—
401C2×C4×C113—41no—
402C2×C4×C113—41no—
403C2×C4×C113—41no—
404C2×C4×C113—41no—
405C2×C4×C113—41no—
406C2×C4×C113—41no—
407C2×C4×C113—41no—
408C2×C4×C113—41no—
409C2×C4×C113—41no—
410C2×C4×C113—41no—
411C2×C4×C113—41no—
412C2×C4×C113—41no—
413C2×C4×C113—81no—
414C2×C4×C113—81no—
415C2×C4×C113—81no—
416C2×C4×C113—81no—
417C2×C4×C113—81no—
418C2×C4×C113—81no—
419C2×C4×C113—81no—
420C2×C4×C113#12011yescharacteristic
421C2×C4×C113#12011yescharacteristic
422C2×C4×C113C22×D411yescharacteristic
423C2×C4×C113C22×D411yescharacteristic
424C8×C113—41no—
425C8×C113—41no—
426C8×C113—41no—
427C8×C113—41no—
428C22×C113—21no—
429C22×C113—21no—
430C22×C113—21no—
431C22×C113—21no—
432C22×C113—21no—
433C22×C113—21no—
434C22×C113—21no—
435C22×C113—21no—
436C22×C113—41no—
437C22×C113—41no—
438C22×C113—41no—
439C22×C113—41no—
440C22×C113—41no—
441C22×C113—41no—
442C22×C113—41no—
443C22×C113—41no—
444C22×C113—41no—
445C22×C113—41no—
446C22×C113—41no—
447C22×C113—41no—
448C22×C113—81no—
449C22×C113—81no—
450C22×C113—81no—
451C22×C113—81no—
452C22×C113—162no—
453C22×C113—162no—
454C22×C113C2×#12011yescharacteristic
455C22×C113#57711yescharacteristic
456C22×C113#57711yescharacteristic
457C4×C113—21no—
458C4×C113—21no—
459C4×C113—21no—
460C4×C113—21no—
461C4×C113—42no—
462C4×C113—41no—
463C4×C113—41no—
464C4×C113—41no—
465C4×C113—41no—
466C4×C113—41no—
467C4×C113—41no—
468C4×C113—41no—
469C4×C113—41no—
470C4×C113—81no—
471C4×C113—81no—
472C4×C113—81no—
473#18415C11311yesmaximal, characteristic, direct product factor, Sylow
474C2×C113—21no—
475C2×C113—21no—
476C2×C113—41no—
477C2×C113—41no—
478C2×C113—81no—
479C2×C113—81no—
480C2×C113—81no—
481C2×C113—81no—
482C2×C113#300911yescharacteristic
483C2×C113#301811yescharacteristic
484C2×C113#302611yescharacteristic
485#3534C2×C11311yescharacteristic
486#3196C2×C11311yescharacteristic, complemented
487#3187C2×C11311yescharacteristic, complemented
488#2663C2×C11311yescharacteristic, complemented
489#1618C2×C11311yescharacteristic, complemented
490#1616C2×C11311yescharacteristic, complemented
491#1615C2×C11311yescharacteristic, complemented
492#1613C2×C11311yescharacteristic, complemented
493#1606C2×C11311yescharacteristic, complemented
494#1604C2×C11311yescharacteristic, complemented
495#1603C2×C11311yescharacteristic, complemented
496#1601C2×C11311yescharacteristic, complemented
497#1507C2×C11311yescharacteristic, complemented
498#1501C2×C11311yescharacteristic, complemented
499#1468C2×C11311yescharacteristic, complemented
500C113#1841511yescharacteristic, direct product factor, Sylow
501#562—21no—
502#560—21no—
503#553—21no—
504#551—21no—
505#546—21no—
506#546—21no—
507#546—21no—
508D42—21no—
509#540—21no—
510#539—21no—
511#539C22×C11311yescharacteristic
512#538—21no—
513#538C22×C11311yescharacteristic
514#537C22×C11311yescharacteristic
515#534—21no—
516#534C22×C11311yescharacteristic
517#525C22×C11311yescharacteristic
518C2×#123C22×C11311yescharacteristic
519C2×C22⋊Q8C22×C11311yescharacteristic, complemented
520C2×#121C22×C11311yescharacteristic
521#485—21no—
522#484C22×C11311yescharacteristic, complemented
523#483—21no—
524#481C22×C11311yescharacteristic
525#481C22×C11311yescharacteristic, complemented
526#481C22×C11311yescharacteristic, complemented
527#470—21no—
528#468—21no—
529#465—21no—
530#465—21no—
531#452—21no—
532#451C22×C11311yescharacteristic, complemented
533#450—21no—
534#448C22×C11311yescharacteristic
535#448C22×C11311yescharacteristic, complemented
536#448C22×C11311yescharacteristic, complemented
537#407C22×C11311yescharacteristic, complemented
538C2×C22⋊C8C22×C11311yescharacteristic, complemented
539#400C22×C11311yescharacteristic, complemented
540#399C22×C11311yescharacteristic, complemented
541#397—21no—
542#395C22×C11311yescharacteristic, complemented
543#394—21no—
544#393C22×C11311yescharacteristic, complemented
545#389—21no—
546#388—21no—
547C4×C22⋊C4C22×C11311yescharacteristic, complemented
548#328C22×C11311yescharacteristic, complemented
549#328C22×C11311yescharacteristic, complemented
550#327C22×C11311yescharacteristic
551#327C22×C11311yescharacteristic
552#327C22×C11311yescharacteristic, complemented
553#327C22×C11311yescharacteristic, complemented
554#327C22×C11311yescharacteristic, complemented
555#327C22×C11311yescharacteristic, complemented
556#324C22×C11311yescharacteristic, complemented
557#324C22×C11311yescharacteristic, complemented
558#323C22×C11311yescharacteristic, complemented
559#323C22×C11311yescharacteristic, complemented
560C2×#41—21no—
561C2×#41D4×C11311yescharacteristic
562C22×Q8C23×C11311yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C11311yescharacteristic
567C22×D4D4×C11311yescharacteristic
568C23×C4C23×C11311yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C11311yescharacteristic
609C22⋊Q8C23×C11311yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C11311yescharacteristic
626#121D4×C11311yescharacteristic
627#121D4×C11311yescharacteristic
628#121C23×C11311yescharacteristic
629#121C23×C11311yescharacteristic
630#121C23×C11311yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C11311yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C11311yescharacteristic
653C2×C4⋊C4D4×C11311yescharacteristic
654C2×C4⋊C4C23×C11311yescharacteristic
655C2×C4⋊C4C23×C11311yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C11311yescharacteristic
664C2×C22⋊C4D4×C11311yescharacteristic
665C2×C22⋊C4C23×C11311yescharacteristic
666C2×C42—21no—
667#107—21no—
668#106—21no—
669#106—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C11311yescharacteristic
682C22⋊C8C23×C11311yescharacteristic
683C22⋊C8C23×C11311yescharacteristic
684C22⋊C8C23×C11311yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C11311yescharacteristic
690#95C23×C11311yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C11311yescharacteristic
694C24C2×D4×C11311yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C11311yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C11311yescharacteristic
728C2×D4C2×D4×C11311yescharacteristic
729C2×D4C2×D4×C11311yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C11311yescharacteristic
743C22×C4C2×D4×C11311yescharacteristic
744C22×C4C2×D4×C11311yescharacteristic
745C22×C4C2×D4×C11311yescharacteristic
746C22×C4C2×D4×C11311yescharacteristic
747C22×C4C2×D4×C11311yescharacteristic
748C22×C4C2×D4×C11311yescharacteristic
749C22×C4C2×D4×C11311yescharacteristic
750C22×C4C24×C11311yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C11311yescharacteristic
781C4⋊C4C2×D4×C11311yescharacteristic
782C4⋊C4C2×D4×C11311yescharacteristic
783C4⋊C4C2×D4×C11311yescharacteristic
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C11311yescharacteristic
837C23#120×C11311yescharacteristic
838C23C22×D4×C11311yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C11311yescharacteristic
906C2×C4#120×C11311yescharacteristic
907C2×C4C22×D4×C11311yescharacteristic
908C2×C4C22×D4×C11311yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C11311yescharacteristic
940C22#577×C11311yescharacteristic
941C22#577×C11311yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C113×#300911yescharacteristic
967C2C113×#301811yescharacteristic
968C2C113×#302611yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#3534C2
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×#3196C2semidirect
3. C113×#3187C2semidirect
4. C113×#2663C2semidirect
5. C113×#1618C2semidirect
6. C113×#1616C2semidirect
7. C113×#1615C2semidirect
8. C113×#1613C2semidirect
9. C113×#1606C2semidirect
10. C113×#1604C2semidirect
11. C113×#1603C2semidirect
12. C113×#1601C2semidirect
13. C113×#1507C2semidirect
14. C113×#1501C2semidirect
15. C113×#1468C2semidirect
34. C2×C22⋊Q8×C113C22semidirect
37. #484×C113C22semidirect
40. #481×C113C22semidirect
41. #481×C113C22semidirect
47. #451×C113C22semidirect
50. #448×C113C22semidirect
51. #448×C113C22semidirect
52. #407×C113C22semidirect
53. C2×C22⋊C8×C113C22semidirect
54. #400×C113C22semidirect
55. #399×C113C22semidirect
57. #395×C113C22semidirect
59. #393×C113C22semidirect
62. C4×C22⋊C4×C113C22semidirect
63. #328×C113C22semidirect
64. #328×C113C22semidirect
67. #327×C113C22semidirect
68. #327×C113C22semidirect
69. #327×C113C22semidirect
70. #327×C113C22semidirect
71. #324×C113C22semidirect
72. #324×C113C22semidirect
73. #323×C113C22semidirect
74. #323×C113C22semidirect
473. #18415C113direct (N × H)
486. #3196C2×C113semidirect
487. #3187C2×C113semidirect
488. #2663C2×C113semidirect
489. #1618C2×C113semidirect
490. #1616C2×C113semidirect
491. #1615C2×C113semidirect
492. #1613C2×C113semidirect
493. #1606C2×C113semidirect
494. #1604C2×C113semidirect
495. #1603C2×C113semidirect
496. #1601C2×C113semidirect
497. #1507C2×C113semidirect
498. #1501C2×C113semidirect
499. #1468C2×C113semidirect
500. C113#18415direct (N × H)
519. C2×C22⋊Q8C22×C113semidirect
522. #484C22×C113semidirect
525. #481C22×C113semidirect
526. #481C22×C113semidirect
532. #451C22×C113semidirect
535. #448C22×C113semidirect
536. #448C22×C113semidirect
537. #407C22×C113semidirect
538. C2×C22⋊C8C22×C113semidirect
539. #400C22×C113semidirect
540. #399C22×C113semidirect
542. #395C22×C113semidirect
544. #393C22×C113semidirect
547. C4×C22⋊C4C22×C113semidirect
548. #328C22×C113semidirect
549. #328C22×C113semidirect
552. #327C22×C113semidirect
553. #327C22×C113semidirect
554. #327C22×C113semidirect
555. #327C22×C113semidirect
556. #324C22×C113semidirect
557. #324C22×C113semidirect
558. #323C22×C113semidirect
559. #323C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35342
C113×#31962
C113×#31872
C113×#26632
C113×#16182
C113×#16162
C113×#16152
C113×#16132
C113×#16062
C113×#16042
C113×#16032
C113×#16012
C113×#15072
C113×#15012
C113×#14682
#18415113