Finite Group Databasebeta

← C113×#18416 #43286436

Subgroups — C113×#18416 #43286436

Order 28928.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3535C211yesmaximal, characteristic, complemented
2C113×#3194C211yesmaximal, characteristic, complemented
3C113×#3187C211yesmaximal, characteristic, complemented
4C113×#2661C211yesmaximal, characteristic, complemented
5C113×#1612C211yesmaximal, characteristic, complemented
6C113×#1611C211yesmaximal, characteristic, complemented
7C113×#1609C211yesmaximal, characteristic, complemented
8C113×#1608C211yesmaximal, characteristic, complemented
9C113×#1600C211yesmaximal, characteristic, complemented
10C113×#1599C211yesmaximal, characteristic, complemented
11C113×#1597C211yesmaximal, characteristic, complemented
12C113×#1596C211yesmaximal, characteristic, complemented
13C113×#1508C211yesmaximal, characteristic, complemented
14C113×#1501C211yesmaximal, 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×#121×C113C2211yescharacteristic
36#483×C113C2211yescharacteristic
37#483×C113C2211yescharacteristic
38#483×C113C2211yescharacteristic
39#482×C113—21no—
40#481×C113—21no—
41#480×C113C2211yescharacteristic
42#469×C113—21no—
43#468×C113—21no—
44#465×C113—21no—
45#465×C113—21no—
46#450×C113C2211yescharacteristic
47#450×C113C2211yescharacteristic
48#450×C113C2211yescharacteristic
49#449×C113—21no—
50#448×C113—21no—
51#447×C113C2211yescharacteristic
52#407×C113C2211yescharacteristic
53C2×C22⋊C8×C113C2211yescharacteristic
54#398×C113C2211yescharacteristic
55#397×C113C2211yescharacteristic
56#394×C113—21no—
57#394×C113C2211yescharacteristic
58#392×C113—21no—
59#392×C113C2211yescharacteristic
60#390×C113—21no—
61#388×C113—21no—
62C4×C22⋊C4×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, complemented
77C22×Q8×C113D411yescharacteristic, complemented
78C22×D4×C113—21no—
79C22×D4×C113—21no—
80C22×D4×C113D411yescharacteristic
81C22×D4×C113C2311yescharacteristic
82C23×C4×C113C2311yescharacteristic
83C2×SD16×C113—21no—
84C2×SD16×C113—21no—
85C2×SD16×C113—21no—
86C2×D8×C113—21no—
87C2×M16×C113—21no—
88C22×C8×C113—21no—
89C4⋊Q8×C113—21no—
90C4⋊Q8×C113—21no—
91C4⋊Q8×C113—21no—
92#126×C113—21no—
93#126×C113—21no—
94#126×C113—21no—
95#126×C113—21no—
96#126×C113—21no—
97#126×C113—21no—
98#125×C113—21no—
99#125×C113—21no—
100#125×C113—21no—
101#125×C113—21no—
102#125×C113—21no—
103#124×C113—21no—
104#124×C113—21no—
105#124×C113—21no—
106#124×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—
115#123×C113—21no—
116#123×C113—21no—
117#123×C113—21no—
118#123×C113—21no—
119#123×C113—21no—
120#123×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×C113—21no—
130C22⋊Q8×C113—21no—
131C22⋊Q8×C113—21no—
132C22⋊Q8×C113—21no—
133C22⋊Q8×C113—21no—
134C22⋊Q8×C113—21no—
135C22⋊Q8×C113D411yescharacteristic, complemented
136C22⋊Q8×C113D411yescharacteristic, complemented
137C22⋊Q8×C113D411yescharacteristic, complemented
138C22⋊Q8×C113C2311yescharacteristic
139C22⋊Q8×C113C2311yescharacteristic
140C22⋊Q8×C113C2311yescharacteristic
141#121×C113—21no—
142#121×C113—21no—
143#121×C113—21no—
144#121×C113—21no—
145#121×C113—21no—
146#121×C113—21no—
147#121×C113—21no—
148#121×C113—21no—
149#121×C113D411yescharacteristic, complemented
150#121×C113C2311yescharacteristic
151#120×C113—21no—
152#120×C113—21no—
153C4×Q8×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—
161#117×C113—21no—
162#117×C113—21no—
163#117×C113—21no—
164#117×C113D411yescharacteristic, complemented
165C2×C4⋊C4×C113—21no—
166C2×C4⋊C4×C113—21no—
167C2×C4⋊C4×C113—21no—
168C2×C4⋊C4×C113D411yescharacteristic
169C2×C4⋊C4×C113D411yescharacteristic, complemented
170C2×C4⋊C4×C113C2311yescharacteristic
171C2×C4⋊C4×C113C2311yescharacteristic
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×C113—21no—
179C2×C22⋊C4×C113—21no—
180C2×C22⋊C4×C113D411yescharacteristic
181C2×C22⋊C4×C113D411yescharacteristic
182C2×C22⋊C4×C113C2311yescharacteristic
183C2×C42×C113—21no—
184#107×C113—21no—
185#106×C113—21no—
186#106×C113—21no—
187#106×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—
194#102×C113—21no—
195#102×C113—21no—
196C22⋊C8×C113—21no—
197C22⋊C8×C113—21no—
198C22⋊C8×C113C2311yescharacteristic
199C22⋊C8×C113C2311yescharacteristic
200C22⋊C8×C113C2311yescharacteristic
201C22⋊C8×C113C2311yescharacteristic
202#95×C113—21no—
203#95×C113—21no—
204#95×C113C2311yescharacteristic
205#95×C113C2311yescharacteristic
206C24×C113—21no—
207C24×C113C2×D411yescharacteristic
208C24×C113C2×D411yescharacteristic
209#41×C113—82no—
210#41×C113—81no—
211C2×Q8×C113—21no—
212C2×Q8×C113—21no—
213C2×Q8×C113—21no—
214C2×Q8×C113—81no—
215C2×Q8×C113C2×D411yescharacteristic
216C2×Q8×C113C2×D411yescharacteristic
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—42no—
228C2×D4×C113—41no—
229C2×D4×C113—41no—
230C2×D4×C113—81no—
231C2×D4×C113—81no—
232C2×D4×C113—81no—
233C2×D4×C113—81no—
234C2×D4×C113—81no—
235C2×D4×C113—81no—
236C2×D4×C113C2×D411yescharacteristic
237C22×C4×C113—21no—
238C22×C4×C113—21no—
239C22×C4×C113—21no—
240C22×C4×C113—21no—
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—81no—
248C22×C4×C113C2×D411yescharacteristic
249C22×C4×C113C2×D411yescharacteristic
250C22×C4×C113C2×D411yescharacteristic
251C22×C4×C113C2×D411yescharacteristic
252C22×C4×C113C2×D411yescharacteristic
253C22×C4×C113C2×D411yescharacteristic
254C22×C4×C113C2×D411yescharacteristic
255C22×C4×C113C2×D411yescharacteristic
256C22×C4×C113C2411yescharacteristic
257SD16×C113—81no—
258SD16×C113—81no—
259SD16×C113—81no—
260D8×C113—81no—
261M16×C113—81no—
262C2×C8×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113—81no—
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—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—21no—
292C4⋊C4×C113—81no—
293C4⋊C4×C113C2×D411yescharacteristic
294C4⋊C4×C113C2×D411yescharacteristic
295C4⋊C4×C113C2×D411yescharacteristic
296C4⋊C4×C113C2×D411yescharacteristic
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—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—42no—
321C22⋊C4×C113—42no—
322C22⋊C4×C113—41no—
323C22⋊C4×C113—41no—
324C22⋊C4×C113—81no—
325C22⋊C4×C113—81no—
326C22⋊C4×C113—81no—
327C42×C113—21no—
328C42×C113—21no—
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—41no—
340C23×C113—41no—
341C23×C113—41no—
342C23×C113—41no—
343C23×C113—41no—
344C23×C113—41no—
345C23×C113—41no—
346C23×C113—41no—
347C23×C113—41no—
348C23×C113—41no—
349C23×C113—41no—
350C23×C113#12011yescharacteristic
351C23×C113#12011yescharacteristic
352C23×C113C22×D411yescharacteristic
353Q8×C113—41no—
354Q8×C113—41no—
355Q8×C113—41no—
356Q8×C113—81no—
357Q8×C113—81no—
358Q8×C113—81no—
359D4×C113—41no—
360D4×C113—41no—
361D4×C113—41no—
362D4×C113—41no—
363D4×C113—41no—
364D4×C113—42no—
365D4×C113—42no—
366D4×C113—41no—
367D4×C113—41no—
368D4×C113—81no—
369D4×C113—81no—
370D4×C113—81no—
371D4×C113—81no—
372D4×C113—84no—
373D4×C113—82no—
374D4×C113—82no—
375C2×C4×C113—22no—
376C2×C4×C113—21no—
377C2×C4×C113—21no—
378C2×C4×C113—21no—
379C2×C4×C113—21no—
380C2×C4×C113—21no—
381C2×C4×C113—21no—
382C2×C4×C113—21no—
383C2×C4×C113—21no—
384C2×C4×C113—21no—
385C2×C4×C113—21no—
386C2×C4×C113—21no—
387C2×C4×C113—21no—
388C2×C4×C113—41no—
389C2×C4×C113—41no—
390C2×C4×C113—41no—
391C2×C4×C113—41no—
392C2×C4×C113—41no—
393C2×C4×C113—41no—
394C2×C4×C113—41no—
395C2×C4×C113—42no—
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—81no—
406C2×C4×C113—81no—
407C2×C4×C113—81no—
408C2×C4×C113—81no—
409C2×C4×C113—81no—
410C2×C4×C113—81no—
411C2×C4×C113#12011yescharacteristic
412C2×C4×C113#12011yescharacteristic
413C2×C4×C113C22×D411yescharacteristic
414C2×C4×C113C22×D411yescharacteristic
415C8×C113—41no—
416C8×C113—41no—
417C8×C113—41no—
418C8×C113—41no—
419C22×C113—21no—
420C22×C113—21no—
421C22×C113—21no—
422C22×C113—21no—
423C22×C113—21no—
424C22×C113—21no—
425C22×C113—21no—
426C22×C113—21no—
427C22×C113—41no—
428C22×C113—41no—
429C22×C113—41no—
430C22×C113—41no—
431C22×C113—41no—
432C22×C113—41no—
433C22×C113—81no—
434C22×C113—81no—
435C22×C113—81no—
436C22×C113—81no—
437C22×C113—81no—
438C22×C113—81no—
439C22×C113—81no—
440C22×C113—81no—
441C22×C113—81no—
442C22×C113—81no—
443C22×C113—81no—
444C22×C113C2×#12011yescharacteristic
445C22×C113#57711yescharacteristic
446C22×C113#57711yescharacteristic
447C4×C113—21no—
448C4×C113—21no—
449C4×C113—21no—
450C4×C113—21no—
451C4×C113—42no—
452C4×C113—41no—
453C4×C113—41no—
454C4×C113—41no—
455C4×C113—41no—
456C4×C113—41no—
457C4×C113—41no—
458C4×C113—41no—
459C4×C113—41no—
460C4×C113—41no—
461C4×C113—41no—
462C4×C113—81no—
463C4×C113—81no—
464#18416C11311yesmaximal, characteristic, direct product factor, Sylow
465C2×C113—21no—
466C2×C113—21no—
467C2×C113—41no—
468C2×C113—41no—
469C2×C113—81no—
470C2×C113—81no—
471C2×C113—161no—
472C2×C113#301011yescharacteristic
473C2×C113#301811yescharacteristic
474C2×C113#302611yescharacteristic
475#3535C2×C11311yescharacteristic, complemented
476#3194C2×C11311yescharacteristic, complemented
477#3187C2×C11311yescharacteristic, complemented
478#2661C2×C11311yescharacteristic, complemented
479#1612C2×C11311yescharacteristic, complemented
480#1611C2×C11311yescharacteristic, complemented
481#1609C2×C11311yescharacteristic, complemented
482#1608C2×C11311yescharacteristic, complemented
483#1600C2×C11311yescharacteristic, complemented
484#1599C2×C11311yescharacteristic, complemented
485#1597C2×C11311yescharacteristic, complemented
486#1596C2×C11311yescharacteristic, complemented
487#1508C2×C11311yescharacteristic, complemented
488#1501C2×C11311yescharacteristic, complemented
489#1468C2×C11311yescharacteristic, complemented
490C113#1841611yescharacteristic, direct product factor, Sylow
491#563—21no—
492#562—21no—
493#554—21no—
494#552—21no—
495#551—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#544C22×C11311yescharacteristic
500#543C22×C11311yescharacteristic
501#542—21no—
502#539—21no—
503#539—21no—
504#539C22×C11311yescharacteristic
505#538C22×C11311yescharacteristic
506#536—21no—
507#525C22×C11311yescharacteristic
508C2×#123C22×C11311yescharacteristic
509C2×C22⋊Q8C22×C11311yescharacteristic
510C2×#121C22×C11311yescharacteristic
511#483C22×C11311yescharacteristic
512#483C22×C11311yescharacteristic
513#483C22×C11311yescharacteristic
514#482—21no—
515#481—21no—
516#480C22×C11311yescharacteristic
517#469—21no—
518#468—21no—
519#465—21no—
520#465—21no—
521#450C22×C11311yescharacteristic
522#450C22×C11311yescharacteristic
523#450C22×C11311yescharacteristic
524#449—21no—
525#448—21no—
526#447C22×C11311yescharacteristic
527#407C22×C11311yescharacteristic
528C2×C22⋊C8C22×C11311yescharacteristic
529#398C22×C11311yescharacteristic
530#397C22×C11311yescharacteristic
531#394—21no—
532#394C22×C11311yescharacteristic
533#392—21no—
534#392C22×C11311yescharacteristic
535#390—21no—
536#388—21no—
537C4×C22⋊C4C22×C11311yescharacteristic
538#328C22×C11311yescharacteristic
539#328C22×C11311yescharacteristic
540#328C22×C11311yescharacteristic
541#328C22×C11311yescharacteristic
542#328C22×C11311yescharacteristic
543#328C22×C11311yescharacteristic
544#327C22×C11311yescharacteristic
545#327C22×C11311yescharacteristic
546#324C22×C11311yescharacteristic
547#324C22×C11311yescharacteristic
548#323C22×C11311yescharacteristic
549#323C22×C11311yescharacteristic
550C2×#41—21no—
551C2×#41D4×C11311yescharacteristic, complemented
552C22×Q8D4×C11311yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C11311yescharacteristic
556C22×D4C23×C11311yescharacteristic
557C23×C4C23×C11311yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—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—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—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⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C11311yescharacteristic, complemented
611C22⋊Q8D4×C11311yescharacteristic, complemented
612C22⋊Q8D4×C11311yescharacteristic, complemented
613C22⋊Q8C23×C11311yescharacteristic
614C22⋊Q8C23×C11311yescharacteristic
615C22⋊Q8C23×C11311yescharacteristic
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#121D4×C11311yescharacteristic, complemented
625#121C23×C11311yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C11311yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C11311yescharacteristic
644C2×C4⋊C4D4×C11311yescharacteristic, complemented
645C2×C4⋊C4C23×C11311yescharacteristic
646C2×C4⋊C4C23×C11311yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C11311yescharacteristic
656C2×C22⋊C4D4×C11311yescharacteristic
657C2×C22⋊C4C23×C11311yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C11311yescharacteristic
674C22⋊C8C23×C11311yescharacteristic
675C22⋊C8C23×C11311yescharacteristic
676C22⋊C8C23×C11311yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C11311yescharacteristic
680#95C23×C11311yescharacteristic
681C24—21no—
682C24C2×D4×C11311yescharacteristic
683C24C2×D4×C11311yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C11311yescharacteristic
691C2×Q8C2×D4×C11311yescharacteristic
692C2×Q8C2×D4×C11311yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C11311yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C11311yescharacteristic
724C22×C4C2×D4×C11311yescharacteristic
725C22×C4C2×D4×C11311yescharacteristic
726C22×C4C2×D4×C11311yescharacteristic
727C22×C4C2×D4×C11311yescharacteristic
728C22×C4C2×D4×C11311yescharacteristic
729C22×C4C2×D4×C11311yescharacteristic
730C22×C4C2×D4×C11311yescharacteristic
731C22×C4C24×C11311yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C11311yescharacteristic
769C4⋊C4C2×D4×C11311yescharacteristic
770C4⋊C4C2×D4×C11311yescharacteristic
771C4⋊C4C2×D4×C11311yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
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—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C11311yescharacteristic
826C23#120×C11311yescharacteristic
827C23C22×D4×C11311yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C11311yescharacteristic
887C2×C4#120×C11311yescharacteristic
888C2×C4C22×D4×C11311yescharacteristic
889C2×C4C22×D4×C11311yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C11311yescharacteristic
920C22#577×C11311yescharacteristic
921C22#577×C11311yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C113×#301011yescharacteristic
947C2C113×#301811yescharacteristic
948C2C113×#302611yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
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
1. C113×#3535C2semidirect
2. C113×#3194C2semidirect
3. C113×#3187C2semidirect
4. C113×#2661C2semidirect
5. C113×#1612C2semidirect
6. C113×#1611C2semidirect
7. C113×#1609C2semidirect
8. C113×#1608C2semidirect
9. C113×#1600C2semidirect
10. C113×#1599C2semidirect
11. C113×#1597C2semidirect
12. C113×#1596C2semidirect
13. C113×#1508C2semidirect
14. C113×#1501C2semidirect
15. C113×#1468C2semidirect
76. C2×#41×C113D4semidirect
77. C22×Q8×C113D4semidirect
135. C22⋊Q8×C113D4semidirect
136. C22⋊Q8×C113D4semidirect
137. C22⋊Q8×C113D4semidirect
149. #121×C113D4semidirect
164. #117×C113D4semidirect
169. C2×C4⋊C4×C113D4semidirect
464. #18416C113direct (N × H)
475. #3535C2×C113semidirect
476. #3194C2×C113semidirect
477. #3187C2×C113semidirect
478. #2661C2×C113semidirect
479. #1612C2×C113semidirect
480. #1611C2×C113semidirect
481. #1609C2×C113semidirect
482. #1608C2×C113semidirect
483. #1600C2×C113semidirect
484. #1599C2×C113semidirect
485. #1597C2×C113semidirect
486. #1596C2×C113semidirect
487. #1508C2×C113semidirect
488. #1501C2×C113semidirect
489. #1468C2×C113semidirect
490. C113#18416direct (N × H)
551. C2×#41D4×C113semidirect
552. C22×Q8D4×C113semidirect
610. C22⋊Q8D4×C113semidirect
611. C22⋊Q8D4×C113semidirect
612. C22⋊Q8D4×C113semidirect
624. #121D4×C113semidirect
639. #117D4×C113semidirect
644. C2×C4⋊C4D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35352
C113×#31942
C113×#31872
C113×#26612
C113×#16122
C113×#16112
C113×#16092
C113×#16082
C113×#16002
C113×#15992
C113×#15972
C113×#15962
C113×#15082
C113×#15012
C113×#14682
#18416113