Finite Group Databasebeta

← C113×#18252 #43286272

Subgroups — C113×#18252 #43286272

Order 28928.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3534C211yesmaximal, characteristic, complemented
2C113×#3006C211yesmaximal, characteristic, complemented
3C113×#3002C211yesmaximal, characteristic, complemented
4C113×#2430C211yesmaximal, characteristic, complemented
5C113×#1606C211yesmaximal, characteristic, complemented
6C113×#1604C211yesmaximal, characteristic, complemented
7C113×#1603C211yesmaximal, characteristic, complemented
8C113×#1601C211yesmaximal, characteristic, complemented
9C113×#1600C211yesmaximal, characteristic, complemented
10C113×#1598C211yesmaximal, characteristic, complemented
11C113×#1597C211yesmaximal, characteristic, complemented
12C113×#1595C211yesmaximal, characteristic, complemented
13C113×#1504C211yesmaximal, characteristic, complemented
14C2×#327×C113C211yesmaximal, characteristic, complemented
15C113×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C113—21no—
18C2×#135×C113—21no—
19#562×C113—21no—
20#560×C113—21no—
21#553×C113—21no—
22#551×C113—21no—
23#546×C113—21no—
24#546×C113—21no—
25#546×C113—21no—
26D42×C113—21no—
27#540×C113—21no—
28#539×C113—21no—
29#539×C113C2211yescharacteristic
30#538×C113—21no—
31#538×C113C2211yescharacteristic
32#537×C113C2211yescharacteristic
33#534×C113—21no—
34#534×C113C2211yescharacteristic
35#525×C113C2211yescharacteristic
36C2×#123×C113C2211yescharacteristic
37C2×#121×C113—21no—
38C2×#121×C113C2211yescharacteristic
39#452×C113—21no—
40#451×C113C2211yescharacteristic, complemented
41#450×C113C2211yescharacteristic, complemented
42#449×C113—21no—
43#449×C113—21no—
44#449×C113—21no—
45#448×C113C2211yescharacteristic
46#448×C113C2211yescharacteristic, complemented
47#448×C113C2211yescharacteristic, complemented
48#447×C113C2211yescharacteristic
49#447×C113C2211yescharacteristic, complemented
50#447×C113C2211yescharacteristic, complemented
51#417×C113—21no—
52#416×C113—21no—
53#407×C113C2211yescharacteristic, complemented
54C2×C22⋊C8×C113C2211yescharacteristic, complemented
55#395×C113C2211yescharacteristic, complemented
56#394×C113C2211yescharacteristic, complemented
57#393×C113C2211yescharacteristic, complemented
58#392×C113C2211yescharacteristic, complemented
59#386×C113—21no—
60#386×C113—21no—
61#385×C113—21no—
62C2×#95×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×C113—21no—
77C2×#41×C113—21no—
78C2×#41×C113—21no—
79C2×#41×C113—21no—
80C2×#41×C113—44no—
81C2×#41×C113D411yescharacteristic, complemented
82C22×Q8×C113C2311yescharacteristic
83C22×D4×C113—21no—
84C22×D4×C113—21no—
85C22×D4×C113—21no—
86C22×D4×C113—21no—
87C22×D4×C113—21no—
88C22×D4×C113D411yescharacteristic
89C22×D4×C113D411yescharacteristic, complemented
90C22×D4×C113C2311yescharacteristic
91C23×C4×C113—21no—
92C23×C4×C113—21no—
93C23×C4×C113C2311yescharacteristic
94AGL(1,ℤ/8)×C113—44no—
95#135×C113—44no—
96C2×Q16×C113—21no—
97C2×SD16×C113—21no—
98C2×SD16×C113—21no—
99C2×SD16×C113—21no—
100C2×SD16×C113—21no—
101C2×D8×C113—21no—
102C2×D8×C113—21no—
103C2×D8×C113—21no—
104C2×M16×C113—21no—
105C22×C8×C113—21no—
106#127×C113—21no—
107#126×C113—21no—
108#126×C113—21no—
109#126×C113—21no—
110#126×C113—21no—
111#125×C113—21no—
112#125×C113—21no—
113#124×C113—21no—
114#124×C113—21no—
115#124×C113—21no—
116#123×C113—21no—
117#123×C113—21no—
118#123×C113—21no—
119#123×C113—21no—
120#123×C113—21no—
121#123×C113—21no—
122#123×C113—21no—
123#123×C113—21no—
124#123×C113—21no—
125#123×C113—21no—
126#123×C113—21no—
127#123×C113—21no—
128#123×C113—21no—
129#123×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×C113C2311yescharacteristic
137#121×C113—21no—
138#121×C113—21no—
139#121×C113—21no—
140#121×C113—21no—
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×C113—21no—
150#121×C113—21no—
151#121×C113—21no—
152#121×C113—44no—
153#121×C113D411yescharacteristic, complemented
154#121×C113D411yescharacteristic, complemented
155#121×C113D411yescharacteristic, complemented
156#121×C113C2311yescharacteristic
157#121×C113C2311yescharacteristic
158#121×C113C2311yescharacteristic
159#120×C113—21no—
160#120×C113—21no—
161#120×C113—21no—
162#120×C113—21no—
163#120×C113—21no—
164#120×C113—21no—
165#120×C113—21no—
166#120×C113—21no—
167C4×D4×C113—21no—
168C4×D4×C113—21no—
169C4×D4×C113—21no—
170C4×D4×C113—21no—
171C4×D4×C113—21no—
172C4×D4×C113—21no—
173C4×D4×C113—21no—
174C4×D4×C113—21no—
175#117×C113—21no—
176#117×C113D411yescharacteristic, complemented
177C2×C4⋊C4×C113—21no—
178C2×C4⋊C4×C113D411yescharacteristic
179C2×C4⋊C4×C113D411yescharacteristic, complemented
180C2×C4⋊C4×C113C2311yescharacteristic
181C2×C22⋊C4×C113—21no—
182C2×C22⋊C4×C113—21no—
183C2×C22⋊C4×C113—21no—
184C2×C22⋊C4×C113—21no—
185C2×C22⋊C4×C113—21no—
186C2×C22⋊C4×C113—21no—
187C2×C22⋊C4×C113—21no—
188C2×C22⋊C4×C113D411yescharacteristic
189C2×C22⋊C4×C113D411yescharacteristic
190C2×C22⋊C4×C113C2311yescharacteristic
191#103×C113—21no—
192#103×C113—21no—
193#103×C113—21no—
194#103×C113—21no—
195#102×C113—21no—
196#102×C113—21no—
197#102×C113—21no—
198#102×C113—21no—
199C22⋊C8×C113—21no—
200C22⋊C8×C113—21no—
201C22⋊C8×C113C2311yescharacteristic
202C22⋊C8×C113C2311yescharacteristic
203C22⋊C8×C113C2311yescharacteristic
204C22⋊C8×C113C2311yescharacteristic
205#95×C113—21no—
206#95×C113—21no—
207#95×C113—21no—
208#95×C113C2311yescharacteristic
209#95×C113C2311yescharacteristic
210C24×C113—21no—
211C24×C113—21no—
212C24×C113—21no—
213C24×C113C2×D411yescharacteristic
214C24×C113C2×D411yescharacteristic
215#41×C113—24no—
216#41×C113—24no—
217#41×C113—42no—
218#41×C113—42no—
219#41×C113—42no—
220#41×C113—42no—
221#41×C113—42no—
222#41×C113—42no—
223#41×C113—42no—
224#41×C113—81no—
225#41×C113—81no—
226C2×Q8×C113—21no—
227C2×Q8×C113—21no—
228C2×Q8×C113—21no—
229C2×Q8×C113—42no—
230C2×Q8×C113C2×D411yescharacteristic
231C2×D4×C113—24no—
232C2×D4×C113—21no—
233C2×D4×C113—21no—
234C2×D4×C113—21no—
235C2×D4×C113—21no—
236C2×D4×C113—21no—
237C2×D4×C113—21no—
238C2×D4×C113—21no—
239C2×D4×C113—21no—
240C2×D4×C113—21no—
241C2×D4×C113—21no—
242C2×D4×C113—21no—
243C2×D4×C113—21no—
244C2×D4×C113—21no—
245C2×D4×C113—21no—
246C2×D4×C113—21no—
247C2×D4×C113—21no—
248C2×D4×C113—21no—
249C2×D4×C113—21no—
250C2×D4×C113—21no—
251C2×D4×C113—42no—
252C2×D4×C113—42no—
253C2×D4×C113—42no—
254C2×D4×C113—42no—
255C2×D4×C113—41no—
256C2×D4×C113—41no—
257C2×D4×C113—42no—
258C2×D4×C113—42no—
259C2×D4×C113—81no—
260C2×D4×C113—81no—
261C2×D4×C113—81no—
262C2×D4×C113—81no—
263C2×D4×C113—81no—
264C2×D4×C113—82no—
265C2×D4×C113C2×D411yescharacteristic
266C2×D4×C113C2×D411yescharacteristic
267C2×D4×C113C2×D411yescharacteristic
268C22×C4×C113—21no—
269C22×C4×C113—21no—
270C22×C4×C113—21no—
271C22×C4×C113—21no—
272C22×C4×C113—21no—
273C22×C4×C113—21no—
274C22×C4×C113—21no—
275C22×C4×C113—21no—
276C22×C4×C113—21no—
277C22×C4×C113—21no—
278C22×C4×C113—42no—
279C22×C4×C113—42no—
280C22×C4×C113—42no—
281C22×C4×C113—42no—
282C22×C4×C113—41no—
283C22×C4×C113—41no—
284C22×C4×C113—42no—
285C22×C4×C113—81no—
286C22×C4×C113C2×D411yescharacteristic
287C22×C4×C113C2×D411yescharacteristic
288C22×C4×C113C2×D411yescharacteristic
289C22×C4×C113C2×D411yescharacteristic
290C22×C4×C113C2×D411yescharacteristic
291C22×C4×C113C2×D411yescharacteristic
292C22×C4×C113C2×D411yescharacteristic
293C22×C4×C113C2×D411yescharacteristic
294C22×C4×C113C2411yescharacteristic
295Q16×C113—42no—
296SD16×C113—42no—
297SD16×C113—42no—
298SD16×C113—42no—
299SD16×C113—42no—
300D8×C113—42no—
301D8×C113—42no—
302D8×C113—42no—
303M16×C113—42no—
304C2×C8×C113—21no—
305C2×C8×C113—21no—
306C2×C8×C113—21no—
307C2×C8×C113—21no—
308C2×C8×C113—42no—
309C4⋊C4×C113—21no—
310C4⋊C4×C113—21no—
311C4⋊C4×C113—21no—
312C4⋊C4×C113—21no—
313C4⋊C4×C113—21no—
314C4⋊C4×C113—21no—
315C4⋊C4×C113—21no—
316C4⋊C4×C113—21no—
317C4⋊C4×C113—21no—
318C4⋊C4×C113—21no—
319C4⋊C4×C113—21no—
320C4⋊C4×C113—21no—
321C4⋊C4×C113—21no—
322C4⋊C4×C113—42no—
323C4⋊C4×C113C2×D411yescharacteristic
324C4⋊C4×C113C2×D411yescharacteristic
325C4⋊C4×C113C2×D411yescharacteristic
326C4⋊C4×C113C2×D411yescharacteristic
327C22⋊C4×C113—21no—
328C22⋊C4×C113—21no—
329C22⋊C4×C113—21no—
330C22⋊C4×C113—21no—
331C22⋊C4×C113—21no—
332C22⋊C4×C113—21no—
333C22⋊C4×C113—21no—
334C22⋊C4×C113—21no—
335C22⋊C4×C113—21no—
336C22⋊C4×C113—21no—
337C22⋊C4×C113—21no—
338C22⋊C4×C113—21no—
339C22⋊C4×C113—21no—
340C22⋊C4×C113—21no—
341C22⋊C4×C113—21no—
342C22⋊C4×C113—21no—
343C22⋊C4×C113—21no—
344C22⋊C4×C113—21no—
345C22⋊C4×C113—21no—
346C22⋊C4×C113—21no—
347C22⋊C4×C113—21no—
348C22⋊C4×C113—21no—
349C22⋊C4×C113—21no—
350C22⋊C4×C113—21no—
351C22⋊C4×C113—21no—
352C22⋊C4×C113—42no—
353C22⋊C4×C113—42no—
354C22⋊C4×C113—42no—
355C22⋊C4×C113—81no—
356C42×C113—21no—
357C42×C113—21no—
358C42×C113—21no—
359C23×C113—21no—
360C23×C113—21no—
361C23×C113—22no—
362C23×C113—22no—
363C23×C113—21no—
364C23×C113—21no—
365C23×C113—21no—
366C23×C113—21no—
367C23×C113—21no—
368C23×C113—21no—
369C23×C113—41no—
370C23×C113—41no—
371C23×C113—41no—
372C23×C113—41no—
373C23×C113—41no—
374C23×C113—41no—
375C23×C113—41no—
376C23×C113—41no—
377C23×C113—41no—
378C23×C113—42no—
379C23×C113—81no—
380C23×C113—81no—
381C23×C113—81no—
382C23×C113—81no—
383C23×C113—81no—
384C23×C113#12011yescharacteristic
385C23×C113#12011yescharacteristic
386C23×C113C22×D411yescharacteristic
387Q8×C113—22no—
388Q8×C113—22no—
389Q8×C113—41no—
390Q8×C113—41no—
391Q8×C113—41no—
392Q8×C113—81no—
393D4×C113—22no—
394D4×C113—22no—
395D4×C113—41no—
396D4×C113—41no—
397D4×C113—41no—
398D4×C113—41no—
399D4×C113—41no—
400D4×C113—44no—
401D4×C113—41no—
402D4×C113—41no—
403D4×C113—41no—
404D4×C113—41no—
405D4×C113—41no—
406D4×C113—41no—
407D4×C113—44no—
408D4×C113—42no—
409D4×C113—42no—
410D4×C113—81no—
411D4×C113—81no—
412D4×C113—81no—
413D4×C113—81no—
414D4×C113—81no—
415D4×C113—81no—
416D4×C113—81no—
417D4×C113—81no—
418D4×C113—81no—
419D4×C113—81no—
420D4×C113—81no—
421D4×C113—81no—
422D4×C113—84no—
423C2×C4×C113—22no—
424C2×C4×C113—22no—
425C2×C4×C113—22no—
426C2×C4×C113—22no—
427C2×C4×C113—21no—
428C2×C4×C113—21no—
429C2×C4×C113—21no—
430C2×C4×C113—21no—
431C2×C4×C113—21no—
432C2×C4×C113—21no—
433C2×C4×C113—21no—
434C2×C4×C113—21no—
435C2×C4×C113—21no—
436C2×C4×C113—21no—
437C2×C4×C113—41no—
438C2×C4×C113—41no—
439C2×C4×C113—41no—
440C2×C4×C113—41no—
441C2×C4×C113—44no—
442C2×C4×C113—44no—
443C2×C4×C113—41no—
444C2×C4×C113—41no—
445C2×C4×C113—41no—
446C2×C4×C113—41no—
447C2×C4×C113—41no—
448C2×C4×C113—41no—
449C2×C4×C113—41no—
450C2×C4×C113—41no—
451C2×C4×C113—41no—
452C2×C4×C113—81no—
453C2×C4×C113—81no—
454C2×C4×C113—81no—
455C2×C4×C113—81no—
456C2×C4×C113—81no—
457C2×C4×C113—81no—
458C2×C4×C113—81no—
459C2×C4×C113—84no—
460C2×C4×C113#12011yescharacteristic
461C2×C4×C113#12011yescharacteristic
462C2×C4×C113C22×D411yescharacteristic
463C2×C4×C113C22×D411yescharacteristic
464C8×C113—41no—
465C8×C113—41no—
466C8×C113—41no—
467C8×C113—41no—
468C22×C113—21no—
469C22×C113—21no—
470C22×C113—21no—
471C22×C113—21no—
472C22×C113—21no—
473C22×C113—21no—
474C22×C113—21no—
475C22×C113—42no—
476C22×C113—42no—
477C22×C113—42no—
478C22×C113—42no—
479C22×C113—41no—
480C22×C113—41no—
481C22×C113—41no—
482C22×C113—41no—
483C22×C113—41no—
484C22×C113—41no—
485C22×C113—41no—
486C22×C113—41no—
487C22×C113—42no—
488C22×C113—41no—
489C22×C113—41no—
490C22×C113—41no—
491C22×C113—41no—
492C22×C113—81no—
493C22×C113—81no—
494C22×C113—81no—
495C22×C113—81no—
496C22×C113—81no—
497C22×C113—81no—
498C22×C113—162no—
499C22×C113—162no—
500C22×C113B(4,𝔽2)12yes—
501C22×C113C2×#12011yescharacteristic
502C22×C113#57611yescharacteristic
503C22×C113#57711yescharacteristic
504C4×C113—21no—
505C4×C113—21no—
506C4×C113—21no—
507C4×C113—21no—
508C4×C113—42no—
509C4×C113—41no—
510C4×C113—41no—
511C4×C113—41no—
512C4×C113—41no—
513C4×C113—41no—
514C4×C113—41no—
515C4×C113—42no—
516C4×C113—41no—
517C4×C113—41no—
518C4×C113—81no—
519#18252C11311yesmaximal, characteristic, direct product factor, Sylow
520C2×C113—21no—
521C2×C113—21no—
522C2×C113—22no—
523C2×C113—41no—
524C2×C113—82no—
525C2×C113—81no—
526C2×C113—81no—
527C2×C113—81no—
528C2×C113—81no—
529C2×C113#301211yescharacteristic
530C2×C113#301811yescharacteristic
531C2×C113C2×B(4,𝔽2)11yescharacteristic
532#3534C2×C11311yescharacteristic, complemented
533#3006C2×C11311yescharacteristic, complemented
534#3002C2×C11311yescharacteristic, complemented
535#2430C2×C11311yescharacteristic, complemented
536#1606C2×C11311yescharacteristic, complemented
537#1604C2×C11311yescharacteristic, complemented
538#1603C2×C11311yescharacteristic, complemented
539#1601C2×C11311yescharacteristic, complemented
540#1600C2×C11311yescharacteristic, complemented
541#1598C2×C11311yescharacteristic, complemented
542#1597C2×C11311yescharacteristic, complemented
543#1595C2×C11311yescharacteristic, complemented
544#1504C2×C11311yescharacteristic, complemented
545C2×#327C2×C11311yescharacteristic, complemented
546#1468C2×C11311yescharacteristic, complemented
547C113#1825211yescharacteristic, direct product factor, Sylow
548C22×#41C22×C11311yescharacteristic, complemented
549C2×AGL(1,ℤ/8)—21no—
550C2×#135—21no—
551#562—21no—
552#560—21no—
553#553—21no—
554#551—21no—
555#546—21no—
556#546—21no—
557#546—21no—
558D42—21no—
559#540—21no—
560#539—21no—
561#539C22×C11311yescharacteristic
562#538—21no—
563#538C22×C11311yescharacteristic
564#537C22×C11311yescharacteristic
565#534—21no—
566#534C22×C11311yescharacteristic
567#525C22×C11311yescharacteristic
568C2×#123C22×C11311yescharacteristic
569C2×#121—21no—
570C2×#121C22×C11311yescharacteristic
571#452—21no—
572#451C22×C11311yescharacteristic, complemented
573#450C22×C11311yescharacteristic, complemented
574#449—21no—
575#449—21no—
576#449—21no—
577#448C22×C11311yescharacteristic
578#448C22×C11311yescharacteristic, complemented
579#448C22×C11311yescharacteristic, complemented
580#447C22×C11311yescharacteristic
581#447C22×C11311yescharacteristic, complemented
582#447C22×C11311yescharacteristic, complemented
583#417—21no—
584#416—21no—
585#407C22×C11311yescharacteristic, complemented
586C2×C22⋊C8C22×C11311yescharacteristic, complemented
587#395C22×C11311yescharacteristic, complemented
588#394C22×C11311yescharacteristic, complemented
589#393C22×C11311yescharacteristic, complemented
590#392C22×C11311yescharacteristic, complemented
591#386—21no—
592#386—21no—
593#385—21no—
594C2×#95C22×C11311yescharacteristic, complemented
595#328C22×C11311yescharacteristic, complemented
596#328C22×C11311yescharacteristic, complemented
597#327C22×C11311yescharacteristic
598#327C22×C11311yescharacteristic
599#327C22×C11311yescharacteristic, complemented
600#327C22×C11311yescharacteristic, complemented
601#327C22×C11311yescharacteristic, complemented
602#327C22×C11311yescharacteristic, complemented
603#324C22×C11311yescharacteristic, complemented
604#324C22×C11311yescharacteristic, complemented
605#323C22×C11311yescharacteristic, complemented
606#323C22×C11311yescharacteristic, complemented
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C11311yescharacteristic, complemented
614C22×Q8C23×C11311yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C11311yescharacteristic
621C22×D4D4×C11311yescharacteristic, complemented
622C22×D4C23×C11311yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C11311yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C11311yescharacteristic, complemented
668C22⋊Q8C23×C11311yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C11311yescharacteristic, complemented
686#121D4×C11311yescharacteristic, complemented
687#121D4×C11311yescharacteristic, complemented
688#121C23×C11311yescharacteristic
689#121C23×C11311yescharacteristic
690#121C23×C11311yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C11311yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C11311yescharacteristic
711C2×C4⋊C4D4×C11311yescharacteristic, complemented
712C2×C4⋊C4C23×C11311yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C11311yescharacteristic
721C2×C22⋊C4D4×C11311yescharacteristic
722C2×C22⋊C4C23×C11311yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C11311yescharacteristic
734C22⋊C8C23×C11311yescharacteristic
735C22⋊C8C23×C11311yescharacteristic
736C22⋊C8C23×C11311yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C11311yescharacteristic
741#95C23×C11311yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C11311yescharacteristic
746C24C2×D4×C11311yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C11311yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C11311yescharacteristic
798C2×D4C2×D4×C11311yescharacteristic
799C2×D4C2×D4×C11311yescharacteristic
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—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C11311yescharacteristic
819C22×C4C2×D4×C11311yescharacteristic
820C22×C4C2×D4×C11311yescharacteristic
821C22×C4C2×D4×C11311yescharacteristic
822C22×C4C2×D4×C11311yescharacteristic
823C22×C4C2×D4×C11311yescharacteristic
824C22×C4C2×D4×C11311yescharacteristic
825C22×C4C2×D4×C11311yescharacteristic
826C22×C4C24×C11311yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C11311yescharacteristic
856C4⋊C4C2×D4×C11311yescharacteristic
857C4⋊C4C2×D4×C11311yescharacteristic
858C4⋊C4C2×D4×C11311yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C11311yescharacteristic
917C23#120×C11311yescharacteristic
918C23C22×D4×C11311yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—44no—
940D4—42no—
941D4—42no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C11311yescharacteristic
993C2×C4#120×C11311yescharacteristic
994C2×C4C22×D4×C11311yescharacteristic
995C2×C4C22×D4×C11311yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22B(4,𝔽2)×C11312yes—
1033C22C2×#120×C11311yescharacteristic
1034C22#576×C11311yescharacteristic
1035C22#577×C11311yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C113×#301211yescharacteristic
1061C2C113×#301811yescharacteristic
1062C2C2×B(4,𝔽2)×C11311yescharacteristic
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×#3534C2semidirect
2. C113×#3006C2semidirect
3. C113×#3002C2semidirect
4. C113×#2430C2semidirect
5. C113×#1606C2semidirect
6. C113×#1604C2semidirect
7. C113×#1603C2semidirect
8. C113×#1601C2semidirect
9. C113×#1600C2semidirect
10. C113×#1598C2semidirect
11. C113×#1597C2semidirect
12. C113×#1595C2semidirect
13. C113×#1504C2semidirect
14. C2×#327×C113C2semidirect
15. C113×#1468C2semidirect
16. C22×#41×C113C22semidirect
40. #451×C113C22semidirect
41. #450×C113C22semidirect
46. #448×C113C22semidirect
47. #448×C113C22semidirect
49. #447×C113C22semidirect
50. #447×C113C22semidirect
53. #407×C113C22semidirect
54. C2×C22⋊C8×C113C22semidirect
55. #395×C113C22semidirect
56. #394×C113C22semidirect
57. #393×C113C22semidirect
58. #392×C113C22semidirect
62. C2×#95×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
81. C2×#41×C113D4semidirect
89. C22×D4×C113D4semidirect
135. C22⋊Q8×C113D4semidirect
153. #121×C113D4semidirect
154. #121×C113D4semidirect
155. #121×C113D4semidirect
176. #117×C113D4semidirect
179. C2×C4⋊C4×C113D4semidirect
519. #18252C113direct (N × H)
532. #3534C2×C113semidirect
533. #3006C2×C113semidirect
534. #3002C2×C113semidirect
535. #2430C2×C113semidirect
536. #1606C2×C113semidirect
537. #1604C2×C113semidirect
538. #1603C2×C113semidirect
539. #1601C2×C113semidirect
540. #1600C2×C113semidirect
541. #1598C2×C113semidirect
542. #1597C2×C113semidirect
543. #1595C2×C113semidirect
544. #1504C2×C113semidirect
545. C2×#327C2×C113semidirect
546. #1468C2×C113semidirect
547. C113#18252direct (N × H)
548. C22×#41C22×C113semidirect
572. #451C22×C113semidirect
573. #450C22×C113semidirect
578. #448C22×C113semidirect
579. #448C22×C113semidirect
581. #447C22×C113semidirect
582. #447C22×C113semidirect
585. #407C22×C113semidirect
586. C2×C22⋊C8C22×C113semidirect
587. #395C22×C113semidirect
588. #394C22×C113semidirect
589. #393C22×C113semidirect
590. #392C22×C113semidirect
594. C2×#95C22×C113semidirect
595. #328C22×C113semidirect
596. #328C22×C113semidirect
599. #327C22×C113semidirect
600. #327C22×C113semidirect
601. #327C22×C113semidirect
602. #327C22×C113semidirect
603. #324C22×C113semidirect
604. #324C22×C113semidirect
605. #323C22×C113semidirect
606. #323C22×C113semidirect
613. C2×#41D4×C113semidirect
621. C22×D4D4×C113semidirect
667. C22⋊Q8D4×C113semidirect
685. #121D4×C113semidirect
686. #121D4×C113semidirect
687. #121D4×C113semidirect
708. #117D4×C113semidirect
711. 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×#35342
C113×#30062
C113×#30022
C113×#24302
C113×#16062
C113×#16042
C113×#16032
C113×#16012
C113×#16002
C113×#15982
C113×#15972
C113×#15952
C113×#15042
C2×#327×C1132
C113×#14682
#18252113