Finite Group Databasebeta

← C113×#22889 #43290909

Subgroups — C113×#22889 #43290909

Order 28928.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3002C211yesmaximal, characteristic
2C2×#443×C113C211yesmaximal, characteristic, complemented
3C113×#2933C211yesmaximal, characteristic, complemented
4C2×#421×C113C211yesmaximal, characteristic, complemented
5C113×#2880C211yesmaximal, characteristic, complemented
6C113×#1975C211yesmaximal, characteristic, complemented
7C113×#1937C211yesmaximal, characteristic, complemented
8C113×#1929C211yesmaximal, characteristic, complemented
9C113×#1897C211yesmaximal, characteristic, complemented
10C113×#1876C211yesmaximal, characteristic, complemented
11C113×#1876C211yesmaximal, characteristic, complemented
12C113×#1866C211yesmaximal, characteristic, complemented
13C113×#1855C211yesmaximal, characteristic, complemented
14C113×#1765C211yesmaximal, characteristic, complemented
15C113×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C2×#135×C113C2211yescharacteristic
18C2×#135×C113C2211yescharacteristic
19C2×#131×C113C2211yescharacteristic
20C2×#131×C113C2211yescharacteristic
21C2×#131×C113C2211yescharacteristic, complemented
22C22×M16×C113C2211yescharacteristic
23#525×C113C2211yescharacteristic
24C2×#117×C113C2211yescharacteristic
25#452×C113C411yescharacteristic, complemented
26#452×C113C411yescharacteristic, complemented
27#451×C113C411yescharacteristic, complemented
28#450×C113C411yescharacteristic, complemented
29#449×C113C411yescharacteristic, complemented
30#449×C113C411yescharacteristic, complemented
31#448×C113C411yescharacteristic, complemented
32#447×C113C411yescharacteristic, complemented
33#443×C113—24no—
34#436×C113—21no—
35#435×C113—21no—
36#435×C113—21no—
37C8×D4×C113—21no—
38C2×#108×C113C2211yescharacteristic, complemented
39C2×#108×C113C2211yescharacteristic, complemented
40#424×C113C2211yescharacteristic, complemented
41#421×C113—24no—
42C2×#104×C113C2211yescharacteristic
43C2×#104×C113C2211yescharacteristic
44C2×#104×C113C2211yescharacteristic
45C2×#104×C113C2211yescharacteristic
46C2×#104×C113C2211yescharacteristic, complemented
47C2×#104×C113C2211yescharacteristic, complemented
48#416×C113C2211yescharacteristic
49#416×C113C2211yescharacteristic
50#408×C113—21no—
51#408×C113—21no—
52#408×C113C2211yescharacteristic
53#408×C113C2211yescharacteristic
54#408×C113C2211yescharacteristic, complemented
55#407×C113—21no—
56#407×C113C2211yescharacteristic
57C2×C22⋊C8×C113—21no—
58C2×C22⋊C8×C113C2211yescharacteristic
59C2×C22⋊C8×C113C2211yescharacteristic
60#405×C113C2211yescharacteristic, complemented
61C2×#97×C113C2211yescharacteristic, complemented
62C2×C4×C8×C113C2211yescharacteristic, complemented
63#341×C113C2211yescharacteristic, complemented
64#341×C113C2211yescharacteristic, complemented
65#339×C113C2211yescharacteristic, complemented
66#339×C113C2211yescharacteristic, complemented
67#336×C113C2211yescharacteristic, complemented
68#336×C113C2211yescharacteristic, complemented
69C2×#41×C113—21no—
70C2×#41×C113—21no—
71C2×#41×C113—22no—
72C2×#41×C113—22no—
73C2×#41×C113—41no—
74C2×#41×C113—41no—
75C2×#41×C113C2×C411yescharacteristic
76C2×#41×C113C2×C411yescharacteristic
77C2×#41×C113C2311yescharacteristic
78C2×#41×C113C2311yescharacteristic
79C2×#41×C113C2311yescharacteristic
80C22×Q8×C113C2×C411yescharacteristic
81C22×D4×C113—21no—
82C22×D4×C113C2×C411yescharacteristic
83C23×C4×C113—21no—
84C23×C4×C113C2311yescharacteristic
85#135×C113—22no—
86#135×C113—22no—
87#135×C113—41no—
88#135×C113—41no—
89C2×Q16×C113C2×C411yescharacteristic
90C2×Q16×C113C2×C411yescharacteristic
91C2×SD16×C113C2×C411yescharacteristic
92C2×SD16×C113C2×C411yescharacteristic
93C2×SD16×C113C2×C411yescharacteristic
94C2×SD16×C113C2×C411yescharacteristic
95C2×D8×C113C2×C411yescharacteristic
96C2×D8×C113C2×C411yescharacteristic
97#131×C113—22no—
98#131×C113—22no—
99#131×C113—22no—
100#131×C113—41no—
101#131×C113—41no—
102#131×C113—41no—
103C2×M16×C113—21no—
104C2×M16×C113—21no—
105C2×M16×C113—21no—
106C2×M16×C113—21no—
107C2×M16×C113—22no—
108C2×M16×C113—41no—
109C2×M16×C113C2311yescharacteristic
110C2×M16×C113C2311yescharacteristic
111C2×M16×C113C2311yescharacteristic
112C2×M16×C113C2311yescharacteristic
113C22×C8×C113—21no—
114C22×C8×C113—21no—
115C22×C8×C113—21no—
116C22×C8×C113—21no—
117C22×C8×C113C2311yescharacteristic
118C22×C8×C113C2311yescharacteristic
119C22×C8×C113C2311yescharacteristic
120C22×C8×C113C2311yescharacteristic
121#123×C113—21no—
122C22⋊Q8×C113C2×C411yescharacteristic
123C22⋊Q8×C113C2×C411yescharacteristic
124#121×C113C2×C411yescharacteristic
125#121×C113C2×C411yescharacteristic
126#120×C113—21no—
127C4×D4×C113—21no—
128C4×D4×C113—21no—
129#117×C113—22no—
130#117×C113—41no—
131#117×C113C2311yescharacteristic
132C2×C4⋊C4×C113—21no—
133C2×C22⋊C4×C113—21no—
134C2×C42×C113C2311yescharacteristic
135C2×C42×C113C2311yescharacteristic
136#108×C113—22no—
137#108×C113—41no—
138C4⋊C8×C113—21no—
139C4⋊C8×C113—21no—
140#104×C113—22no—
141#104×C113—22no—
142#104×C113—22no—
143#104×C113—22no—
144#104×C113—41no—
145#104×C113D414yescomplemented
146#103×C113C2×C411yescharacteristic
147#103×C113C2×C411yescharacteristic
148#103×C113C2×C411yescharacteristic
149#103×C113C2×C411yescharacteristic
150#102×C113C2×C411yescharacteristic
151#102×C113C2×C411yescharacteristic
152#102×C113C2×C411yescharacteristic
153#102×C113C2×C411yescharacteristic
154C22⋊C8×C113—21no—
155C22⋊C8×C113—21no—
156C22⋊C8×C113—21no—
157C22⋊C8×C113—21no—
158C22⋊C8×C113—21no—
159C22⋊C8×C113—21no—
160C22⋊C8×C113—21no—
161C22⋊C8×C113—21no—
162C22⋊C8×C113C2×C411yescharacteristic
163C22⋊C8×C113C2×C411yescharacteristic
164C22⋊C8×C113C2×C411yescharacteristic
165C22⋊C8×C113C2×C411yescharacteristic
166C22⋊C8×C113D411yescharacteristic
167C22⋊C8×C113D411yescharacteristic
168C22⋊C8×C113D411yescharacteristic
169C22⋊C8×C113D411yescharacteristic
170#97×C113—21no—
171#97×C113—41no—
172C4×C8×C113—21no—
173C4×C8×C113—22no—
174C24×C113—21no—
175C24×C113#4111yescharacteristic
176#41×C113—21no—
177#41×C113—21no—
178#41×C113—22no—
179#41×C113—22no—
180#41×C113—21no—
181#41×C113—21no—
182#41×C113—21no—
183#41×C113—21no—
184#41×C113—21no—
185#41×C113—21no—
186#41×C113—21no—
187#41×C113—21no—
188#41×C113—42no—
189#41×C113—42no—
190#41×C113—41no—
191#41×C113—41no—
192#41×C113—42no—
193#41×C113—42no—
194#41×C113C2×D412yes—
195#41×C113#4112yes—
196C2×Q8×C113—21no—
197C2×Q8×C113—22no—
198C2×Q8×C113—41no—
199C2×Q8×C113C22×C411yescharacteristic
200C2×Q8×C113C22×C411yescharacteristic
201C2×Q8×C113C22×C411yescharacteristic
202C2×D4×C113—21no—
203C2×D4×C113—22no—
204C2×D4×C113—21no—
205C2×D4×C113—21no—
206C2×D4×C113—21no—
207C2×D4×C113—21no—
208C2×D4×C113—21no—
209C2×D4×C113—21no—
210C2×D4×C113—21no—
211C2×D4×C113—41no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113C22×C411yescharacteristic
215C2×D4×C113C22×C411yescharacteristic
216C2×D4×C113C22×C411yescharacteristic
217C22×C4×C113—21no—
218C22×C4×C113—21no—
219C22×C4×C113—21no—
220C22×C4×C113—21no—
221C22×C4×C113—21no—
222C22×C4×C113—21no—
223C22×C4×C113—21no—
224C22×C4×C113—21no—
225C22×C4×C113—21no—
226C22×C4×C113—21no—
227C22×C4×C113—21no—
228C22×C4×C113—21no—
229C22×C4×C113—42no—
230C22×C4×C113—42no—
231C22×C4×C113C22×C411yescharacteristic
232C22×C4×C113C22×C411yescharacteristic
233C22×C4×C113C2×D411yescharacteristic
234C22×C4×C113C2×D411yescharacteristic
235C22×C4×C113#4111yescharacteristic
236C22×C4×C113C2411yescharacteristic
237Q16×C113—22no—
238Q16×C113—41no—
239SD16×C113—22no—
240SD16×C113—22no—
241SD16×C113—41no—
242SD16×C113—41no—
243D8×C113—22no—
244D8×C113—41no—
245M16×C113—21no—
246M16×C113—21no—
247M16×C113—21no—
248M16×C113—21no—
249M16×C113—21no—
250M16×C113—21no—
251M16×C113—21no—
252M16×C113—42no—
253M16×C113—42no—
254M16×C113—42no—
255M16×C113—42no—
256M16×C113C2×D412yes—
257C2×C8×C113—21no—
258C2×C8×C113—21no—
259C2×C8×C113—21no—
260C2×C8×C113—21no—
261C2×C8×C113—21no—
262C2×C8×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113—21no—
267C2×C8×C113—21no—
268C2×C8×C113—21no—
269C2×C8×C113—42no—
270C2×C8×C113—42no—
271C2×C8×C113—42no—
272C2×C8×C113—42no—
273C2×C8×C113C22×C411yescharacteristic
274C2×C8×C113C22×C411yescharacteristic
275C2×C8×C113C22×C411yescharacteristic
276C2×C8×C113C22×C411yescharacteristic
277C2×C8×C113C2×D411yescharacteristic
278C2×C8×C113C2×D411yescharacteristic
279C2×C8×C113C2×D411yescharacteristic
280C2×C8×C113C2×D411yescharacteristic
281C4⋊C4×C113—21no—
282C4⋊C4×C113—21no—
283C4⋊C4×C113—42no—
284C4⋊C4×C113C22×C411yescharacteristic
285C4⋊C4×C113C22×C411yescharacteristic
286C22⋊C4×C113—21no—
287C22⋊C4×C113—21no—
288C22⋊C4×C113—21no—
289C22⋊C4×C113—21no—
290C22⋊C4×C113—21no—
291C22⋊C4×C113—42no—
292C42×C113—21no—
293C42×C113—21no—
294C42×C113—21no—
295C42×C113—21no—
296C42×C113C2×D412yes—
297C23×C113—21no—
298C23×C113—21no—
299C23×C113—21no—
300C23×C113—21no—
301C23×C113—21no—
302C23×C113—41no—
303C23×C113—41no—
304C23×C113—42no—
305C23×C113—42no—
306C23×C113—81no—
307C23×C113C4×D411yescharacteristic
308C23×C113C4×D411yescharacteristic
309C23×C113C2×#4111yescharacteristic
310Q8×C113—21no—
311Q8×C113—21no—
312Q8×C113—21no—
313Q8×C113—21no—
314Q8×C113—21no—
315Q8×C113—42no—
316Q8×C113C4×D412yes—
317D4×C113—22no—
318D4×C113—22no—
319D4×C113—21no—
320D4×C113—21no—
321D4×C113—21no—
322D4×C113—21no—
323D4×C113—21no—
324D4×C113—42no—
325D4×C113—42no—
326D4×C113—42no—
327D4×C113—42no—
328D4×C113—41no—
329D4×C113—41no—
330D4×C113—41no—
331D4×C113—41no—
332D4×C113—81no—
333D4×C113C4×D412yes—
334C2×C4×C113—21no—
335C2×C4×C113—21no—
336C2×C4×C113—21no—
337C2×C4×C113—21no—
338C2×C4×C113—21no—
339C2×C4×C113—21no—
340C2×C4×C113—21no—
341C2×C4×C113—21no—
342C2×C4×C113—22no—
343C2×C4×C113—21no—
344C2×C4×C113—22no—
345C2×C4×C113—21no—
346C2×C4×C113—21no—
347C2×C4×C113—21no—
348C2×C4×C113—21no—
349C2×C4×C113—21no—
350C2×C4×C113—21no—
351C2×C4×C113—22no—
352C2×C4×C113—42no—
353C2×C4×C113—42no—
354C2×C4×C113—42no—
355C2×C4×C113—41no—
356C2×C4×C113—41no—
357C2×C4×C113—41no—
358C2×C4×C113—41no—
359C2×C4×C113—41no—
360C2×C4×C113—41no—
361C2×C4×C113—41no—
362C2×C4×C113—41no—
363C2×C4×C113—41no—
364C2×C4×C113C4×D411yescharacteristic
365C2×C4×C113C4×D411yescharacteristic
366C2×C4×C113C23×C411yescharacteristic
367C2×C4×C113C22×D411yescharacteristic
368C2×C4×C113C22×D411yescharacteristic
369C2×C4×C113C2×#4111yescharacteristic
370C2×C4×C113H(5,𝔽2)11yescharacteristic
371C2×C4×C113H(5,𝔽2)11yescharacteristic
372C8×C113—21no—
373C8×C113—21no—
374C8×C113—21no—
375C8×C113—21no—
376C8×C113—21no—
377C8×C113—21no—
378C8×C113—22no—
379C8×C113—21no—
380C8×C113—21no—
381C8×C113—41no—
382C8×C113—41no—
383C8×C113—41no—
384C22×C113—21no—
385C22×C113—21no—
386C22×C113—21no—
387C22×C113—21no—
388C22×C113—22no—
389C22×C113—21no—
390C22×C113—21no—
391C22×C113—21no—
392C22×C113—21no—
393C22×C113—41no—
394C22×C113—41no—
395C22×C113—41no—
396C22×C113—41no—
397C22×C113—41no—
398C22×C113—41no—
399C22×C113—41no—
400C22×C113—41no—
401C22×C113—81no—
402C22×C113—81no—
403C22×C113—84no—
404C22×C113C2×C4×D411yescharacteristic
405C22×C113#54611yescharacteristic
406C22×C113#55111yescharacteristic
407C4×C113—21no—
408C4×C113—21no—
409C4×C113—22no—
410C4×C113—42no—
411C4×C113—41no—
412C4×C113—41no—
413C4×C113—41no—
414C4×C113—41no—
415C4×C113—81no—
416C4×C113C2×C4×D411yescharacteristic
417C4×C113#51811yescharacteristic
418C4×C113D4211yescharacteristic
419C4×C113#54611yescharacteristic
420#22889C11311yesmaximal, characteristic, direct product factor, Sylow
421C2×C113—21no—
422C2×C113—21no—
423C2×C113—41no—
424C2×C113—41no—
425C2×C113—42no—
426C2×C113—81no—
427C2×C113—81no—
428C2×C113#235811yescharacteristic
429C2×C113#295511yescharacteristic
430C2×C113#295711yescharacteristic
431#3002C2×C11311yescharacteristic
432C2×#443C2×C11311yescharacteristic, complemented
433#2933C2×C11311yescharacteristic, complemented
434C2×#421C2×C11311yescharacteristic, complemented
435#2880C2×C11311yescharacteristic, complemented
436#1975C2×C11311yescharacteristic, complemented
437#1937C2×C11311yescharacteristic, complemented
438#1929C2×C11311yescharacteristic, complemented
439#1897C2×C11311yescharacteristic, complemented
440#1876C2×C11311yescharacteristic, complemented
441#1876C2×C11311yescharacteristic, complemented
442#1866C2×C11311yescharacteristic, complemented
443#1855C2×C11311yescharacteristic, complemented
444#1765C2×C11311yescharacteristic, complemented
445#1750C2×C11311yescharacteristic, complemented
446C113#2288911yescharacteristic, direct product factor, Sylow
447C22×#41C22×C11311yescharacteristic
448C2×#135C22×C11311yescharacteristic
449C2×#135C22×C11311yescharacteristic
450C2×#131C22×C11311yescharacteristic
451C2×#131C22×C11311yescharacteristic
452C2×#131C22×C11311yescharacteristic, complemented
453C22×M16C22×C11311yescharacteristic
454#525C22×C11311yescharacteristic
455C2×#117C22×C11311yescharacteristic
456#452C4×C11311yescharacteristic, complemented
457#452C4×C11311yescharacteristic, complemented
458#451C4×C11311yescharacteristic, complemented
459#450C4×C11311yescharacteristic, complemented
460#449C4×C11311yescharacteristic, complemented
461#449C4×C11311yescharacteristic, complemented
462#448C4×C11311yescharacteristic, complemented
463#447C4×C11311yescharacteristic, complemented
464#443—24no—
465#436—21no—
466#435—21no—
467#435—21no—
468C8×D4—21no—
469C2×#108C22×C11311yescharacteristic, complemented
470C2×#108C22×C11311yescharacteristic, complemented
471#424C22×C11311yescharacteristic, complemented
472#421—24no—
473C2×#104C22×C11311yescharacteristic
474C2×#104C22×C11311yescharacteristic
475C2×#104C22×C11311yescharacteristic
476C2×#104C22×C11311yescharacteristic
477C2×#104C22×C11311yescharacteristic, complemented
478C2×#104C22×C11311yescharacteristic, complemented
479#416C22×C11311yescharacteristic
480#416C22×C11311yescharacteristic
481#408—21no—
482#408—21no—
483#408C22×C11311yescharacteristic
484#408C22×C11311yescharacteristic
485#408C22×C11311yescharacteristic, complemented
486#407—21no—
487#407C22×C11311yescharacteristic
488C2×C22⋊C8—21no—
489C2×C22⋊C8C22×C11311yescharacteristic
490C2×C22⋊C8C22×C11311yescharacteristic
491#405C22×C11311yescharacteristic, complemented
492C2×#97C22×C11311yescharacteristic, complemented
493C2×C4×C8C22×C11311yescharacteristic, complemented
494#341C22×C11311yescharacteristic, complemented
495#341C22×C11311yescharacteristic, complemented
496#339C22×C11311yescharacteristic, complemented
497#339C22×C11311yescharacteristic, complemented
498#336C22×C11311yescharacteristic, complemented
499#336C22×C11311yescharacteristic, complemented
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×C4×C11311yescharacteristic
507C2×#41C2×C4×C11311yescharacteristic
508C2×#41C23×C11311yescharacteristic
509C2×#41C23×C11311yescharacteristic
510C2×#41C23×C11311yescharacteristic
511C22×Q8C2×C4×C11311yescharacteristic
512C22×D4—21no—
513C22×D4C2×C4×C11311yescharacteristic
514C23×C4—21no—
515C23×C4C23×C11311yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×C4×C11311yescharacteristic
521C2×Q16C2×C4×C11311yescharacteristic
522C2×SD16C2×C4×C11311yescharacteristic
523C2×SD16C2×C4×C11311yescharacteristic
524C2×SD16C2×C4×C11311yescharacteristic
525C2×SD16C2×C4×C11311yescharacteristic
526C2×D8C2×C4×C11311yescharacteristic
527C2×D8C2×C4×C11311yescharacteristic
528#131—22no—
529#131—22no—
530#131—22no—
531#131—41no—
532#131—41no—
533#131—41no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16C23×C11311yescharacteristic
541C2×M16C23×C11311yescharacteristic
542C2×M16C23×C11311yescharacteristic
543C2×M16C23×C11311yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—21no—
547C22×C8—21no—
548C22×C8C23×C11311yescharacteristic
549C22×C8C23×C11311yescharacteristic
550C22×C8C23×C11311yescharacteristic
551C22×C8C23×C11311yescharacteristic
552#123—21no—
553C22⋊Q8C2×C4×C11311yescharacteristic
554C22⋊Q8C2×C4×C11311yescharacteristic
555#121C2×C4×C11311yescharacteristic
556#121C2×C4×C11311yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C23×C11311yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C23×C11311yescharacteristic
566C2×C42C23×C11311yescharacteristic
567#108—22no—
568#108—41no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—22no—
575#104—41no—
576#104D4×C11314yescomplemented
577#103C2×C4×C11311yescharacteristic
578#103C2×C4×C11311yescharacteristic
579#103C2×C4×C11311yescharacteristic
580#103C2×C4×C11311yescharacteristic
581#102C2×C4×C11311yescharacteristic
582#102C2×C4×C11311yescharacteristic
583#102C2×C4×C11311yescharacteristic
584#102C2×C4×C11311yescharacteristic
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8C2×C4×C11311yescharacteristic
594C22⋊C8C2×C4×C11311yescharacteristic
595C22⋊C8C2×C4×C11311yescharacteristic
596C22⋊C8C2×C4×C11311yescharacteristic
597C22⋊C8D4×C11311yescharacteristic
598C22⋊C8D4×C11311yescharacteristic
599C22⋊C8D4×C11311yescharacteristic
600C22⋊C8D4×C11311yescharacteristic
601#97—21no—
602#97—41no—
603C4×C8—21no—
604C4×C8—22no—
605C24—21no—
606C24#41×C11311yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41C2×D4×C11312yes—
626#41#41×C11312yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×C4×C11311yescharacteristic
631C2×Q8C22×C4×C11311yescharacteristic
632C2×Q8C22×C4×C11311yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×C4×C11311yescharacteristic
646C2×D4C22×C4×C11311yescharacteristic
647C2×D4C22×C4×C11311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4C22×C4×C11311yescharacteristic
663C22×C4C22×C4×C11311yescharacteristic
664C22×C4C2×D4×C11311yescharacteristic
665C22×C4C2×D4×C11311yescharacteristic
666C22×C4#41×C11311yescharacteristic
667C22×C4C24×C11311yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C11312yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8C22×C4×C11311yescharacteristic
705C2×C8C22×C4×C11311yescharacteristic
706C2×C8C22×C4×C11311yescharacteristic
707C2×C8C22×C4×C11311yescharacteristic
708C2×C8C2×D4×C11311yescharacteristic
709C2×C8C2×D4×C11311yescharacteristic
710C2×C8C2×D4×C11311yescharacteristic
711C2×C8C2×D4×C11311yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C22×C4×C11311yescharacteristic
716C4⋊C4C22×C4×C11311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C11312yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C11311yescharacteristic
739C23C4×D4×C11311yescharacteristic
740C23C2×#41×C11311yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C11312yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C11312yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C11311yescharacteristic
796C2×C4C4×D4×C11311yescharacteristic
797C2×C4C23×C4×C11311yescharacteristic
798C2×C4C22×D4×C11311yescharacteristic
799C2×C4C22×D4×C11311yescharacteristic
800C2×C4C2×#41×C11311yescharacteristic
801C2×C4H(5,𝔽2)×C11311yescharacteristic
802C2×C4H(5,𝔽2)×C11311yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C11311yescharacteristic
836C22#546×C11311yescharacteristic
837C22#551×C11311yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C11311yescharacteristic
848C4#518×C11311yescharacteristic
849C4D42×C11311yescharacteristic
850C4#546×C11311yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2C113×#235811yescharacteristic
859C2C113×#295511yescharacteristic
860C2C113×#295711yescharacteristic
subgroupG/H
centerC2×C4×C113C22×D4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
socleC22×C113C2×C4×D4
prime radicalC113×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C113 ◁ C2×C22⋊C8×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#443×C113C2semidirect
3. C113×#2933C2semidirect
4. C2×#421×C113C2semidirect
5. C113×#2880C2semidirect
6. C113×#1975C2semidirect
7. C113×#1937C2semidirect
8. C113×#1929C2semidirect
9. C113×#1897C2semidirect
10. C113×#1876C2semidirect
11. C113×#1876C2semidirect
12. C113×#1866C2semidirect
13. C113×#1855C2semidirect
14. C113×#1765C2semidirect
15. C113×#1750C2semidirect
21. C2×#131×C113C22semidirect
25. #452×C113C4semidirect
26. #452×C113C4semidirect
27. #451×C113C4semidirect
28. #450×C113C4semidirect
29. #449×C113C4semidirect
30. #449×C113C4semidirect
31. #448×C113C4semidirect
32. #447×C113C4semidirect
38. C2×#108×C113C22semidirect
39. C2×#108×C113C22semidirect
40. #424×C113C22semidirect
46. C2×#104×C113C22semidirect
47. C2×#104×C113C22semidirect
54. #408×C113C22semidirect
60. #405×C113C22semidirect
61. C2×#97×C113C22semidirect
62. C2×C4×C8×C113C22semidirect
63. #341×C113C22semidirect
64. #341×C113C22semidirect
65. #339×C113C22semidirect
66. #339×C113C22semidirect
67. #336×C113C22semidirect
68. #336×C113C22semidirect
145. #104×C113D4semidirect
420. #22889C113direct (N × H)
432. C2×#443C2×C113semidirect
433. #2933C2×C113semidirect
434. C2×#421C2×C113semidirect
435. #2880C2×C113semidirect
436. #1975C2×C113semidirect
437. #1937C2×C113semidirect
438. #1929C2×C113semidirect
439. #1897C2×C113semidirect
440. #1876C2×C113semidirect
441. #1876C2×C113semidirect
442. #1866C2×C113semidirect
443. #1855C2×C113semidirect
444. #1765C2×C113semidirect
445. #1750C2×C113semidirect
446. C113#22889direct (N × H)
452. C2×#131C22×C113semidirect
456. #452C4×C113semidirect
457. #452C4×C113semidirect
458. #451C4×C113semidirect
459. #450C4×C113semidirect
460. #449C4×C113semidirect
461. #449C4×C113semidirect
462. #448C4×C113semidirect
463. #447C4×C113semidirect
469. C2×#108C22×C113semidirect
470. C2×#108C22×C113semidirect
471. #424C22×C113semidirect
477. C2×#104C22×C113semidirect
478. C2×#104C22×C113semidirect
485. #408C22×C113semidirect
491. #405C22×C113semidirect
492. C2×#97C22×C113semidirect
493. C2×C4×C8C22×C113semidirect
494. #341C22×C113semidirect
495. #341C22×C113semidirect
496. #339C22×C113semidirect
497. #339C22×C113semidirect
498. #336C22×C113semidirect
499. #336C22×C113semidirect
576. #104D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#30022
C2×#443×C1132
C113×#29332
C2×#421×C1132
C113×#28802
C113×#19752
C113×#19372
C113×#19292
C113×#18972
C113×#18762
C113×#18662
C113×#18552
C113×#17652
C113×#17502
#22889113