Finite Group Databasebeta

← C113×#26149 #43294169

Subgroups — C113×#26149 #43294169

Order 28928.

868 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#483×C113C211yesmaximal, characteristic, complemented
2C2×#428×C113C211yesmaximal, characteristic, complemented
3C113×#2417C211yesmaximal, characteristic
4C113×#2352C211yesmaximal, characteristic
5C113×#2097C211yesmaximal, characteristic, complemented
6C113×#2085C211yesmaximal, characteristic, complemented
7C113×#2076C211yesmaximal, characteristic, complemented
8C113×#2036C211yesmaximal, characteristic, complemented
9C113×#1927C211yesmaximal, characteristic, complemented
10C113×#1919C211yesmaximal, characteristic, complemented
11C113×#1894C211yesmaximal, characteristic, complemented
12C113×#1873C211yesmaximal, characteristic, complemented
13C113×#1870C211yesmaximal, characteristic
14C113×#1853C211yesmaximal, characteristic, complemented
15C113×#1853C211yesmaximal, characteristic, complemented
16C22×M16×C113C2211yescharacteristic
17C2×C22⋊Q8×C113C2211yescharacteristic
18C2×C22⋊Q8×C113C2211yescharacteristic
19C2×C4×D4×C113C2211yescharacteristic
20C2×#117×C113C2211yescharacteristic
21C22×C4⋊C4×C113C2211yescharacteristic
22C22×C4⋊C4×C113C2211yescharacteristic
23#483×C113—24no—
24#428×C113—24no—
25C2×#107×C113C2211yescharacteristic
26C2×#107×C113C2211yescharacteristic
27C2×#106×C113C2211yescharacteristic
28C2×#106×C113C2211yescharacteristic
29C2×#106×C113C2211yescharacteristic
30C2×#106×C113C2211yescharacteristic
31C2×#103×C113C2211yescharacteristic
32C2×#103×C113C2211yescharacteristic
33C2×#103×C113C2211yescharacteristic
34C2×#103×C113C2211yescharacteristic
35C2×C22⋊C8×C113C2211yescharacteristic
36C2×C22⋊C8×C113C2211yescharacteristic
37C2×C22⋊C8×C113C2211yescharacteristic
38#398×C113—21no—
39#396×C113—21no—
40#391×C113C2211yescharacteristic
41#389×C113C2211yescharacteristic
42#388×C113—21no—
43#387×C113—21no—
44#386×C113—21no—
45#386×C113—21no—
46#382×C113C2211yescharacteristic
47#380×C113—21no—
48#380×C113C2211yescharacteristic
49#380×C113C2211yescharacteristic
50#380×C113C2211yescharacteristic
51C4×C4⋊C4×C113C2211yescharacteristic
52C4×C22⋊C4×C113—21no—
53#340×C113C2211yescharacteristic
54#340×C113C2211yescharacteristic
55#340×C113C2211yescharacteristic
56#340×C113C2211yescharacteristic
57#340×C113C2211yescharacteristic
58#340×C113C2211yescharacteristic
59#336×C113C2211yescharacteristic
60#336×C113C2211yescharacteristic
61C22×Q8×C113C2311yescharacteristic
62C22×D4×C113D411yescharacteristic
63C23×C4×C113—21no—
64C23×C4×C113—21no—
65C23×C4×C113C2311yescharacteristic
66C23×C4×C113C2311yescharacteristic
67C2×M16×C113—22no—
68C2×M16×C113—22no—
69C2×M16×C113—22no—
70C22×C8×C113C2311yescharacteristic
71C22×C8×C113C2311yescharacteristic
72C22×C8×C113C2311yescharacteristic
73C22×C8×C113C2311yescharacteristic
74C22⋊Q8×C113—22no—
75C22⋊Q8×C113—22no—
76C22⋊Q8×C113—22no—
77C22⋊Q8×C113—41no—
78C4×D4×C113—22no—
79C4×D4×C113—22no—
80#117×C113—22no—
81#117×C113—41no—
82C2×C4⋊C4×C113—22no—
83C2×C4⋊C4×C113—22no—
84C2×C4⋊C4×C113—21no—
85C2×C4⋊C4×C113—21no—
86C2×C4⋊C4×C113—21no—
87C2×C4⋊C4×C113—21no—
88C2×C4⋊C4×C113—21no—
89C2×C4⋊C4×C113—41no—
90C2×C4⋊C4×C113—41no—
91C2×C4⋊C4×C113D411yescharacteristic
92C2×C4⋊C4×C113C2311yescharacteristic
93C2×C4⋊C4×C113C2311yescharacteristic
94C2×C4⋊C4×C113C2311yescharacteristic
95C2×C4⋊C4×C113C2311yescharacteristic
96C2×C4⋊C4×C113C2311yescharacteristic
97C2×C4⋊C4×C113C2311yescharacteristic
98C2×C4⋊C4×C113C2311yescharacteristic
99C2×C22⋊C4×C113—21no—
100C2×C22⋊C4×C113—21no—
101C2×C22⋊C4×C113—21no—
102C2×C22⋊C4×C113—21no—
103C2×C22⋊C4×C113—21no—
104C2×C22⋊C4×C113—21no—
105C2×C22⋊C4×C113D411yescharacteristic
106C2×C22⋊C4×C113D411yescharacteristic
107C2×C42×C113—21no—
108C2×C42×C113—21no—
109C2×C42×C113C2311yescharacteristic
110#107×C113—22no—
111#107×C113—22no—
112#106×C113—22no—
113#106×C113—22no—
114#106×C113—41no—
115#106×C113D414yescomplemented
116#103×C113—22no—
117#103×C113—22no—
118#103×C113—22no—
119#103×C113—41no—
120C22⋊C8×C113—22no—
121C22⋊C8×C113—22no—
122C22⋊C8×C113—22no—
123#95×C113—21no—
124#95×C113—21no—
125#95×C113—21no—
126#95×C113—21no—
127#95×C113—21no—
128#95×C113—21no—
129#95×C113—21no—
130#95×C113—21no—
131#95×C113—21no—
132C24×C113C2×D411yescharacteristic
133C24×C113C2×D411yescharacteristic
134C2×Q8×C113—21no—
135C2×Q8×C113—21no—
136C2×Q8×C113—21no—
137C2×Q8×C113—21no—
138C2×Q8×C113—21no—
139C2×Q8×C113—21no—
140C2×D4×C113—22no—
141C2×D4×C113—22no—
142C2×D4×C113—41no—
143C22×C4×C113—21no—
144C22×C4×C113—21no—
145C22×C4×C113—21no—
146C22×C4×C113—21no—
147C22×C4×C113—21no—
148C22×C4×C113—21no—
149C22×C4×C113—21no—
150C22×C4×C113—21no—
151C22×C4×C113—21no—
152C22×C4×C113—21no—
153C22×C4×C113—21no—
154C22×C4×C113—21no—
155C22×C4×C113—21no—
156C22×C4×C113—21no—
157C22×C4×C113—21no—
158C22×C4×C113—21no—
159C22×C4×C113—21no—
160C22×C4×C113—21no—
161C22×C4×C113—42no—
162C22×C4×C113—42no—
163C22×C4×C113—42no—
164C22×C4×C113—42no—
165C22×C4×C113—81no—
166C22×C4×C113—81no—
167C22×C4×C113C2×D411yescharacteristic
168C22×C4×C113C2×D411yescharacteristic
169C22×C4×C113C2×D411yescharacteristic
170C22×C4×C113C2×D411yescharacteristic
171C22×C4×C113#4112yes—
172C22×C4×C113#4112yes—
173C22×C4×C113C2411yescharacteristic
174M16×C113—28no—
175C2×C8×C113—21no—
176C2×C8×C113—21no—
177C2×C8×C113—21no—
178C2×C8×C113—21no—
179C2×C8×C113—21no—
180C2×C8×C113—21no—
181C2×C8×C113—21no—
182C2×C8×C113—21no—
183C2×C8×C113—21no—
184C2×C8×C113—21no—
185C2×C8×C113C2×D412yes—
186C2×C8×C113#4112yes—
187C4⋊C4×C113—22no—
188C4⋊C4×C113—21no—
189C4⋊C4×C113—21no—
190C4⋊C4×C113—21no—
191C4⋊C4×C113—21no—
192C4⋊C4×C113—21no—
193C4⋊C4×C113—21no—
194C4⋊C4×C113—21no—
195C4⋊C4×C113—21no—
196C4⋊C4×C113—21no—
197C4⋊C4×C113—21no—
198C4⋊C4×C113—21no—
199C4⋊C4×C113—21no—
200C4⋊C4×C113—42no—
201C4⋊C4×C113—42no—
202C4⋊C4×C113—42no—
203C4⋊C4×C113—42no—
204C4⋊C4×C113—81no—
205C4⋊C4×C113C2×D412yes—
206C4⋊C4×C113C2×D412yes—
207C22⋊C4×C113—22no—
208C22⋊C4×C113—22no—
209C22⋊C4×C113—42no—
210C22⋊C4×C113—42no—
211C22⋊C4×C113—42no—
212C22⋊C4×C113—42no—
213C22⋊C4×C113—81no—
214C22⋊C4×C113—81no—
215C42×C113—21no—
216C42×C113—21no—
217C42×C113—42no—
218C42×C113—81no—
219C23×C113—21no—
220C23×C113—21no—
221C23×C113—21no—
222C23×C113—21no—
223C23×C113—21no—
224C23×C113—21no—
225C23×C113—21no—
226C23×C113—21no—
227C23×C113—21no—
228C23×C113—21no—
229C23×C113—21no—
230C23×C113—21no—
231C23×C113#12312yes—
232C23×C113#13712yes—
233C23×C113C22×D411yescharacteristic
234Q8×C113—41no—
235Q8×C113—41no—
236Q8×C113—41no—
237Q8×C113—41no—
238D4×C113—44no—
239C2×C4×C113—21no—
240C2×C4×C113—21no—
241C2×C4×C113—22no—
242C2×C4×C113—22no—
243C2×C4×C113—22no—
244C2×C4×C113—22no—
245C2×C4×C113—21no—
246C2×C4×C113—21no—
247C2×C4×C113—21no—
248C2×C4×C113—22no—
249C2×C4×C113—22no—
250C2×C4×C113—21no—
251C2×C4×C113—21no—
252C2×C4×C113—21no—
253C2×C4×C113—21no—
254C2×C4×C113—21no—
255C2×C4×C113—21no—
256C2×C4×C113—41no—
257C2×C4×C113—41no—
258C2×C4×C113—41no—
259C2×C4×C113—41no—
260C2×C4×C113—41no—
261C2×C4×C113—41no—
262C2×C4×C113—41no—
263C2×C4×C113—41no—
264C2×C4×C113—41no—
265C2×C4×C113—41no—
266C2×C4×C113—41no—
267C2×C4×C113—41no—
268C2×C4×C113—41no—
269C2×C4×C113—41no—
270C2×C4×C113—41no—
271C2×C4×C113—41no—
272C2×C4×C113—41no—
273C2×C4×C113—41no—
274C2×C4×C113—41no—
275C2×C4×C113—41no—
276C2×C4×C113—41no—
277C2×C4×C113—41no—
278C2×C4×C113—41no—
279C2×C4×C113—41no—
280C2×C4×C113—41no—
281C2×C4×C113—41no—
282C2×C4×C113—84no—
283C2×C4×C113—84no—
284C2×C4×C113#12312yes—
285C2×C4×C113C22×D411yescharacteristic
286C2×C4×C113C2×#4111yescharacteristic
287C2×C4×C113C2×#4111yescharacteristic
288C2×C4×C113C2×#4111yescharacteristic
289C2×C4×C113H(5,𝔽2)11yescharacteristic
290C2×C4×C1132−1+411yescharacteristic
291C8×C113—22no—
292C8×C113—22no—
293C8×C113—41no—
294C8×C113—41no—
295C22×C113—22no—
296C22×C113—22no—
297C22×C113—22no—
298C22×C113—22no—
299C22×C113—22no—
300C22×C113—22no—
301C22×C113—41no—
302C22×C113—41no—
303C22×C113—41no—
304C22×C113—41no—
305C22×C113—41no—
306C22×C113—41no—
307C22×C113—41no—
308C22×C113—41no—
309C22×C113C2×#12311yescharacteristic
310C22×C113D4211yescharacteristic
311C22×C113#54711yescharacteristic
312C22×C113C2×#13711yescharacteristic
313C22×C113#57511yescharacteristic
314C22×C113#57711yescharacteristic
315C22×C113#57711yescharacteristic
316C4×C113—22no—
317C4×C113—41no—
318C4×C113—41no—
319C4×C113—41no—
320C4×C113—42no—
321C4×C113—42no—
322C4×C113—81no—
323C4×C113—81no—
324C4×C113—81no—
325C4×C113—81no—
326C4×C113—81no—
327C4×C113—81no—
328C4×C113#52511yescharacteristic
329C4×C113#53911yescharacteristic
330C4×C113#54811yescharacteristic
331C4×C113#55311yescharacteristic
332#26149C11311yesmaximal, characteristic, direct product factor, Sylow
333C2×C113—42no—
334C2×C113—42no—
335C2×C113#244311yescharacteristic
336C2×C113#309511yescharacteristic
337C2×C113#309911yescharacteristic
338C2×C113#326611yescharacteristic
339C2×C113#327511yescharacteristic
340C2×C113#334411yescharacteristic
341C2×C113#335111yescharacteristic
342C2×#483C2×C11311yescharacteristic, complemented
343C2×#428C2×C11311yescharacteristic, complemented
344#2417C2×C11311yescharacteristic
345#2352C2×C11311yescharacteristic
346#2097C2×C11311yescharacteristic, complemented
347#2085C2×C11311yescharacteristic, complemented
348#2076C2×C11311yescharacteristic, complemented
349#2036C2×C11311yescharacteristic, complemented
350#1927C2×C11311yescharacteristic, complemented
351#1919C2×C11311yescharacteristic, complemented
352#1894C2×C11311yescharacteristic, complemented
353#1873C2×C11311yescharacteristic, complemented
354#1870C2×C11311yescharacteristic
355#1853C2×C11311yescharacteristic, complemented
356#1853C2×C11311yescharacteristic, complemented
357C113#2614911yescharacteristic, direct product factor, Sylow
358C22×M16C22×C11311yescharacteristic
359C2×C22⋊Q8C22×C11311yescharacteristic
360C2×C22⋊Q8C22×C11311yescharacteristic
361C2×C4×D4C22×C11311yescharacteristic
362C2×#117C22×C11311yescharacteristic
363C22×C4⋊C4C22×C11311yescharacteristic
364C22×C4⋊C4C22×C11311yescharacteristic
365#483—24no—
366#428—24no—
367C2×#107C22×C11311yescharacteristic
368C2×#107C22×C11311yescharacteristic
369C2×#106C22×C11311yescharacteristic
370C2×#106C22×C11311yescharacteristic
371C2×#106C22×C11311yescharacteristic
372C2×#106C22×C11311yescharacteristic
373C2×#103C22×C11311yescharacteristic
374C2×#103C22×C11311yescharacteristic
375C2×#103C22×C11311yescharacteristic
376C2×#103C22×C11311yescharacteristic
377C2×C22⋊C8C22×C11311yescharacteristic
378C2×C22⋊C8C22×C11311yescharacteristic
379C2×C22⋊C8C22×C11311yescharacteristic
380#398—21no—
381#396—21no—
382#391C22×C11311yescharacteristic
383#389C22×C11311yescharacteristic
384#388—21no—
385#387—21no—
386#386—21no—
387#386—21no—
388#382C22×C11311yescharacteristic
389#380—21no—
390#380C22×C11311yescharacteristic
391#380C22×C11311yescharacteristic
392#380C22×C11311yescharacteristic
393C4×C4⋊C4C22×C11311yescharacteristic
394C4×C22⋊C4—21no—
395#340C22×C11311yescharacteristic
396#340C22×C11311yescharacteristic
397#340C22×C11311yescharacteristic
398#340C22×C11311yescharacteristic
399#340C22×C11311yescharacteristic
400#340C22×C11311yescharacteristic
401#336C22×C11311yescharacteristic
402#336C22×C11311yescharacteristic
403C22×Q8C23×C11311yescharacteristic
404C22×D4D4×C11311yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C23×C4C23×C11311yescharacteristic
408C23×C4C23×C11311yescharacteristic
409C2×M16—22no—
410C2×M16—22no—
411C2×M16—22no—
412C22×C8C23×C11311yescharacteristic
413C22×C8C23×C11311yescharacteristic
414C22×C8C23×C11311yescharacteristic
415C22×C8C23×C11311yescharacteristic
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—41no—
420C4×D4—22no—
421C4×D4—22no—
422#117—22no—
423#117—41no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4D4×C11311yescharacteristic
434C2×C4⋊C4C23×C11311yescharacteristic
435C2×C4⋊C4C23×C11311yescharacteristic
436C2×C4⋊C4C23×C11311yescharacteristic
437C2×C4⋊C4C23×C11311yescharacteristic
438C2×C4⋊C4C23×C11311yescharacteristic
439C2×C4⋊C4C23×C11311yescharacteristic
440C2×C4⋊C4C23×C11311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4D4×C11311yescharacteristic
448C2×C22⋊C4D4×C11311yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C11311yescharacteristic
452#107—22no—
453#107—22no—
454#106—22no—
455#106—22no—
456#106—41no—
457#106D4×C11314yescomplemented
458#103—22no—
459#103—22no—
460#103—22no—
461#103—41no—
462C22⋊C8—22no—
463C22⋊C8—22no—
464C22⋊C8—22no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474C24C2×D4×C11311yescharacteristic
475C24C2×D4×C11311yescharacteristic
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—41no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4C2×D4×C11311yescharacteristic
510C22×C4C2×D4×C11311yescharacteristic
511C22×C4C2×D4×C11311yescharacteristic
512C22×C4C2×D4×C11311yescharacteristic
513C22×C4#41×C11312yes—
514C22×C4#41×C11312yes—
515C22×C4C24×C11311yescharacteristic
516M16—28no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8C2×D4×C11312yes—
528C2×C8#41×C11312yes—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—81no—
547C4⋊C4C2×D4×C11312yes—
548C4⋊C4C2×D4×C11312yes—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C42—21no—
558C42—21no—
559C42—42no—
560C42—81no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#123×C11312yes—
574C23#137×C11312yes—
575C23C22×D4×C11311yescharacteristic
576Q8—41no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580D4—44no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—84no—
625C2×C4—84no—
626C2×C4#123×C11312yes—
627C2×C4C22×D4×C11311yescharacteristic
628C2×C4C2×#41×C11311yescharacteristic
629C2×C4C2×#41×C11311yescharacteristic
630C2×C4C2×#41×C11311yescharacteristic
631C2×C4H(5,𝔽2)×C11311yescharacteristic
632C2×C42−1+4×C11311yescharacteristic
633C8—22no—
634C8—22no—
635C8—41no—
636C8—41no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C2×#123×C11311yescharacteristic
652C22D42×C11311yescharacteristic
653C22#547×C11311yescharacteristic
654C22C2×#137×C11311yescharacteristic
655C22#575×C11311yescharacteristic
656C22#577×C11311yescharacteristic
657C22#577×C11311yescharacteristic
658C4—22no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—42no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4#525×C11311yescharacteristic
671C4#539×C11311yescharacteristic
672C4#548×C11311yescharacteristic
673C4#553×C11311yescharacteristic
674C2—42no—
675C2—42no—
676C2C113×#244311yescharacteristic
677C2C113×#309511yescharacteristic
678C2C113×#309911yescharacteristic
679C2C113×#326611yescharacteristic
680C2C113×#327511yescharacteristic
681C2C113×#334411yescharacteristic
682C2C113×#335111yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC22×D4×C113D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#483×C113C2semidirect
2. C2×#428×C113C2semidirect
5. C113×#2097C2semidirect
6. C113×#2085C2semidirect
7. C113×#2076C2semidirect
8. C113×#2036C2semidirect
9. C113×#1927C2semidirect
10. C113×#1919C2semidirect
11. C113×#1894C2semidirect
12. C113×#1873C2semidirect
14. C113×#1853C2semidirect
15. C113×#1853C2semidirect
115. #106×C113D4semidirect
332. #26149C113direct (N × H)
342. C2×#483C2×C113semidirect
343. C2×#428C2×C113semidirect
346. #2097C2×C113semidirect
347. #2085C2×C113semidirect
348. #2076C2×C113semidirect
349. #2036C2×C113semidirect
350. #1927C2×C113semidirect
351. #1919C2×C113semidirect
352. #1894C2×C113semidirect
353. #1873C2×C113semidirect
355. #1853C2×C113semidirect
356. #1853C2×C113semidirect
357. C113#26149direct (N × H)
457. #106D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#483×C1132
C2×#428×C1132
C113×#24172
C113×#23522
C113×#20972
C113×#20852
C113×#20762
C113×#20362
C113×#19272
C113×#19192
C113×#18942
C113×#18732
C113×#18702
C113×#18532
#26149113