Finite Group Databasebeta

← C113×#26146 #43294166

Subgroups — C113×#26146 #43294166

Order 28928.

954 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C113C211yesmaximal, characteristic, complemented
2C2×#428×C113C211yesmaximal, characteristic, complemented
3C113×#2414C211yesmaximal, characteristic
4D4×C4⋊C4×C113C211yesmaximal, characteristic, complemented
5C113×#2093C211yesmaximal, characteristic, complemented
6C113×#2084C211yesmaximal, characteristic, complemented
7C113×#2076C211yesmaximal, characteristic, complemented
8C113×#2034C211yesmaximal, characteristic, complemented
9C113×#1925C211yesmaximal, characteristic, complemented
10C113×#1920C211yesmaximal, characteristic, complemented
11C113×#1895C211yesmaximal, characteristic, complemented
12C113×#1874C211yesmaximal, characteristic, complemented
13C113×#1870C211yesmaximal, characteristic, complemented
14C113×#1854C211yesmaximal, characteristic, complemented
15C113×#1852C211yesmaximal, characteristic, complemented
16C22×M16×C113C2211yescharacteristic
17C2×#121×C113C2211yescharacteristic
18C2×#121×C113C2211yescharacteristic
19C2×C4×D4×C113—21no—
20C2×C4×D4×C113C2211yescharacteristic
21C2×#117×C113C2211yescharacteristic
22C22×C4⋊C4×C113C2211yescharacteristic
23C22×C4⋊C4×C113C2211yescharacteristic
24#481×C113—24no—
25#428×C113—24no—
26C2×#107×C113C2211yescharacteristic
27C2×#107×C113C2211yescharacteristic
28C2×#107×C113C2211yescharacteristic
29C2×#106×C113C2211yescharacteristic
30C2×#106×C113C2211yescharacteristic
31C2×#106×C113C2211yescharacteristic
32C2×#102×C113C2211yescharacteristic
33C2×#102×C113C2211yescharacteristic
34C2×#102×C113C2211yescharacteristic
35C2×#102×C113C2211yescharacteristic
36C2×C22⋊C8×C113C2211yescharacteristic
37C2×C22⋊C8×C113C2211yescharacteristic
38C2×C22⋊C8×C113C2211yescharacteristic
39#394×C113—21no—
40#392×C113—21no—
41#390×C113—21no—
42#390×C113C2211yescharacteristic
43#389×C113—21no—
44#389×C113C2211yescharacteristic
45#388×C113—21no—
46#385×C113—21no—
47#385×C113—21no—
48#384×C113C2211yescharacteristic
49#380×C113C2211yescharacteristic
50#380×C113C2211yescharacteristic
51#380×C113C2211yescharacteristic
52C4×C4⋊C4×C113C2211yescharacteristic
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×D4×C113—21no—
62C22×D4×C113—21no—
63C22×D4×C113D411yescharacteristic
64C22×D4×C113C2311yescharacteristic
65C23×C4×C113—21no—
66C23×C4×C113—21no—
67C23×C4×C113C2311yescharacteristic
68C23×C4×C113C2311yescharacteristic
69C2×M16×C113—22no—
70C2×M16×C113—22no—
71C2×M16×C113—22no—
72C22×C8×C113C2311yescharacteristic
73C22×C8×C113C2311yescharacteristic
74C22×C8×C113C2311yescharacteristic
75C22×C8×C113C2311yescharacteristic
76#121×C113—22no—
77#121×C113—22no—
78#121×C113—22no—
79#121×C113—41no—
80C4×D4×C113—22no—
81C4×D4×C113—22no—
82C4×D4×C113—44no—
83#117×C113—22no—
84#117×C113—41no—
85C2×C4⋊C4×C113—22no—
86C2×C4⋊C4×C113—22no—
87C2×C4⋊C4×C113—21no—
88C2×C4⋊C4×C113—21no—
89C2×C4⋊C4×C113—21no—
90C2×C4⋊C4×C113—21no—
91C2×C4⋊C4×C113—21no—
92C2×C4⋊C4×C113—41no—
93C2×C4⋊C4×C113—41no—
94C2×C4⋊C4×C113D411yescharacteristic
95C2×C4⋊C4×C113C2311yescharacteristic
96C2×C4⋊C4×C113C2311yescharacteristic
97C2×C4⋊C4×C113C2311yescharacteristic
98C2×C4⋊C4×C113C2311yescharacteristic
99C2×C4⋊C4×C113C2311yescharacteristic
100C2×C4⋊C4×C113C2311yescharacteristic
101C2×C4⋊C4×C113C2311yescharacteristic
102C2×C22⋊C4×C113—21no—
103C2×C22⋊C4×C113—21no—
104C2×C22⋊C4×C113—21no—
105C2×C22⋊C4×C113—21no—
106C2×C22⋊C4×C113—21no—
107C2×C22⋊C4×C113—21no—
108C2×C22⋊C4×C113—21no—
109C2×C22⋊C4×C113—21no—
110C2×C22⋊C4×C113D411yescharacteristic
111C2×C22⋊C4×C113D411yescharacteristic
112C2×C42×C113—21no—
113C2×C42×C113—21no—
114C2×C42×C113C2311yescharacteristic
115#107×C113—22no—
116#107×C113—22no—
117#107×C113—41no—
118#106×C113—22no—
119#106×C113—22no—
120#106×C113D414yescomplemented
121#102×C113—22no—
122#102×C113—22no—
123#102×C113—22no—
124#102×C113—41no—
125C22⋊C8×C113—22no—
126C22⋊C8×C113—22no—
127C22⋊C8×C113—22no—
128#95×C113—21no—
129#95×C113—21no—
130#95×C113—21no—
131#95×C113—21no—
132#95×C113—21no—
133C24×C113—21no—
134C24×C113C2×D411yescharacteristic
135C24×C113C2×D411yescharacteristic
136C2×D4×C113—22no—
137C2×D4×C113—22no—
138C2×D4×C113—22no—
139C2×D4×C113—21no—
140C2×D4×C113—21no—
141C2×D4×C113—21no—
142C2×D4×C113—21no—
143C2×D4×C113—21no—
144C2×D4×C113—21no—
145C2×D4×C113—42no—
146C2×D4×C113—42no—
147C2×D4×C113—42no—
148C2×D4×C113—81no—
149C2×D4×C113—81no—
150C2×D4×C113—81no—
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—21no—
162C22×C4×C113—21no—
163C22×C4×C113—21no—
164C22×C4×C113—21no—
165C22×C4×C113—21no—
166C22×C4×C113—21no—
167C22×C4×C113—21no—
168C22×C4×C113—42no—
169C22×C4×C113—42no—
170C22×C4×C113—42no—
171C22×C4×C113—42no—
172C22×C4×C113—81no—
173C22×C4×C113—81no—
174C22×C4×C113C2×D411yescharacteristic
175C22×C4×C113C2×D411yescharacteristic
176C22×C4×C113C2×D411yescharacteristic
177C22×C4×C113C2×D411yescharacteristic
178C22×C4×C113#4112yes—
179C22×C4×C113#4112yes—
180C22×C4×C113C2411yescharacteristic
181M16×C113—28no—
182C2×C8×C113—21no—
183C2×C8×C113—21no—
184C2×C8×C113—21no—
185C2×C8×C113—21no—
186C2×C8×C113—21no—
187C2×C8×C113—21no—
188C2×C8×C113—21no—
189C2×C8×C113—21no—
190C2×C8×C113—21no—
191C2×C8×C113—21no—
192C2×C8×C113C2×D412yes—
193C2×C8×C113#4112yes—
194C4⋊C4×C113—22no—
195C4⋊C4×C113—21no—
196C4⋊C4×C113—21no—
197C4⋊C4×C113—21no—
198C4⋊C4×C113—21no—
199C4⋊C4×C113—21no—
200C4⋊C4×C113—21no—
201C4⋊C4×C113—21no—
202C4⋊C4×C113—21no—
203C4⋊C4×C113—21no—
204C4⋊C4×C113—21no—
205C4⋊C4×C113—21no—
206C4⋊C4×C113—21no—
207C4⋊C4×C113—42no—
208C4⋊C4×C113—42no—
209C4⋊C4×C113—42no—
210C4⋊C4×C113—81no—
211C4⋊C4×C113—81no—
212C4⋊C4×C113C2×D412yes—
213C4⋊C4×C113C2×D412yes—
214C22⋊C4×C113—22no—
215C22⋊C4×C113—22no—
216C22⋊C4×C113—42no—
217C22⋊C4×C113—42no—
218C22⋊C4×C113—42no—
219C22⋊C4×C113—42no—
220C22⋊C4×C113—42no—
221C22⋊C4×C113—42no—
222C22⋊C4×C113—81no—
223C22⋊C4×C113—81no—
224C42×C113—21no—
225C42×C113—21no—
226C42×C113—42no—
227C42×C113—42no—
228C23×C113—21no—
229C23×C113—21no—
230C23×C113—21no—
231C23×C113—21no—
232C23×C113—21no—
233C23×C113—21no—
234C23×C113—21no—
235C23×C113—21no—
236C23×C113—21no—
237C23×C113—21no—
238C23×C113—21no—
239C23×C113—21no—
240C23×C113—41no—
241C23×C113—41no—
242C23×C113—41no—
243C23×C113—41no—
244C23×C113—41no—
245C23×C113—41no—
246C23×C113—41no—
247C23×C113#12312yes—
248C23×C113#13712yes—
249C23×C113C22×D411yescharacteristic
250D4×C113—28no—
251D4×C113—41no—
252D4×C113—41no—
253D4×C113—41no—
254D4×C113—41no—
255D4×C113—84no—
256D4×C113—84no—
257C2×C4×C113—21no—
258C2×C4×C113—21no—
259C2×C4×C113—21no—
260C2×C4×C113—21no—
261C2×C4×C113—22no—
262C2×C4×C113—22no—
263C2×C4×C113—22no—
264C2×C4×C113—22no—
265C2×C4×C113—21no—
266C2×C4×C113—21no—
267C2×C4×C113—22no—
268C2×C4×C113—21no—
269C2×C4×C113—22no—
270C2×C4×C113—21no—
271C2×C4×C113—21no—
272C2×C4×C113—21no—
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—41no—
283C2×C4×C113—41no—
284C2×C4×C113—41no—
285C2×C4×C113—41no—
286C2×C4×C113—41no—
287C2×C4×C113—41no—
288C2×C4×C113—41no—
289C2×C4×C113—41no—
290C2×C4×C113—41no—
291C2×C4×C113—41no—
292C2×C4×C113—41no—
293C2×C4×C113—41no—
294C2×C4×C113—41no—
295C2×C4×C113—41no—
296C2×C4×C113—84no—
297C2×C4×C113—84no—
298C2×C4×C113#12312yes—
299C2×C4×C113AGL(1,ℤ/8)12yes—
300C2×C4×C113C22×D411yescharacteristic
301C2×C4×C113C2×#4111yescharacteristic
302C2×C4×C113C2×#4111yescharacteristic
303C2×C4×C113C2×#4111yescharacteristic
304C2×C4×C113H(5,𝔽2)11yescharacteristic
305C2×C4×C1132−1+411yescharacteristic
306C8×C113—22no—
307C8×C113—22no—
308C8×C113—41no—
309C8×C113—41no—
310C22×C113—22no—
311C22×C113—22no—
312C22×C113—22no—
313C22×C113—22no—
314C22×C113—22no—
315C22×C113—22no—
316C22×C113—41no—
317C22×C113—41no—
318C22×C113—41no—
319C22×C113—41no—
320C22×C113—41no—
321C22×C113—41no—
322C22×C113—41no—
323C22×C113—41no—
324C22×C113—81no—
325C22×C113—81no—
326C22×C113—81no—
327C22×C113—81no—
328C22×C113—81no—
329C22×C113—81no—
330C22×C113—81no—
331C22×C113C2×#12311yescharacteristic
332C22×C113D4211yescharacteristic
333C22×C113#54711yescharacteristic
334C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C113C2×#13711yescharacteristic
336C22×C113#57611yescharacteristic
337C22×C113#57711yescharacteristic
338C4×C113—22no—
339C4×C113—22no—
340C4×C113—41no—
341C4×C113—41no—
342C4×C113—42no—
343C4×C113—42no—
344C4×C113—81no—
345C4×C113—81no—
346C4×C113—81no—
347C4×C113—81no—
348C4×C113—81no—
349C4×C113#52511yescharacteristic
350C4×C113#53911yescharacteristic
351C4×C113#54811yescharacteristic
352C4×C113#55311yescharacteristic
353#26146C11311yesmaximal, characteristic, direct product factor, Sylow
354C2×C113—42no—
355C2×C113—42no—
356C2×C113—161no—
357C2×C113#244311yescharacteristic
358C2×C113#309211yescharacteristic
359C2×C113#309611yescharacteristic
360C2×C113#326611yescharacteristic
361C2×C113#327411yescharacteristic
362C2×C113#334611yescharacteristic
363C2×C113#335411yescharacteristic
364C2×#481C2×C11311yescharacteristic, complemented
365C2×#428C2×C11311yescharacteristic, complemented
366#2414C2×C11311yescharacteristic
367D4×C4⋊C4C2×C11311yescharacteristic, complemented
368#2093C2×C11311yescharacteristic, complemented
369#2084C2×C11311yescharacteristic, complemented
370#2076C2×C11311yescharacteristic, complemented
371#2034C2×C11311yescharacteristic, complemented
372#1925C2×C11311yescharacteristic, complemented
373#1920C2×C11311yescharacteristic, complemented
374#1895C2×C11311yescharacteristic, complemented
375#1874C2×C11311yescharacteristic, complemented
376#1870C2×C11311yescharacteristic, complemented
377#1854C2×C11311yescharacteristic, complemented
378#1852C2×C11311yescharacteristic, complemented
379C113#2614611yescharacteristic, direct product factor, Sylow
380C22×M16C22×C11311yescharacteristic
381C2×#121C22×C11311yescharacteristic
382C2×#121C22×C11311yescharacteristic
383C2×C4×D4—21no—
384C2×C4×D4C22×C11311yescharacteristic
385C2×#117C22×C11311yescharacteristic
386C22×C4⋊C4C22×C11311yescharacteristic
387C22×C4⋊C4C22×C11311yescharacteristic
388#481—24no—
389#428—24no—
390C2×#107C22×C11311yescharacteristic
391C2×#107C22×C11311yescharacteristic
392C2×#107C22×C11311yescharacteristic
393C2×#106C22×C11311yescharacteristic
394C2×#106C22×C11311yescharacteristic
395C2×#106C22×C11311yescharacteristic
396C2×#102C22×C11311yescharacteristic
397C2×#102C22×C11311yescharacteristic
398C2×#102C22×C11311yescharacteristic
399C2×#102C22×C11311yescharacteristic
400C2×C22⋊C8C22×C11311yescharacteristic
401C2×C22⋊C8C22×C11311yescharacteristic
402C2×C22⋊C8C22×C11311yescharacteristic
403#394—21no—
404#392—21no—
405#390—21no—
406#390C22×C11311yescharacteristic
407#389—21no—
408#389C22×C11311yescharacteristic
409#388—21no—
410#385—21no—
411#385—21no—
412#384C22×C11311yescharacteristic
413#380C22×C11311yescharacteristic
414#380C22×C11311yescharacteristic
415#380C22×C11311yescharacteristic
416C4×C4⋊C4C22×C11311yescharacteristic
417#340C22×C11311yescharacteristic
418#340C22×C11311yescharacteristic
419#340C22×C11311yescharacteristic
420#340C22×C11311yescharacteristic
421#340C22×C11311yescharacteristic
422#340C22×C11311yescharacteristic
423#336C22×C11311yescharacteristic
424#336C22×C11311yescharacteristic
425C22×D4—21no—
426C22×D4—21no—
427C22×D4D4×C11311yescharacteristic
428C22×D4C23×C11311yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4C23×C11311yescharacteristic
432C23×C4C23×C11311yescharacteristic
433C2×M16—22no—
434C2×M16—22no—
435C2×M16—22no—
436C22×C8C23×C11311yescharacteristic
437C22×C8C23×C11311yescharacteristic
438C22×C8C23×C11311yescharacteristic
439C22×C8C23×C11311yescharacteristic
440#121—22no—
441#121—22no—
442#121—22no—
443#121—41no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—44no—
447#117—22no—
448#117—41no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4D4×C11311yescharacteristic
459C2×C4⋊C4C23×C11311yescharacteristic
460C2×C4⋊C4C23×C11311yescharacteristic
461C2×C4⋊C4C23×C11311yescharacteristic
462C2×C4⋊C4C23×C11311yescharacteristic
463C2×C4⋊C4C23×C11311yescharacteristic
464C2×C4⋊C4C23×C11311yescharacteristic
465C2×C4⋊C4C23×C11311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4D4×C11311yescharacteristic
475C2×C22⋊C4D4×C11311yescharacteristic
476C2×C42—21no—
477C2×C42—21no—
478C2×C42C23×C11311yescharacteristic
479#107—22no—
480#107—22no—
481#107—41no—
482#106—22no—
483#106—22no—
484#106D4×C11314yescomplemented
485#102—22no—
486#102—22no—
487#102—22no—
488#102—41no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24—21no—
498C24C2×D4×C11311yescharacteristic
499C24C2×D4×C11311yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4—81no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4C2×D4×C11311yescharacteristic
539C22×C4C2×D4×C11311yescharacteristic
540C22×C4C2×D4×C11311yescharacteristic
541C22×C4C2×D4×C11311yescharacteristic
542C22×C4#41×C11312yes—
543C22×C4#41×C11312yes—
544C22×C4C24×C11311yescharacteristic
545M16—28no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8C2×D4×C11312yes—
557C2×C8#41×C11312yes—
558C4⋊C4—22no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—81no—
575C4⋊C4—81no—
576C4⋊C4C2×D4×C11312yes—
577C4⋊C4C2×D4×C11312yes—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C42—21no—
589C42—21no—
590C42—42no—
591C42—42no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23#123×C11312yes—
612C23#137×C11312yes—
613C23C22×D4×C11311yescharacteristic
614D4—28no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—84no—
620D4—84no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4#123×C11312yes—
663C2×C4AGL(1,ℤ/8)×C11312yes—
664C2×C4C22×D4×C11311yescharacteristic
665C2×C4C2×#41×C11311yescharacteristic
666C2×C4C2×#41×C11311yescharacteristic
667C2×C4C2×#41×C11311yescharacteristic
668C2×C4H(5,𝔽2)×C11311yescharacteristic
669C2×C42−1+4×C11311yescharacteristic
670C8—22no—
671C8—22no—
672C8—41no—
673C8—41no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22C2×#123×C11311yescharacteristic
696C22D42×C11311yescharacteristic
697C22#547×C11311yescharacteristic
698C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
699C22C2×#137×C11311yescharacteristic
700C22#576×C11311yescharacteristic
701C22#577×C11311yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—42no—
707C4—42no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4—81no—
713C4#525×C11311yescharacteristic
714C4#539×C11311yescharacteristic
715C4#548×C11311yescharacteristic
716C4#553×C11311yescharacteristic
717C2—42no—
718C2—42no—
719C2—161no—
720C2C113×#244311yescharacteristic
721C2C113×#309211yescharacteristic
722C2C113×#309611yescharacteristic
723C2C113×#326611yescharacteristic
724C2C113×#327411yescharacteristic
725C2C113×#334611yescharacteristic
726C2C113×#335411yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#2414C2
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×#481×C113C2semidirect
2. C2×#428×C113C2semidirect
4. D4×C4⋊C4×C113C2semidirect
5. C113×#2093C2semidirect
6. C113×#2084C2semidirect
7. C113×#2076C2semidirect
8. C113×#2034C2semidirect
9. C113×#1925C2semidirect
10. C113×#1920C2semidirect
11. C113×#1895C2semidirect
12. C113×#1874C2semidirect
13. C113×#1870C2semidirect
14. C113×#1854C2semidirect
15. C113×#1852C2semidirect
120. #106×C113D4semidirect
353. #26146C113direct (N × H)
364. C2×#481C2×C113semidirect
365. C2×#428C2×C113semidirect
367. D4×C4⋊C4C2×C113semidirect
368. #2093C2×C113semidirect
369. #2084C2×C113semidirect
370. #2076C2×C113semidirect
371. #2034C2×C113semidirect
372. #1925C2×C113semidirect
373. #1920C2×C113semidirect
374. #1895C2×C113semidirect
375. #1874C2×C113semidirect
376. #1870C2×C113semidirect
377. #1854C2×C113semidirect
378. #1852C2×C113semidirect
379. C113#26146direct (N × H)
484. #106D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1132
C2×#428×C1132
C113×#24142
D4×C4⋊C4×C1132
C113×#20932
C113×#20842
C113×#20762
C113×#20342
C113×#19252
C113×#19202
C113×#18952
C113×#18742
C113×#18702
C113×#18542
C113×#18522
#26146113