Finite Group Databasebeta

← C113×#26130 #43294150

Subgroups — C113×#26130 #43294150

Order 28928.

1008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C113C211yesmaximal, characteristic, complemented
2C22×#106×C113C211yesmaximal, characteristic, complemented
3C113×#2416C211yesmaximal, characteristic
4D4×C4⋊C4×C113C211yesmaximal, characteristic, complemented
5C113×#2094C211yesmaximal, characteristic, complemented
6C113×#2084C211yesmaximal, characteristic, complemented
7C113×#2077C211yesmaximal, characteristic, complemented
8C113×#2034C211yesmaximal, characteristic, complemented
9C113×#1926C211yesmaximal, characteristic, complemented
10C113×#1919C211yesmaximal, characteristic, complemented
11C113×#1893C211yesmaximal, characteristic, complemented
12C113×#1874C211yesmaximal, characteristic, complemented
13C113×#1869C211yesmaximal, characteristic, complemented
14C113×#1853C211yesmaximal, characteristic, complemented
15C113×#1853C211yesmaximal, characteristic, complemented
16C23×C8×C113C2211yescharacteristic
17C2×#121×C113—21no—
18C2×#121×C113C2211yescharacteristic
19C2×#121×C113C2211yescharacteristic
20C2×C4×D4×C113—21no—
21C2×C4×D4×C113C2211yescharacteristic
22C22×C4⋊C4×C113C2211yescharacteristic
23C22×C4⋊C4×C113C2211yescharacteristic
24C22×C4⋊C4×C113C2211yescharacteristic
25#481×C113—24no—
26C2×#106×C113—24no—
27C2×#106×C113C2211yescharacteristic
28C2×#106×C113C2211yescharacteristic
29C2×#106×C113C2211yescharacteristic
30C2×#106×C113C2211yescharacteristic
31C2×#106×C113C2211yescharacteristic
32C2×#106×C113C2211yescharacteristic
33C2×#102×C113C2211yescharacteristic
34C2×#102×C113C2211yescharacteristic
35C2×#102×C113C2211yescharacteristic
36C2×#102×C113C2211yescharacteristic
37C2×C22⋊C8×C113C2211yescharacteristic
38C2×C22⋊C8×C113C2211yescharacteristic
39C2×C22⋊C8×C113C2211yescharacteristic
40#396×C113—21no—
41#394×C113—21no—
42#390×C113C2211yescharacteristic
43#389×C113—21no—
44#389×C113C2211yescharacteristic
45#386×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×C113—21no—
68C23×C4×C113C2311yescharacteristic
69C23×C4×C113C2311yescharacteristic
70C22×C8×C113—22no—
71C22×C8×C113—22no—
72C22×C8×C113—22no—
73C22×C8×C113C2311yescharacteristic
74C22×C8×C113C2311yescharacteristic
75C22×C8×C113C2311yescharacteristic
76C22×C8×C113C2311yescharacteristic
77#121×C113—22no—
78#121×C113—22no—
79#121×C113—22no—
80#121×C113—41no—
81#121×C113—44no—
82C4×D4×C113—22no—
83C4×D4×C113—22no—
84C4×D4×C113—44no—
85C2×C4⋊C4×C113—22no—
86C2×C4⋊C4×C113—22no—
87C2×C4⋊C4×C113—22no—
88C2×C4⋊C4×C113—21no—
89C2×C4⋊C4×C113—21no—
90C2×C4⋊C4×C113—21no—
91C2×C4⋊C4×C113—21no—
92C2×C4⋊C4×C113—21no—
93C2×C4⋊C4×C113—21no—
94C2×C4⋊C4×C113—41no—
95C2×C4⋊C4×C113—41no—
96C2×C4⋊C4×C113—41no—
97C2×C4⋊C4×C113D411yescharacteristic
98C2×C4⋊C4×C113C2311yescharacteristic
99C2×C4⋊C4×C113C2311yescharacteristic
100C2×C4⋊C4×C113C2311yescharacteristic
101C2×C4⋊C4×C113C2311yescharacteristic
102C2×C4⋊C4×C113C2311yescharacteristic
103C2×C4⋊C4×C113C2311yescharacteristic
104C2×C4⋊C4×C113C2311yescharacteristic
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×C113—21no—
111C2×C22⋊C4×C113—21no—
112C2×C22⋊C4×C113D411yescharacteristic
113C2×C22⋊C4×C113D411yescharacteristic
114C2×C42×C113—21no—
115C2×C42×C113C2311yescharacteristic
116#106×C113—22no—
117#106×C113—22no—
118#106×C113—22no—
119#106×C113—22no—
120#106×C113—41no—
121#106×C113D414yescomplemented
122#102×C113—22no—
123#102×C113—22no—
124#102×C113—22no—
125#102×C113—41no—
126C22⋊C8×C113—22no—
127C22⋊C8×C113—22no—
128C22⋊C8×C113—22no—
129#95×C113—21no—
130#95×C113—21no—
131#95×C113—21no—
132#95×C113—21no—
133#95×C113—21no—
134C24×C113—21no—
135C24×C113C2×D411yescharacteristic
136C24×C113C2×D411yescharacteristic
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—42no—
149C2×D4×C113—42no—
150C2×D4×C113—81no—
151C2×D4×C113SD1614yes—
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—21no—
169C22×C4×C113—42no—
170C22×C4×C113—42no—
171C22×C4×C113—42no—
172C22×C4×C113—42no—
173C22×C4×C113—42no—
174C22×C4×C113—42no—
175C22×C4×C113—81no—
176C22×C4×C113—81no—
177C22×C4×C113—81no—
178C22×C4×C113C2×D411yescharacteristic
179C22×C4×C113C2×D411yescharacteristic
180C22×C4×C113C2×D411yescharacteristic
181C22×C4×C113C2×D411yescharacteristic
182C22×C4×C113#4112yes—
183C22×C4×C113#4112yes—
184C22×C4×C113C2411yescharacteristic
185C2×C8×C113—28no—
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×C113—21no—
193C2×C8×C113—21no—
194C2×C8×C113—21no—
195C2×C8×C113—21no—
196C2×C8×C113C2×D412yes—
197C2×C8×C113#4112yes—
198C4⋊C4×C113—22no—
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—21no—
208C4⋊C4×C113—21no—
209C4⋊C4×C113—21no—
210C4⋊C4×C113—21no—
211C4⋊C4×C113—42no—
212C4⋊C4×C113—42no—
213C4⋊C4×C113—42no—
214C4⋊C4×C113—42no—
215C4⋊C4×C113—42no—
216C4⋊C4×C113—81no—
217C4⋊C4×C113C2×D412yes—
218C4⋊C4×C113C2×D412yes—
219C22⋊C4×C113—22no—
220C22⋊C4×C113—22no—
221C22⋊C4×C113—42no—
222C22⋊C4×C113—42no—
223C22⋊C4×C113—42no—
224C22⋊C4×C113—42no—
225C22⋊C4×C113—42no—
226C22⋊C4×C113—42no—
227C22⋊C4×C113—81no—
228C42×C113—21no—
229C42×C113—21no—
230C42×C113—42no—
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—21no—
241C23×C113—41no—
242C23×C113—41no—
243C23×C113—41no—
244C23×C113—41no—
245C23×C113—41no—
246C23×C113—41no—
247C23×C113—41no—
248C23×C113#12312yes—
249C23×C113C2×SD1612yes—
250C23×C113C2×SD1612yes—
251C23×C113AGL(1,ℤ/8)12yes—
252C23×C113C22×D411yescharacteristic
253D4×C113—28no—
254D4×C113—41no—
255D4×C113—41no—
256D4×C113—41no—
257D4×C113—41no—
258D4×C113—84no—
259D4×C113—84no—
260C2×C4×C113—21no—
261C2×C4×C113—21no—
262C2×C4×C113—21no—
263C2×C4×C113—21no—
264C2×C4×C113—22no—
265C2×C4×C113—22no—
266C2×C4×C113—22no—
267C2×C4×C113—22no—
268C2×C4×C113—21no—
269C2×C4×C113—21no—
270C2×C4×C113—21no—
271C2×C4×C113—22no—
272C2×C4×C113—22no—
273C2×C4×C113—21no—
274C2×C4×C113—21no—
275C2×C4×C113—21no—
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—41no—
297C2×C4×C113—41no—
298C2×C4×C113—41no—
299C2×C4×C113—84no—
300C2×C4×C113—84no—
301C2×C4×C113—84no—
302C2×C4×C113#12312yes—
303C2×C4×C113C2×SD1612yes—
304C2×C4×C113C22×D411yescharacteristic
305C2×C4×C113C2×#4111yescharacteristic
306C2×C4×C113C2×#4111yescharacteristic
307C2×C4×C113C2×#4111yescharacteristic
308C2×C4×C113H(5,𝔽2)11yescharacteristic
309C2×C4×C1132−1+411yescharacteristic
310C8×C113—22no—
311C8×C113—22no—
312C8×C113—41no—
313C8×C113—41no—
314C22×C113—22no—
315C22×C113—22no—
316C22×C113—22no—
317C22×C113—22no—
318C22×C113—22no—
319C22×C113—22no—
320C22×C113—22no—
321C22×C113—22no—
322C22×C113—22no—
323C22×C113—41no—
324C22×C113—41no—
325C22×C113—41no—
326C22×C113—41no—
327C22×C113—81no—
328C22×C113—81no—
329C22×C113—81no—
330C22×C113—81no—
331C22×C113—81no—
332C22×C113—81no—
333C22×C113—81no—
334C22×C113#48114yescomplemented
335C22×C113C2×#12311yescharacteristic
336C22×C113D4211yescharacteristic
337C22×C113#54711yescharacteristic
338C22×C113C22×SD1611yescharacteristic
339C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C113#57711yescharacteristic
341C22×C113#57711yescharacteristic
342C4×C113—22no—
343C4×C113—22no—
344C4×C113—41no—
345C4×C113—41no—
346C4×C113—42no—
347C4×C113—42no—
348C4×C113—81no—
349C4×C113—81no—
350C4×C113—81no—
351C4×C113—81no—
352C4×C113—81no—
353C4×C113#52511yescharacteristic
354C4×C113#53911yescharacteristic
355C4×C113#54811yescharacteristic
356C4×C113#55311yescharacteristic
357#26130C11311yesmaximal, characteristic, direct product factor, Sylow
358C2×C113—24no—
359C2×C113—42no—
360C2×C113—161no—
361C2×C113#244311yescharacteristic
362C2×C113C2×#48111yescharacteristic
363C2×C113#309911yescharacteristic
364C2×C113#326511yescharacteristic
365C2×C113D4×SD1611yescharacteristic
366C2×C113#333511yescharacteristic
367C2×C113#334511yescharacteristic
368C2×#481C2×C11311yescharacteristic, complemented
369C22×#106C2×C11311yescharacteristic, complemented
370#2416C2×C11311yescharacteristic
371D4×C4⋊C4C2×C11311yescharacteristic, complemented
372#2094C2×C11311yescharacteristic, complemented
373#2084C2×C11311yescharacteristic, complemented
374#2077C2×C11311yescharacteristic, complemented
375#2034C2×C11311yescharacteristic, complemented
376#1926C2×C11311yescharacteristic, complemented
377#1919C2×C11311yescharacteristic, complemented
378#1893C2×C11311yescharacteristic, complemented
379#1874C2×C11311yescharacteristic, complemented
380#1869C2×C11311yescharacteristic, complemented
381#1853C2×C11311yescharacteristic, complemented
382#1853C2×C11311yescharacteristic, complemented
383C113#2613011yescharacteristic, direct product factor, Sylow
384C23×C8C22×C11311yescharacteristic
385C2×#121—21no—
386C2×#121C22×C11311yescharacteristic
387C2×#121C22×C11311yescharacteristic
388C2×C4×D4—21no—
389C2×C4×D4C22×C11311yescharacteristic
390C22×C4⋊C4C22×C11311yescharacteristic
391C22×C4⋊C4C22×C11311yescharacteristic
392C22×C4⋊C4C22×C11311yescharacteristic
393#481—24no—
394C2×#106—24no—
395C2×#106C22×C11311yescharacteristic
396C2×#106C22×C11311yescharacteristic
397C2×#106C22×C11311yescharacteristic
398C2×#106C22×C11311yescharacteristic
399C2×#106C22×C11311yescharacteristic
400C2×#106C22×C11311yescharacteristic
401C2×#102C22×C11311yescharacteristic
402C2×#102C22×C11311yescharacteristic
403C2×#102C22×C11311yescharacteristic
404C2×#102C22×C11311yescharacteristic
405C2×C22⋊C8C22×C11311yescharacteristic
406C2×C22⋊C8C22×C11311yescharacteristic
407C2×C22⋊C8C22×C11311yescharacteristic
408#396—21no—
409#394—21no—
410#390C22×C11311yescharacteristic
411#389—21no—
412#389C22×C11311yescharacteristic
413#386—21no—
414#385—21no—
415#385—21no—
416#384C22×C11311yescharacteristic
417#380C22×C11311yescharacteristic
418#380C22×C11311yescharacteristic
419#380C22×C11311yescharacteristic
420C4×C4⋊C4C22×C11311yescharacteristic
421#340C22×C11311yescharacteristic
422#340C22×C11311yescharacteristic
423#340C22×C11311yescharacteristic
424#340C22×C11311yescharacteristic
425#340C22×C11311yescharacteristic
426#340C22×C11311yescharacteristic
427#336C22×C11311yescharacteristic
428#336C22×C11311yescharacteristic
429C22×D4—21no—
430C22×D4—21no—
431C22×D4D4×C11311yescharacteristic
432C22×D4C23×C11311yescharacteristic
433C23×C4—21no—
434C23×C4—21no—
435C23×C4—21no—
436C23×C4C23×C11311yescharacteristic
437C23×C4C23×C11311yescharacteristic
438C22×C8—22no—
439C22×C8—22no—
440C22×C8—22no—
441C22×C8C23×C11311yescharacteristic
442C22×C8C23×C11311yescharacteristic
443C22×C8C23×C11311yescharacteristic
444C22×C8C23×C11311yescharacteristic
445#121—22no—
446#121—22no—
447#121—22no—
448#121—41no—
449#121—44no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—44no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—41no—
464C2×C4⋊C4—41no—
465C2×C4⋊C4D4×C11311yescharacteristic
466C2×C4⋊C4C23×C11311yescharacteristic
467C2×C4⋊C4C23×C11311yescharacteristic
468C2×C4⋊C4C23×C11311yescharacteristic
469C2×C4⋊C4C23×C11311yescharacteristic
470C2×C4⋊C4C23×C11311yescharacteristic
471C2×C4⋊C4C23×C11311yescharacteristic
472C2×C4⋊C4C23×C11311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4D4×C11311yescharacteristic
481C2×C22⋊C4D4×C11311yescharacteristic
482C2×C42—21no—
483C2×C42C23×C11311yescharacteristic
484#106—22no—
485#106—22no—
486#106—22no—
487#106—22no—
488#106—41no—
489#106D4×C11314yescomplemented
490#102—22no—
491#102—22no—
492#102—22no—
493#102—41no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502C24—21no—
503C24C2×D4×C11311yescharacteristic
504C24C2×D4×C11311yescharacteristic
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—81no—
519C2×D4SD16×C11314yes—
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—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4C2×D4×C11311yescharacteristic
547C22×C4C2×D4×C11311yescharacteristic
548C22×C4C2×D4×C11311yescharacteristic
549C22×C4C2×D4×C11311yescharacteristic
550C22×C4#41×C11312yes—
551C22×C4#41×C11312yes—
552C22×C4C24×C11311yescharacteristic
553C2×C8—28no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8C2×D4×C11312yes—
565C2×C8#41×C11312yes—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—81no—
585C4⋊C4C2×D4×C11312yes—
586C4⋊C4C2×D4×C11312yes—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—81no—
596C42—21no—
597C42—21no—
598C42—42no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23#123×C11312yes—
617C23C2×SD16×C11312yes—
618C23C2×SD16×C11312yes—
619C23AGL(1,ℤ/8)×C11312yes—
620C23C22×D4×C11311yescharacteristic
621D4—28no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—84no—
627D4—84no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
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—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—84no—
670C2×C4#123×C11312yes—
671C2×C4C2×SD16×C11312yes—
672C2×C4C22×D4×C11311yescharacteristic
673C2×C4C2×#41×C11311yescharacteristic
674C2×C4C2×#41×C11311yescharacteristic
675C2×C4C2×#41×C11311yescharacteristic
676C2×C4H(5,𝔽2)×C11311yescharacteristic
677C2×C42−1+4×C11311yescharacteristic
678C8—22no—
679C8—22no—
680C8—41no—
681C8—41no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22#481×C11314yescomplemented
703C22C2×#123×C11311yescharacteristic
704C22D42×C11311yescharacteristic
705C22#547×C11311yescharacteristic
706C22C22×SD16×C11311yescharacteristic
707C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
708C22#577×C11311yescharacteristic
709C22#577×C11311yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—42no—
715C4—42no—
716C4—81no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4#525×C11311yescharacteristic
722C4#539×C11311yescharacteristic
723C4#548×C11311yescharacteristic
724C4#553×C11311yescharacteristic
725C2—24no—
726C2—42no—
727C2—161no—
728C2C113×#244311yescharacteristic
729C2C2×#481×C11311yescharacteristic
730C2C113×#309911yescharacteristic
731C2C113×#326511yescharacteristic
732C2D4×SD16×C11311yescharacteristic
733C2C113×#333511yescharacteristic
734C2C113×#334511yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#2416C2
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. C22×#106×C113C2semidirect
4. D4×C4⋊C4×C113C2semidirect
5. C113×#2094C2semidirect
6. C113×#2084C2semidirect
7. C113×#2077C2semidirect
8. C113×#2034C2semidirect
9. C113×#1926C2semidirect
10. C113×#1919C2semidirect
11. C113×#1893C2semidirect
12. C113×#1874C2semidirect
13. C113×#1869C2semidirect
14. C113×#1853C2semidirect
15. C113×#1853C2semidirect
121. #106×C113D4semidirect
334. C22×C113#481semidirect
357. #26130C113direct (N × H)
368. C2×#481C2×C113semidirect
369. C22×#106C2×C113semidirect
371. D4×C4⋊C4C2×C113semidirect
372. #2094C2×C113semidirect
373. #2084C2×C113semidirect
374. #2077C2×C113semidirect
375. #2034C2×C113semidirect
376. #1926C2×C113semidirect
377. #1919C2×C113semidirect
378. #1893C2×C113semidirect
379. #1874C2×C113semidirect
380. #1869C2×C113semidirect
381. #1853C2×C113semidirect
382. #1853C2×C113semidirect
383. C113#26130direct (N × H)
489. #106D4×C113semidirect
702. C22#481×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1132
C22×#106×C1132
C113×#24162
D4×C4⋊C4×C1132
C113×#20942
C113×#20842
C113×#20772
C113×#20342
C113×#19262
C113×#19192
C113×#18932
C113×#18742
C113×#18692
C113×#18532
#26130113