Finite Group Databasebeta

← C113×#22847 #43290867

Subgroups — C113×#22847 #43290867

Order 28928.

1178 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C113C211yesmaximal, characteristic, complemented
2C2×C8×D4×C113C211yesmaximal, characteristic, complemented
3C2×#408×C113C211yesmaximal, characteristic, complemented
4C2×#408×C113C211yesmaximal, characteristic, complemented
5C113×#2388C211yesmaximal, characteristic
6C113×#1954C211yesmaximal, characteristic, complemented
7C113×#1924C211yesmaximal, characteristic, complemented
8C113×#1923C211yesmaximal, characteristic, complemented
9C113×#1870C211yesmaximal, characteristic, complemented
10C113×#1869C211yesmaximal, characteristic, complemented
11C113×#1869C211yesmaximal, characteristic, complemented
12C113×#1851C211yesmaximal, characteristic, complemented
13C113×#1850C211yesmaximal, characteristic, complemented
14C113×#1753C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C113C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×M16×C113C2211yescharacteristic
18C22×M16×C113C2211yescharacteristic
19C23×C8×C113C2211yescharacteristic
20C23×C8×C113C2211yescharacteristic
21C23×C8×C113C2211yescharacteristic
22C2×C4×D4×C113C2211yescharacteristic
23C2×C4×D4×C113C2211yescharacteristic
24C2×C4×D4×C113C2211yescharacteristic
25#435×C113—24no—
26C8×D4×C113—24no—
27C2×C4⋊C8×C113C2211yescharacteristic
28C2×C4⋊C8×C113C2211yescharacteristic
29C2×C4⋊C8×C113C2211yescharacteristic
30#408×C113—24no—
31#408×C113—24no—
32C2×C22⋊C8×C113C2211yescharacteristic
33C2×C22⋊C8×C113C2211yescharacteristic
34C2×C22⋊C8×C113C2211yescharacteristic
35C2×C22⋊C8×C113C2211yescharacteristic
36C2×C22⋊C8×C113C2211yescharacteristic
37C2×C22⋊C8×C113C2211yescharacteristic
38C2×C22⋊C8×C113C2211yescharacteristic
39C2×C22⋊C8×C113C2211yescharacteristic
40C2×C22⋊C8×C113C2211yescharacteristic
41C2×C22⋊C8×C113C2211yescharacteristic
42C2×C22⋊C8×C113C2211yescharacteristic
43C2×#97×C113C2211yescharacteristic
44C2×C4×C8×C113C2211yescharacteristic
45C2×C4×C8×C113C2211yescharacteristic
46#395×C113C411yescharacteristic
47#394×C113C411yescharacteristic
48#394×C113C411yescharacteristic
49#394×C113C411yescharacteristic
50#393×C113C411yescharacteristic
51#392×C113C411yescharacteristic
52#392×C113C411yescharacteristic
53#392×C113C411yescharacteristic
54C4×C22⋊C4×C113C2211yescharacteristic
55C4×C22⋊C4×C113C2211yescharacteristic
56C4×C22⋊C4×C113C2211yescharacteristic
57#336×C113C2211yescharacteristic
58#336×C113C2211yescharacteristic
59#336×C113C2211yescharacteristic
60#336×C113C2211yescharacteristic
61#336×C113C2211yescharacteristic
62#336×C113C2211yescharacteristic
63C2×#41×C113—22no—
64C2×#41×C113—22no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—41no—
68C2×#41×C113—41no—
69C22×Q8×C113C2×C411yescharacteristic
70C22×D4×C113C2×C411yescharacteristic
71C22×D4×C113C2×C411yescharacteristic
72C22×D4×C113C2×C411yescharacteristic
73C22×D4×C113C2×C411yescharacteristic
74C22×D4×C113C2×C411yescharacteristic
75C22×D4×C113C2×C411yescharacteristic
76C23×C4×C113C2311yescharacteristic
77C23×C4×C113C2311yescharacteristic
78C23×C4×C113C2311yescharacteristic
79C23×C4×C113C2311yescharacteristic
80C2×M16×C113—22no—
81C2×M16×C113—22no—
82C2×M16×C113—22no—
83C2×M16×C113—22no—
84C2×M16×C113—41no—
85C2×M16×C113—41no—
86C22×C8×C113—22no—
87C22×C8×C113—22no—
88C22×C8×C113—22no—
89C22×C8×C113—22no—
90C22×C8×C113—22no—
91C22×C8×C113—22no—
92C22×C8×C113—41no—
93C22×C8×C113—41no—
94C22×C8×C113—41no—
95C22×C8×C113C2311yescharacteristic
96C22×C8×C113C2311yescharacteristic
97C22×C8×C113C2311yescharacteristic
98C22×C8×C113C2311yescharacteristic
99C22×C8×C113C2311yescharacteristic
100C22×C8×C113C2311yescharacteristic
101C22×C8×C113C2311yescharacteristic
102C22×C8×C113C2311yescharacteristic
103C4×D4×C113—22no—
104C4×D4×C113—22no—
105C4×D4×C113—22no—
106C4×D4×C113—22no—
107C4×D4×C113—41no—
108C4×D4×C113—41no—
109C2×C4⋊C4×C113C2×C411yescharacteristic
110C2×C4⋊C4×C113C2×C411yescharacteristic
111C2×C4⋊C4×C113C2×C411yescharacteristic
112C2×C22⋊C4×C113C2×C411yescharacteristic
113C2×C22⋊C4×C113C2×C411yescharacteristic
114C2×C22⋊C4×C113C2×C411yescharacteristic
115C2×C22⋊C4×C113C2×C411yescharacteristic
116C2×C22⋊C4×C113C2×C411yescharacteristic
117C2×C22⋊C4×C113C2×C411yescharacteristic
118C2×C22⋊C4×C113C2×C411yescharacteristic
119C2×C22⋊C4×C113C2×C411yescharacteristic
120C2×C22⋊C4×C113C2×C411yescharacteristic
121C2×C22⋊C4×C113C2×C411yescharacteristic
122C2×C22⋊C4×C113C2×C411yescharacteristic
123C2×C22⋊C4×C113C2×C411yescharacteristic
124C2×C42×C113C2311yescharacteristic
125C2×C42×C113C2311yescharacteristic
126C2×C42×C113C2311yescharacteristic
127C4⋊C8×C113—22no—
128C4⋊C8×C113—22no—
129C4⋊C8×C113—41no—
130C22⋊C8×C113—22no—
131C22⋊C8×C113—22no—
132C22⋊C8×C113—22no—
133C22⋊C8×C113—22no—
134C22⋊C8×C113—22no—
135C22⋊C8×C113—22no—
136C22⋊C8×C113—22no—
137C22⋊C8×C113—22no—
138C22⋊C8×C113—41no—
139C22⋊C8×C113D414yescomplemented
140C22⋊C8×C113D414yescomplemented
141#97×C113—22no—
142C4×C8×C113—22no—
143C4×C8×C113—41no—
144#95×C113C2×C411yescharacteristic
145#95×C113C2×C411yescharacteristic
146#95×C113C2×C411yescharacteristic
147#95×C113C2×C411yescharacteristic
148#95×C113C2×C411yescharacteristic
149#95×C113C2×C411yescharacteristic
150C24×C113C22×C411yescharacteristic
151C24×C113C22×C411yescharacteristic
152C24×C113C22×C411yescharacteristic
153C24×C113C22×C411yescharacteristic
154#41×C113—44no—
155#41×C113—44no—
156#41×C113—44no—
157#41×C113—44no—
158C2×Q8×C113—22no—
159C2×Q8×C113—22no—
160C2×Q8×C113—41no—
161C2×D4×C113—22no—
162C2×D4×C113—22no—
163C2×D4×C113—22no—
164C2×D4×C113—22no—
165C2×D4×C113—22no—
166C2×D4×C113—22no—
167C2×D4×C113—22no—
168C2×D4×C113—22no—
169C2×D4×C113—22no—
170C2×D4×C113—22no—
171C2×D4×C113—22no—
172C2×D4×C113—22no—
173C2×D4×C113—22no—
174C2×D4×C113—41no—
175C2×D4×C113—41no—
176C2×D4×C113—41no—
177C2×D4×C113—41no—
178C2×D4×C113—41no—
179C22×C4×C113—21no—
180C22×C4×C113—21no—
181C22×C4×C113—21no—
182C22×C4×C113—21no—
183C22×C4×C113—21no—
184C22×C4×C113—21no—
185C22×C4×C113—21no—
186C22×C4×C113—21no—
187C22×C4×C113—21no—
188C22×C4×C113—21no—
189C22×C4×C113—21no—
190C22×C4×C113—21no—
191C22×C4×C113—21no—
192C22×C4×C113—21no—
193C22×C4×C113—21no—
194C22×C4×C113—21no—
195C22×C4×C113—21no—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113C22×C411yescharacteristic
200C22×C4×C113C22×C411yescharacteristic
201C22×C4×C113C22×C411yescharacteristic
202C22×C4×C113C22×C411yescharacteristic
203C22×C4×C113C22×C411yescharacteristic
204C22×C4×C113C22×C411yescharacteristic
205C22×C4×C113C22×C411yescharacteristic
206C22×C4×C113C22×C411yescharacteristic
207C22×C4×C113C22×C411yescharacteristic
208C22×C4×C113C22×C411yescharacteristic
209C22×C4×C113C2×D412yes—
210C22×C4×C113C2×D412yes—
211C22×C4×C113#4112yes—
212C22×C4×C113#4112yes—
213C22×C4×C113C2411yescharacteristic
214M16×C113—44no—
215M16×C113—44no—
216C2×C8×C113—21no—
217C2×C8×C113—21no—
218C2×C8×C113—21no—
219C2×C8×C113—21no—
220C2×C8×C113—21no—
221C2×C8×C113—21no—
222C2×C8×C113—21no—
223C2×C8×C113—21no—
224C2×C8×C113—21no—
225C2×C8×C113—21no—
226C2×C8×C113—21no—
227C2×C8×C113—21no—
228C2×C8×C113—21no—
229C2×C8×C113—21no—
230C2×C8×C113—21no—
231C2×C8×C113—21no—
232C2×C8×C113—21no—
233C2×C8×C113—21no—
234C2×C8×C113—21no—
235C2×C8×C113—21no—
236C2×C8×C113—44no—
237C2×C8×C113—44no—
238C2×C8×C113—44no—
239C2×C8×C113C2×D412yes—
240C2×C8×C113C2×D412yes—
241C2×C8×C113C2×D412yes—
242C2×C8×C113C2×D412yes—
243C4⋊C4×C113—22no—
244C4⋊C4×C113—22no—
245C4⋊C4×C113—41no—
246C22⋊C4×C113—22no—
247C22⋊C4×C113—22no—
248C22⋊C4×C113—22no—
249C22⋊C4×C113—22no—
250C22⋊C4×C113—22no—
251C22⋊C4×C113—22no—
252C22⋊C4×C113—22no—
253C22⋊C4×C113—22no—
254C22⋊C4×C113—41no—
255C22⋊C4×C113—41no—
256C22⋊C4×C113—41no—
257C22⋊C4×C113—41no—
258C42×C113—21no—
259C42×C113—21no—
260C42×C113—21no—
261C42×C113—21no—
262C42×C113—21no—
263C42×C113—21no—
264C23×C113—21no—
265C23×C113—21no—
266C23×C113—21no—
267C23×C113—21no—
268C23×C113—21no—
269C23×C113—21no—
270C23×C113—21no—
271C23×C113—21no—
272C23×C113—21no—
273C23×C113—21no—
274C23×C113—21no—
275C23×C113—21no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—21no—
279C23×C113—21no—
280C23×C113—21no—
281C23×C113—21no—
282C23×C113—21no—
283C23×C113—21no—
284C23×C113—21no—
285C23×C113—21no—
286C23×C113—21no—
287C23×C113—21no—
288C23×C113—21no—
289C23×C113C4×D412yes—
290C23×C113C4×D412yes—
291C23×C113#13112yes—
292C23×C113C23×C411yescharacteristic
293Q8×C113—44no—
294D4×C113—28no—
295D4×C113—44no—
296D4×C113—44no—
297D4×C113—44no—
298D4×C113—44no—
299D4×C113—44no—
300C2×C4×C113—21no—
301C2×C4×C113—21no—
302C2×C4×C113—21no—
303C2×C4×C113—21no—
304C2×C4×C113—21no—
305C2×C4×C113—21no—
306C2×C4×C113—21no—
307C2×C4×C113—21no—
308C2×C4×C113—22no—
309C2×C4×C113—22no—
310C2×C4×C113—22no—
311C2×C4×C113—22no—
312C2×C4×C113—22no—
313C2×C4×C113—22no—
314C2×C4×C113—22no—
315C2×C4×C113—22no—
316C2×C4×C113—21no—
317C2×C4×C113—21no—
318C2×C4×C113—21no—
319C2×C4×C113—21no—
320C2×C4×C113—21no—
321C2×C4×C113—21no—
322C2×C4×C113—21no—
323C2×C4×C113—21no—
324C2×C4×C113—21no—
325C2×C4×C113—21no—
326C2×C4×C113—21no—
327C2×C4×C113—21no—
328C2×C4×C113—21no—
329C2×C4×C113—21no—
330C2×C4×C113—21no—
331C2×C4×C113—21no—
332C2×C4×C113—21no—
333C2×C4×C113—21no—
334C2×C4×C113—41no—
335C2×C4×C113—41no—
336C2×C4×C113—41no—
337C2×C4×C113—41no—
338C2×C4×C113—41no—
339C2×C4×C113—41no—
340C2×C4×C113—41no—
341C2×C4×C113—41no—
342C2×C4×C113C4×D412yes—
343C2×C4×C113C4×D412yes—
344C2×C4×C113#13112yes—
345C2×C4×C113#13112yes—
346C2×C4×C113C22×D411yescharacteristic
347C2×C4×C113C22×D411yescharacteristic
348C2×C4×C113C2×#4111yescharacteristic
349C2×C4×C113C2×#4111yescharacteristic
350C2×C4×C113H(5,𝔽2)11yescharacteristic
351C2×C4×C113H(5,𝔽2)11yescharacteristic
352C8×C113—22no—
353C8×C113—22no—
354C8×C113—22no—
355C8×C113—22no—
356C8×C113—41no—
357C8×C113—41no—
358C8×C113—41no—
359C8×C113—41no—
360C22×C113—22no—
361C22×C113—22no—
362C22×C113—22no—
363C22×C113—22no—
364C22×C113—22no—
365C22×C113—22no—
366C22×C113—22no—
367C22×C113—22no—
368C22×C113—22no—
369C22×C113—41no—
370C22×C113—41no—
371C22×C113—41no—
372C22×C113—41no—
373C22×C113—41no—
374C22×C113—41no—
375C22×C113—41no—
376C22×C113—41no—
377C22×C113—41no—
378C22×C113—41no—
379C22×C113—41no—
380C22×C113—41no—
381C22×C113—41no—
382C22×C113—41no—
383C22×C113—41no—
384C22×C113—41no—
385C22×C113—41no—
386C22×C113—41no—
387C22×C113—41no—
388C22×C113C2×C4×D411yescharacteristic
389C22×C113C2×C4×D411yescharacteristic
390C22×C113#51811yescharacteristic
391C22×C113C2×#13111yescharacteristic
392C22×C113C2×#13111yescharacteristic
393C22×C113C2×#13111yescharacteristic
394C22×C113#56811yescharacteristic
395C4×C113—22no—
396C4×C113—22no—
397C4×C113—22no—
398C4×C113—22no—
399C4×C113—41no—
400C4×C113—41no—
401C4×C113—41no—
402C4×C113—41no—
403C4×C113—41no—
404C4×C113—41no—
405C4×C113D4211yescharacteristic
406C4×C113#54611yescharacteristic
407C4×C113#54611yescharacteristic
408C4×C113#55111yescharacteristic
409#22847C11311yesmaximal, characteristic, direct product factor, Sylow
410C2×C113—42no—
411C2×C113—42no—
412C2×C113—42no—
413C2×C113—81no—
414C2×C113#235811yescharacteristic
415C2×C113#292911yescharacteristic
416C2×C113#293111yescharacteristic
417C2×C113#293311yescharacteristic
418C2×C113#293511yescharacteristic
419C2×C113#297711yescharacteristic
420C2×C113#298111yescharacteristic
421C2×#435C2×C11311yescharacteristic, complemented
422C2×C8×D4C2×C11311yescharacteristic, complemented
423C2×#408C2×C11311yescharacteristic, complemented
424C2×#408C2×C11311yescharacteristic, complemented
425#2388C2×C11311yescharacteristic
426#1954C2×C11311yescharacteristic, complemented
427#1924C2×C11311yescharacteristic, complemented
428#1923C2×C11311yescharacteristic, complemented
429#1870C2×C11311yescharacteristic, complemented
430#1869C2×C11311yescharacteristic, complemented
431#1869C2×C11311yescharacteristic, complemented
432#1851C2×C11311yescharacteristic, complemented
433#1850C2×C11311yescharacteristic, complemented
434#1753C2×C11311yescharacteristic, complemented
435C8×C22⋊C4C2×C11311yescharacteristic, complemented
436C113#2284711yescharacteristic, direct product factor, Sylow
437C22×#41C22×C11311yescharacteristic
438C22×M16C22×C11311yescharacteristic
439C22×M16C22×C11311yescharacteristic
440C23×C8C22×C11311yescharacteristic
441C23×C8C22×C11311yescharacteristic
442C23×C8C22×C11311yescharacteristic
443C2×C4×D4C22×C11311yescharacteristic
444C2×C4×D4C22×C11311yescharacteristic
445C2×C4×D4C22×C11311yescharacteristic
446#435—24no—
447C8×D4—24no—
448C2×C4⋊C8C22×C11311yescharacteristic
449C2×C4⋊C8C22×C11311yescharacteristic
450C2×C4⋊C8C22×C11311yescharacteristic
451#408—24no—
452#408—24no—
453C2×C22⋊C8C22×C11311yescharacteristic
454C2×C22⋊C8C22×C11311yescharacteristic
455C2×C22⋊C8C22×C11311yescharacteristic
456C2×C22⋊C8C22×C11311yescharacteristic
457C2×C22⋊C8C22×C11311yescharacteristic
458C2×C22⋊C8C22×C11311yescharacteristic
459C2×C22⋊C8C22×C11311yescharacteristic
460C2×C22⋊C8C22×C11311yescharacteristic
461C2×C22⋊C8C22×C11311yescharacteristic
462C2×C22⋊C8C22×C11311yescharacteristic
463C2×C22⋊C8C22×C11311yescharacteristic
464C2×#97C22×C11311yescharacteristic
465C2×C4×C8C22×C11311yescharacteristic
466C2×C4×C8C22×C11311yescharacteristic
467#395C4×C11311yescharacteristic
468#394C4×C11311yescharacteristic
469#394C4×C11311yescharacteristic
470#394C4×C11311yescharacteristic
471#393C4×C11311yescharacteristic
472#392C4×C11311yescharacteristic
473#392C4×C11311yescharacteristic
474#392C4×C11311yescharacteristic
475C4×C22⋊C4C22×C11311yescharacteristic
476C4×C22⋊C4C22×C11311yescharacteristic
477C4×C22⋊C4C22×C11311yescharacteristic
478#336C22×C11311yescharacteristic
479#336C22×C11311yescharacteristic
480#336C22×C11311yescharacteristic
481#336C22×C11311yescharacteristic
482#336C22×C11311yescharacteristic
483#336C22×C11311yescharacteristic
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C22×Q8C2×C4×C11311yescharacteristic
491C22×D4C2×C4×C11311yescharacteristic
492C22×D4C2×C4×C11311yescharacteristic
493C22×D4C2×C4×C11311yescharacteristic
494C22×D4C2×C4×C11311yescharacteristic
495C22×D4C2×C4×C11311yescharacteristic
496C22×D4C2×C4×C11311yescharacteristic
497C23×C4C23×C11311yescharacteristic
498C23×C4C23×C11311yescharacteristic
499C23×C4C23×C11311yescharacteristic
500C23×C4C23×C11311yescharacteristic
501C2×M16—22no—
502C2×M16—22no—
503C2×M16—22no—
504C2×M16—22no—
505C2×M16—41no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—22no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—22no—
513C22×C8—41no—
514C22×C8—41no—
515C22×C8—41no—
516C22×C8C23×C11311yescharacteristic
517C22×C8C23×C11311yescharacteristic
518C22×C8C23×C11311yescharacteristic
519C22×C8C23×C11311yescharacteristic
520C22×C8C23×C11311yescharacteristic
521C22×C8C23×C11311yescharacteristic
522C22×C8C23×C11311yescharacteristic
523C22×C8C23×C11311yescharacteristic
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—41no—
529C4×D4—41no—
530C2×C4⋊C4C2×C4×C11311yescharacteristic
531C2×C4⋊C4C2×C4×C11311yescharacteristic
532C2×C4⋊C4C2×C4×C11311yescharacteristic
533C2×C22⋊C4C2×C4×C11311yescharacteristic
534C2×C22⋊C4C2×C4×C11311yescharacteristic
535C2×C22⋊C4C2×C4×C11311yescharacteristic
536C2×C22⋊C4C2×C4×C11311yescharacteristic
537C2×C22⋊C4C2×C4×C11311yescharacteristic
538C2×C22⋊C4C2×C4×C11311yescharacteristic
539C2×C22⋊C4C2×C4×C11311yescharacteristic
540C2×C22⋊C4C2×C4×C11311yescharacteristic
541C2×C22⋊C4C2×C4×C11311yescharacteristic
542C2×C22⋊C4C2×C4×C11311yescharacteristic
543C2×C22⋊C4C2×C4×C11311yescharacteristic
544C2×C22⋊C4C2×C4×C11311yescharacteristic
545C2×C42C23×C11311yescharacteristic
546C2×C42C23×C11311yescharacteristic
547C2×C42C23×C11311yescharacteristic
548C4⋊C8—22no—
549C4⋊C8—22no—
550C4⋊C8—41no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—22no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—22no—
559C22⋊C8—41no—
560C22⋊C8D4×C11314yescomplemented
561C22⋊C8D4×C11314yescomplemented
562#97—22no—
563C4×C8—22no—
564C4×C8—41no—
565#95C2×C4×C11311yescharacteristic
566#95C2×C4×C11311yescharacteristic
567#95C2×C4×C11311yescharacteristic
568#95C2×C4×C11311yescharacteristic
569#95C2×C4×C11311yescharacteristic
570#95C2×C4×C11311yescharacteristic
571C24C22×C4×C11311yescharacteristic
572C24C22×C4×C11311yescharacteristic
573C24C22×C4×C11311yescharacteristic
574C24C22×C4×C11311yescharacteristic
575#41—44no—
576#41—44no—
577#41—44no—
578#41—44no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—41no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4C22×C4×C11311yescharacteristic
621C22×C4C22×C4×C11311yescharacteristic
622C22×C4C22×C4×C11311yescharacteristic
623C22×C4C22×C4×C11311yescharacteristic
624C22×C4C22×C4×C11311yescharacteristic
625C22×C4C22×C4×C11311yescharacteristic
626C22×C4C22×C4×C11311yescharacteristic
627C22×C4C22×C4×C11311yescharacteristic
628C22×C4C22×C4×C11311yescharacteristic
629C22×C4C22×C4×C11311yescharacteristic
630C22×C4C2×D4×C11312yes—
631C22×C4C2×D4×C11312yes—
632C22×C4#41×C11312yes—
633C22×C4#41×C11312yes—
634C22×C4C24×C11311yescharacteristic
635M16—44no—
636M16—44no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—44no—
658C2×C8—44no—
659C2×C8—44no—
660C2×C8C2×D4×C11312yes—
661C2×C8C2×D4×C11312yes—
662C2×C8C2×D4×C11312yes—
663C2×C8C2×D4×C11312yes—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—41no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23C4×D4×C11312yes—
711C23C4×D4×C11312yes—
712C23#131×C11312yes—
713C23C23×C4×C11311yescharacteristic
714Q8—44no—
715D4—28no—
716D4—44no—
717D4—44no—
718D4—44no—
719D4—44no—
720D4—44no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4C4×D4×C11312yes—
764C2×C4C4×D4×C11312yes—
765C2×C4#131×C11312yes—
766C2×C4#131×C11312yes—
767C2×C4C22×D4×C11311yescharacteristic
768C2×C4C22×D4×C11311yescharacteristic
769C2×C4C2×#41×C11311yescharacteristic
770C2×C4C2×#41×C11311yescharacteristic
771C2×C4H(5,𝔽2)×C11311yescharacteristic
772C2×C4H(5,𝔽2)×C11311yescharacteristic
773C8—22no—
774C8—22no—
775C8—22no—
776C8—22no—
777C8—41no—
778C8—41no—
779C8—41no—
780C8—41no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22C2×C4×D4×C11311yescharacteristic
810C22C2×C4×D4×C11311yescharacteristic
811C22#518×C11311yescharacteristic
812C22C2×#131×C11311yescharacteristic
813C22C2×#131×C11311yescharacteristic
814C22C2×#131×C11311yescharacteristic
815C22#568×C11311yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4D42×C11311yescharacteristic
827C4#546×C11311yescharacteristic
828C4#546×C11311yescharacteristic
829C4#551×C11311yescharacteristic
830C2—42no—
831C2—42no—
832C2—42no—
833C2—81no—
834C2C113×#235811yescharacteristic
835C2C113×#292911yescharacteristic
836C2C113×#293111yescharacteristic
837C2C113×#293311yescharacteristic
838C2C113×#293511yescharacteristic
839C2C113×#297711yescharacteristic
840C2C113×#298111yescharacteristic
subgroupG/H
centerC22×C4×C113C24
commutatorC23C23×C4×C113
Frattini, cosocleC22×C4C24×C113
socleC23×C113C23×C4
prime radicalC113×#2388C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#435×C113C2semidirect
2. C2×C8×D4×C113C2semidirect
3. C2×#408×C113C2semidirect
4. C2×#408×C113C2semidirect
6. C113×#1954C2semidirect
7. C113×#1924C2semidirect
8. C113×#1923C2semidirect
9. C113×#1870C2semidirect
10. C113×#1869C2semidirect
11. C113×#1869C2semidirect
12. C113×#1851C2semidirect
13. C113×#1850C2semidirect
14. C113×#1753C2semidirect
15. C8×C22⋊C4×C113C2semidirect
139. C22⋊C8×C113D4semidirect
140. C22⋊C8×C113D4semidirect
409. #22847C113direct (N × H)
421. C2×#435C2×C113semidirect
422. C2×C8×D4C2×C113semidirect
423. C2×#408C2×C113semidirect
424. C2×#408C2×C113semidirect
426. #1954C2×C113semidirect
427. #1924C2×C113semidirect
428. #1923C2×C113semidirect
429. #1870C2×C113semidirect
430. #1869C2×C113semidirect
431. #1869C2×C113semidirect
432. #1851C2×C113semidirect
433. #1850C2×C113semidirect
434. #1753C2×C113semidirect
435. C8×C22⋊C4C2×C113semidirect
436. C113#22847direct (N × H)
560. C22⋊C8D4×C113semidirect
561. C22⋊C8D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1132
C2×C8×D4×C1132
C2×#408×C1132
C113×#23882
C113×#19542
C113×#19242
C113×#19232
C113×#18702
C113×#18692
C113×#18512
C113×#18502
C113×#17532
C8×C22⋊C4×C1132
#22847113