Finite Group Databasebeta

← C113×#21273 #43289293

Subgroups — C113×#21273 #43289293

Order 28928.

860 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#433×C113C211yesmaximal, characteristic, complemented
2C2×#432×C113C211yesmaximal, characteristic, complemented
3C113×#2290C211yesmaximal, characteristic
4C113×#1955C211yesmaximal, characteristic
5C113×#1954C211yesmaximal, characteristic
6C113×#1940C211yesmaximal, characteristic, complemented
7C113×#1939C211yesmaximal, characteristic, complemented
8C113×#1924C211yesmaximal, characteristic, complemented
9C113×#1924C211yesmaximal, characteristic, complemented
10C113×#1923C211yesmaximal, characteristic, complemented
11C113×#1923C211yesmaximal, characteristic, complemented
12C113×#1768C211yesmaximal, characteristic, complemented
13C113×#1750C211yesmaximal, characteristic, complemented
14C4×C22⋊C8×C113C211yesmaximal, characteristic, complemented
15C113×#1726C211yesmaximal, characteristic, complemented
16C2×C4×D4×C113C2211yescharacteristic
17C2×#117×C113C2211yescharacteristic
18C22×C42×C113C2211yescharacteristic
19#433×C113—24no—
20#432×C113—24no—
21C2×C4⋊C8×C113C2211yescharacteristic
22C2×C4⋊C8×C113C2211yescharacteristic
23C2×C4⋊C8×C113C2211yescharacteristic
24C2×C4⋊C8×C113C2211yescharacteristic
25C2×C4⋊C8×C113C2211yescharacteristic
26C2×C4⋊C8×C113C2211yescharacteristic
27C2×C22⋊C8×C113C2211yescharacteristic
28C2×C22⋊C8×C113C2211yescharacteristic
29C2×C22⋊C8×C113C2211yescharacteristic
30C2×C22⋊C8×C113C2211yescharacteristic
31C2×C22⋊C8×C113C2211yescharacteristic
32C2×C22⋊C8×C113C2211yescharacteristic
33C2×C22⋊C8×C113C2211yescharacteristic
34C2×C22⋊C8×C113C2211yescharacteristic
35C2×#97×C113C2211yescharacteristic
36C2×#97×C113C2211yescharacteristic
37C2×#97×C113C2211yescharacteristic
38C2×#97×C113C2211yescharacteristic
39C2×C4×C8×C113C2211yescharacteristic
40C2×C4×C8×C113C2211yescharacteristic
41C2×C4×C8×C113C2211yescharacteristic
42C2×C4×C8×C113C2211yescharacteristic
43#388×C113C411yescharacteristic
44#388×C113C411yescharacteristic
45#387×C113C411yescharacteristic
46#387×C113C411yescharacteristic
47#386×C113C411yescharacteristic
48#386×C113C411yescharacteristic
49#385×C113C411yescharacteristic
50#385×C113C411yescharacteristic
51C4×C4⋊C4×C113C2211yescharacteristic
52C4×C22⋊C4×C113C2211yescharacteristic
53C4×C22⋊C4×C113C2211yescharacteristic
54#376×C113C2211yescharacteristic
55#336×C113C2211yescharacteristic
56#336×C113C2211yescharacteristic
57#336×C113C2211yescharacteristic
58#336×C113C2211yescharacteristic
59#336×C113C2211yescharacteristic
60#336×C113C2211yescharacteristic
61C22×D4×C113C2×C411yescharacteristic
62C23×C4×C113C2×C411yescharacteristic
63C23×C4×C113C2×C411yescharacteristic
64C23×C4×C113C2311yescharacteristic
65C23×C4×C113C2311yescharacteristic
66C22×C8×C113C2311yescharacteristic
67C22×C8×C113C2311yescharacteristic
68C22×C8×C113C2311yescharacteristic
69C22×C8×C113C2311yescharacteristic
70C22×C8×C113C2311yescharacteristic
71C22×C8×C113C2311yescharacteristic
72C22×C8×C113C2311yescharacteristic
73C22×C8×C113C2311yescharacteristic
74C4×D4×C113—22no—
75C4×D4×C113—22no—
76#117×C113—22no—
77#117×C113—22no—
78C2×C4⋊C4×C113C2×C411yescharacteristic
79C2×C4⋊C4×C113C2×C411yescharacteristic
80C2×C4⋊C4×C113C2×C411yescharacteristic
81C2×C4⋊C4×C113C2×C411yescharacteristic
82C2×C4⋊C4×C113C2×C411yescharacteristic
83C2×C22⋊C4×C113C2×C411yescharacteristic
84C2×C22⋊C4×C113C2×C411yescharacteristic
85C2×C22⋊C4×C113C2×C411yescharacteristic
86C2×C22⋊C4×C113C2×C411yescharacteristic
87C2×C22⋊C4×C113C2×C411yescharacteristic
88C2×C22⋊C4×C113C2×C411yescharacteristic
89C2×C22⋊C4×C113C2×C411yescharacteristic
90C2×C22⋊C4×C113C2×C411yescharacteristic
91C2×C42×C113—22no—
92C2×C42×C113—22no—
93C2×C42×C113C2×C411yescharacteristic
94C2×C42×C113C2×C411yescharacteristic
95C2×C42×C113C2311yescharacteristic
96C2×C42×C113C2311yescharacteristic
97C2×C42×C113C2311yescharacteristic
98C2×C42×C113C2311yescharacteristic
99C2×C42×C113C2311yescharacteristic
100C4⋊C8×C113—22no—
101C4⋊C8×C113—22no—
102C4⋊C8×C113—22no—
103C4⋊C8×C113—22no—
104C4⋊C8×C113—22no—
105C4⋊C8×C113—22no—
106C22⋊C8×C113—22no—
107C22⋊C8×C113—22no—
108C22⋊C8×C113—22no—
109C22⋊C8×C113—22no—
110C22⋊C8×C113—22no—
111C22⋊C8×C113—22no—
112C22⋊C8×C113—22no—
113C22⋊C8×C113—22no—
114#97×C113—22no—
115#97×C113—22no—
116#97×C113—22no—
117#97×C113D414yescomplemented
118C4×C8×C113—22no—
119C4×C8×C113—22no—
120C4×C8×C113—22no—
121C4×C8×C113—22no—
122#95×C113C2×C411yescharacteristic
123#95×C113C2×C411yescharacteristic
124#95×C113C2×C411yescharacteristic
125#95×C113C2×C411yescharacteristic
126#95×C113C2×C411yescharacteristic
127#95×C113C2×C411yescharacteristic
128#95×C113C2×C411yescharacteristic
129#95×C113C2×C411yescharacteristic
130#95×C113C2×C411yescharacteristic
131#95×C113C2×C411yescharacteristic
132C24×C113C22×C411yescharacteristic
133C24×C113C22×C411yescharacteristic
134C2×D4×C113—22no—
135C2×D4×C113—22no—
136C2×D4×C113—41no—
137C22×C4×C113—22no—
138C22×C4×C113—22no—
139C22×C4×C113—22no—
140C22×C4×C113—22no—
141C22×C4×C113—21no—
142C22×C4×C113—21no—
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—41no—
154C22×C4×C113—41no—
155C22×C4×C113C22×C411yescharacteristic
156C22×C4×C113C22×C411yescharacteristic
157C22×C4×C113C22×C411yescharacteristic
158C22×C4×C113C22×C411yescharacteristic
159C22×C4×C113C22×C411yescharacteristic
160C22×C4×C113C22×C411yescharacteristic
161C22×C4×C113C22×C411yescharacteristic
162C22×C4×C113C22×C411yescharacteristic
163C22×C4×C113C22×C411yescharacteristic
164C22×C4×C113C22×C411yescharacteristic
165C22×C4×C113C22×C411yescharacteristic
166C22×C4×C113C22×C411yescharacteristic
167C22×C4×C113C2411yescharacteristic
168C2×C8×C113—21no—
169C2×C8×C113—21no—
170C2×C8×C113—21no—
171C2×C8×C113—21no—
172C2×C8×C113—21no—
173C2×C8×C113—21no—
174C2×C8×C113—21no—
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×C113—21no—
186C2×C8×C113—21no—
187C2×C8×C113—21no—
188C2×C8×C113C2×D412yes—
189C2×C8×C113C2×D412yes—
190C2×C8×C113#4112yes—
191C2×C8×C113#4112yes—
192C4⋊C4×C113—22no—
193C4⋊C4×C113—22no—
194C4⋊C4×C113—22no—
195C4⋊C4×C113—22no—
196C4⋊C4×C113—41no—
197C22⋊C4×C113—22no—
198C22⋊C4×C113—22no—
199C22⋊C4×C113—22no—
200C22⋊C4×C113—22no—
201C22⋊C4×C113—22no—
202C22⋊C4×C113—22no—
203C22⋊C4×C113—41no—
204C22⋊C4×C113—41no—
205C42×C113—22no—
206C42×C113—22no—
207C42×C113—21no—
208C42×C113—21no—
209C42×C113—21no—
210C42×C113—21no—
211C42×C113—21no—
212C42×C113—21no—
213C42×C113C2×D412yes—
214C42×C113#4112yes—
215C42×C113#4112yes—
216C42×C113#4112yes—
217C23×C113—21no—
218C23×C113—21no—
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#13112yes—
231C23×C113C23×C411yescharacteristic
232D4×C113—44no—
233C2×C4×C113—21no—
234C2×C4×C113—21no—
235C2×C4×C113—21no—
236C2×C4×C113—21no—
237C2×C4×C113—21no—
238C2×C4×C113—21no—
239C2×C4×C113—21no—
240C2×C4×C113—21no—
241C2×C4×C113—21no—
242C2×C4×C113—21no—
243C2×C4×C113—21no—
244C2×C4×C113—21no—
245C2×C4×C113—21no—
246C2×C4×C113—21no—
247C2×C4×C113—21no—
248C2×C4×C113—21no—
249C2×C4×C113—21no—
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—21no—
257C2×C4×C113—21no—
258C2×C4×C113—21no—
259C2×C4×C113—21no—
260C2×C4×C113—21no—
261C2×C4×C113—21no—
262C2×C4×C113—21no—
263C2×C4×C113—21no—
264C2×C4×C113—44no—
265C2×C4×C113—44no—
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#11712yes—
275C2×C4×C113#11712yes—
276C2×C4×C113C4×D412yes—
277C2×C4×C113C4×D412yes—
278C2×C4×C113#13112yes—
279C2×C4×C113C22×D411yescharacteristic
280C2×C4×C113C2×#4111yescharacteristic
281C2×C4×C113C2×#4111yescharacteristic
282C2×C4×C113C2×#4111yescharacteristic
283C2×C4×C113C2×#4111yescharacteristic
284C2×C4×C113C2×#4111yescharacteristic
285C8×C113—22no—
286C8×C113—22no—
287C8×C113—22no—
288C8×C113—22no—
289C8×C113—41no—
290C8×C113—41no—
291C8×C113—41no—
292C8×C113—41no—
293C22×C113—22no—
294C22×C113—22no—
295C22×C113—22no—
296C22×C113—41no—
297C22×C113—41no—
298C22×C113—41no—
299C22×C113—41no—
300C22×C113—41no—
301C22×C113—41no—
302C22×C113—41no—
303C22×C113—41no—
304C22×C113—41no—
305C22×C113—41no—
306C22×C113—41no—
307C22×C113C2×#11711yescharacteristic
308C22×C113C2×C4×D411yescharacteristic
309C22×C113C4×#4111yescharacteristic
310C22×C113C2×#13111yescharacteristic
311C22×C113C2×#13111yescharacteristic
312C22×C113#56811yescharacteristic
313C22×C113#56811yescharacteristic
314C4×C113—22no—
315C4×C113—22no—
316C4×C113—22no—
317C4×C113—22no—
318C4×C113—22no—
319C4×C113—41no—
320C4×C113—41no—
321C4×C113—41no—
322C4×C113—41no—
323C4×C113—41no—
324C4×C113—41no—
325C4×C113—41no—
326C4×C113#52911yescharacteristic
327C4×C113#52911yescharacteristic
328C4×C113#53211yescharacteristic
329C4×C113#53211yescharacteristic
330#21273C11311yesmaximal, characteristic, direct product factor, Sylow
331C2×C113—42no—
332C2×C113—81no—
333C2×C113#229311yescharacteristic
334C2×C113#292411yescharacteristic
335C2×C113#292511yescharacteristic
336C2×C113#293311yescharacteristic
337C2×C113#293311yescharacteristic
338C2×C113#296611yescharacteristic
339C2×C113#296711yescharacteristic
340C2×#433C2×C11311yescharacteristic, complemented
341C2×#432C2×C11311yescharacteristic, complemented
342#2290C2×C11311yescharacteristic
343#1955C2×C11311yescharacteristic
344#1954C2×C11311yescharacteristic
345#1940C2×C11311yescharacteristic, complemented
346#1939C2×C11311yescharacteristic, complemented
347#1924C2×C11311yescharacteristic, complemented
348#1924C2×C11311yescharacteristic, complemented
349#1923C2×C11311yescharacteristic, complemented
350#1923C2×C11311yescharacteristic, complemented
351#1768C2×C11311yescharacteristic, complemented
352#1750C2×C11311yescharacteristic, complemented
353C4×C22⋊C8C2×C11311yescharacteristic, complemented
354#1726C2×C11311yescharacteristic, complemented
355C113#2127311yescharacteristic, direct product factor, Sylow
356C2×C4×D4C22×C11311yescharacteristic
357C2×#117C22×C11311yescharacteristic
358C22×C42C22×C11311yescharacteristic
359#433—24no—
360#432—24no—
361C2×C4⋊C8C22×C11311yescharacteristic
362C2×C4⋊C8C22×C11311yescharacteristic
363C2×C4⋊C8C22×C11311yescharacteristic
364C2×C4⋊C8C22×C11311yescharacteristic
365C2×C4⋊C8C22×C11311yescharacteristic
366C2×C4⋊C8C22×C11311yescharacteristic
367C2×C22⋊C8C22×C11311yescharacteristic
368C2×C22⋊C8C22×C11311yescharacteristic
369C2×C22⋊C8C22×C11311yescharacteristic
370C2×C22⋊C8C22×C11311yescharacteristic
371C2×C22⋊C8C22×C11311yescharacteristic
372C2×C22⋊C8C22×C11311yescharacteristic
373C2×C22⋊C8C22×C11311yescharacteristic
374C2×C22⋊C8C22×C11311yescharacteristic
375C2×#97C22×C11311yescharacteristic
376C2×#97C22×C11311yescharacteristic
377C2×#97C22×C11311yescharacteristic
378C2×#97C22×C11311yescharacteristic
379C2×C4×C8C22×C11311yescharacteristic
380C2×C4×C8C22×C11311yescharacteristic
381C2×C4×C8C22×C11311yescharacteristic
382C2×C4×C8C22×C11311yescharacteristic
383#388C4×C11311yescharacteristic
384#388C4×C11311yescharacteristic
385#387C4×C11311yescharacteristic
386#387C4×C11311yescharacteristic
387#386C4×C11311yescharacteristic
388#386C4×C11311yescharacteristic
389#385C4×C11311yescharacteristic
390#385C4×C11311yescharacteristic
391C4×C4⋊C4C22×C11311yescharacteristic
392C4×C22⋊C4C22×C11311yescharacteristic
393C4×C22⋊C4C22×C11311yescharacteristic
394#376C22×C11311yescharacteristic
395#336C22×C11311yescharacteristic
396#336C22×C11311yescharacteristic
397#336C22×C11311yescharacteristic
398#336C22×C11311yescharacteristic
399#336C22×C11311yescharacteristic
400#336C22×C11311yescharacteristic
401C22×D4C2×C4×C11311yescharacteristic
402C23×C4C2×C4×C11311yescharacteristic
403C23×C4C2×C4×C11311yescharacteristic
404C23×C4C23×C11311yescharacteristic
405C23×C4C23×C11311yescharacteristic
406C22×C8C23×C11311yescharacteristic
407C22×C8C23×C11311yescharacteristic
408C22×C8C23×C11311yescharacteristic
409C22×C8C23×C11311yescharacteristic
410C22×C8C23×C11311yescharacteristic
411C22×C8C23×C11311yescharacteristic
412C22×C8C23×C11311yescharacteristic
413C22×C8C23×C11311yescharacteristic
414C4×D4—22no—
415C4×D4—22no—
416#117—22no—
417#117—22no—
418C2×C4⋊C4C2×C4×C11311yescharacteristic
419C2×C4⋊C4C2×C4×C11311yescharacteristic
420C2×C4⋊C4C2×C4×C11311yescharacteristic
421C2×C4⋊C4C2×C4×C11311yescharacteristic
422C2×C4⋊C4C2×C4×C11311yescharacteristic
423C2×C22⋊C4C2×C4×C11311yescharacteristic
424C2×C22⋊C4C2×C4×C11311yescharacteristic
425C2×C22⋊C4C2×C4×C11311yescharacteristic
426C2×C22⋊C4C2×C4×C11311yescharacteristic
427C2×C22⋊C4C2×C4×C11311yescharacteristic
428C2×C22⋊C4C2×C4×C11311yescharacteristic
429C2×C22⋊C4C2×C4×C11311yescharacteristic
430C2×C22⋊C4C2×C4×C11311yescharacteristic
431C2×C42—22no—
432C2×C42—22no—
433C2×C42C2×C4×C11311yescharacteristic
434C2×C42C2×C4×C11311yescharacteristic
435C2×C42C23×C11311yescharacteristic
436C2×C42C23×C11311yescharacteristic
437C2×C42C23×C11311yescharacteristic
438C2×C42C23×C11311yescharacteristic
439C2×C42C23×C11311yescharacteristic
440C4⋊C8—22no—
441C4⋊C8—22no—
442C4⋊C8—22no—
443C4⋊C8—22no—
444C4⋊C8—22no—
445C4⋊C8—22no—
446C22⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8—22no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451C22⋊C8—22no—
452C22⋊C8—22no—
453C22⋊C8—22no—
454#97—22no—
455#97—22no—
456#97—22no—
457#97D4×C11314yescomplemented
458C4×C8—22no—
459C4×C8—22no—
460C4×C8—22no—
461C4×C8—22no—
462#95C2×C4×C11311yescharacteristic
463#95C2×C4×C11311yescharacteristic
464#95C2×C4×C11311yescharacteristic
465#95C2×C4×C11311yescharacteristic
466#95C2×C4×C11311yescharacteristic
467#95C2×C4×C11311yescharacteristic
468#95C2×C4×C11311yescharacteristic
469#95C2×C4×C11311yescharacteristic
470#95C2×C4×C11311yescharacteristic
471#95C2×C4×C11311yescharacteristic
472C24C22×C4×C11311yescharacteristic
473C24C22×C4×C11311yescharacteristic
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—41no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
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—41no—
494C22×C4—41no—
495C22×C4C22×C4×C11311yescharacteristic
496C22×C4C22×C4×C11311yescharacteristic
497C22×C4C22×C4×C11311yescharacteristic
498C22×C4C22×C4×C11311yescharacteristic
499C22×C4C22×C4×C11311yescharacteristic
500C22×C4C22×C4×C11311yescharacteristic
501C22×C4C22×C4×C11311yescharacteristic
502C22×C4C22×C4×C11311yescharacteristic
503C22×C4C22×C4×C11311yescharacteristic
504C22×C4C22×C4×C11311yescharacteristic
505C22×C4C22×C4×C11311yescharacteristic
506C22×C4C22×C4×C11311yescharacteristic
507C22×C4C24×C11311yescharacteristic
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
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×C8—21no—
528C2×C8C2×D4×C11312yes—
529C2×C8C2×D4×C11312yes—
530C2×C8#41×C11312yes—
531C2×C8#41×C11312yes—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—41no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C42—22no—
546C42—22no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42C2×D4×C11312yes—
554C42#41×C11312yes—
555C42#41×C11312yes—
556C42#41×C11312yes—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23#131×C11312yes—
571C23C23×C4×C11311yescharacteristic
572D4—44no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—44no—
605C2×C4—44no—
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#117×C11312yes—
615C2×C4#117×C11312yes—
616C2×C4C4×D4×C11312yes—
617C2×C4C4×D4×C11312yes—
618C2×C4#131×C11312yes—
619C2×C4C22×D4×C11311yescharacteristic
620C2×C4C2×#41×C11311yescharacteristic
621C2×C4C2×#41×C11311yescharacteristic
622C2×C4C2×#41×C11311yescharacteristic
623C2×C4C2×#41×C11311yescharacteristic
624C2×C4C2×#41×C11311yescharacteristic
625C8—22no—
626C8—22no—
627C8—22no—
628C8—22no—
629C8—41no—
630C8—41no—
631C8—41no—
632C8—41no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C2×#117×C11311yescharacteristic
648C22C2×C4×D4×C11311yescharacteristic
649C22C4×#41×C11311yescharacteristic
650C22C2×#131×C11311yescharacteristic
651C22C2×#131×C11311yescharacteristic
652C22#568×C11311yescharacteristic
653C22#568×C11311yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—22no—
658C4—22no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4#529×C11311yescharacteristic
667C4#529×C11311yescharacteristic
668C4#532×C11311yescharacteristic
669C4#532×C11311yescharacteristic
670C2—42no—
671C2—81no—
672C2C113×#229311yescharacteristic
673C2C113×#292411yescharacteristic
674C2C113×#292511yescharacteristic
675C2C113×#293311yescharacteristic
676C2C113×#293311yescharacteristic
677C2C113×#296611yescharacteristic
678C2C113×#296711yescharacteristic
subgroupG/H
centerC22×C4×C113C24
commutatorC23C23×C4×C113
Frattini, cosocleC22×C4C24×C113
socleC23×C113C23×C4
prime radicalC22×D4×C113C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#433×C113C2semidirect
2. C2×#432×C113C2semidirect
6. C113×#1940C2semidirect
7. C113×#1939C2semidirect
8. C113×#1924C2semidirect
9. C113×#1924C2semidirect
10. C113×#1923C2semidirect
11. C113×#1923C2semidirect
12. C113×#1768C2semidirect
13. C113×#1750C2semidirect
14. C4×C22⋊C8×C113C2semidirect
15. C113×#1726C2semidirect
117. #97×C113D4semidirect
330. #21273C113direct (N × H)
340. C2×#433C2×C113semidirect
341. C2×#432C2×C113semidirect
345. #1940C2×C113semidirect
346. #1939C2×C113semidirect
347. #1924C2×C113semidirect
348. #1924C2×C113semidirect
349. #1923C2×C113semidirect
350. #1923C2×C113semidirect
351. #1768C2×C113semidirect
352. #1750C2×C113semidirect
353. C4×C22⋊C8C2×C113semidirect
354. #1726C2×C113semidirect
355. C113#21273direct (N × H)
457. #97D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#433×C1132
C2×#432×C1132
C113×#22902
C113×#19552
C113×#19542
C113×#19402
C113×#19392
C113×#19242
C113×#19232
C113×#17682
C113×#17502
C4×C22⋊C8×C1132
C113×#17262
#21273113