Finite Group Databasebeta

← #14764895

Subgroups — #14764895

Order 2816.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C211yesmaximal, characteristic, complemented
2C2×#10622847C211yesmaximal, characteristic, complemented
3#13069415C211yesmaximal, characteristic, complemented
4#13069411C211yesmaximal, characteristic, complemented
5#13069231C211yesmaximal, characteristic, complemented
6#13069224C211yesmaximal, characteristic, complemented
7#13069224C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic, complemented
9#13068914C211yesmaximal, characteristic, complemented
10#13068914C211yesmaximal, characteristic, complemented
11#13068909C211yesmaximal, characteristic, complemented
12#13068796C211yesmaximal, characteristic, complemented
13#13068528C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#2388C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C11×#395C411yescharacteristic
24C11×#394C411yescharacteristic
25C11×#394C411yescharacteristic
26C11×#394C411yescharacteristic
27C11×#393C411yescharacteristic
28C11×#392C411yescharacteristic
29C11×#392C411yescharacteristic
30C11×#392C411yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33C4×C11×C22⋊C4C2211yescharacteristic
34#10622847—24no—
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2211yescharacteristic
47C2×C22⋊(C11⋊C8)C2211yescharacteristic
48#10622625—24no—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2×C411yescharacteristic
68C22×D4×C11C2×C411yescharacteristic
69C22×D4×C11C2×C411yescharacteristic
70C22×D4×C11C2×C411yescharacteristic
71C22×D4×C11C2×C411yescharacteristic
72C22×D4×C11C2×C411yescharacteristic
73C22×D4×C11C2×C411yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—41no—
81C4×D4×C11—41no—
82C4×D4×C11—41no—
83C4×D4×C11—41no—
84C2×C11×C4⋊C4C2×C411yescharacteristic
85C2×C11×C4⋊C4C2×C411yescharacteristic
86C2×C11×C4⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4C2×C411yescharacteristic
91C2×C11×C22⋊C4C2×C411yescharacteristic
92C2×C11×C22⋊C4C2×C411yescharacteristic
93C2×C11×C22⋊C4C2×C411yescharacteristic
94C2×C11×C22⋊C4C2×C411yescharacteristic
95C2×C11×C22⋊C4C2×C411yescharacteristic
96C2×C11×C22⋊C4C2×C411yescharacteristic
97C2×C11×C22⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2×C411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×#4318—22no—
103C2×#4318—41no—
104C2×#4318—41no—
105C2×#4318—41no—
106C2×#4318—41no—
107C2×#4318D414yescomplemented
108C22×C11⋊C8—22no—
109C22×C11⋊C8—41no—
110C22×C11⋊C8—41no—
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C11×#95C2×C411yescharacteristic
120C11×#95C2×C411yescharacteristic
121C11×#95C2×C411yescharacteristic
122C11×#95C2×C411yescharacteristic
123C11×#95C2×C411yescharacteristic
124C11×#95C2×C411yescharacteristic
125C22⋊(C11⋊C8)—22no—
126C22⋊(C11⋊C8)—22no—
127C22⋊(C11⋊C8)—22no—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—41no—
133C22⋊(C11⋊C8)—41no—
134C22⋊(C11⋊C8)—41no—
135C22⋊(C11⋊C8)—41no—
136C22⋊(C11⋊C8)—41no—
137C22⋊(C11⋊C8)—41no—
138C4⋊(C11⋊C8)—22no—
139C4⋊(C11⋊C8)—41no—
140C4⋊(C11⋊C8)—41no—
141#66867—41no—
142C4×C11⋊C8—22no—
143C4×C11⋊C8—41no—
144#22039—111nomaximal, Sylow
145C24×C11C22×C411yescharacteristic
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C24×C11C22×C411yescharacteristic
149C11×#41—44no—
150C11×#41—44no—
151C11×#41—44no—
152C11×#41—44no—
153C2×Q8×C11—22no—
154C2×Q8×C11—41no—
155C2×Q8×C11—41no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11—41no—
167C2×D4×C11—41no—
168C2×D4×C11—41no—
169C2×D4×C11—41no—
170C2×D4×C11—41no—
171C2×D4×C11—41no—
172C2×D4×C11—41no—
173C2×D4×C11—41no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C22×C411yescharacteristic
197C22×C4×C11C22×C411yescharacteristic
198C22×C4×C11C22×C411yescharacteristic
199C22×C4×C11C22×C411yescharacteristic
200C22×C4×C11C22×C411yescharacteristic
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C2×D412yes—
207C22×C4×C11#4112yes—
208C22×C4×C11C2411yescharacteristic
209C11×C4⋊C4—22no—
210C11×C4⋊C4—41no—
211C11×C4⋊C4—41no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—41no—
219C11×C22⋊C4—41no—
220C11×C22⋊C4—41no—
221C11×C22⋊C4—41no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—41no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230#4318—44no—
231#4318—44no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—44no—
255C2×C11⋊C8C2×D412yes—
256C2×C11⋊C8C2×D412yes—
257C2×#436—111no—
258C2×#408—111no—
259#2388D1111yescharacteristic
260#1955—111no—
261#1954—111no—
262#1924—111no—
263#1923—111no—
264#1923—111no—
265#1923—111no—
266#1870—111no—
267#1870—111no—
268#1869—111no—
269#1850—111no—
270#1780—111no—
271#1753—111no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11C4×D412yes—
300C23×C11C23×C411yescharacteristic
301Q8×C11—44no—
302D4×C11—44no—
303D4×C11—44no—
304D4×C11—44no—
305D4×C11—44no—
306D4×C11—44no—
307D4×C11—44no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11C4×D412yes—
352C2×C4×C11#13112yes—
353C2×C4×C11#13112yes—
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C2×#4111yescharacteristic
356C2×C4×C11H(5,𝔽2)11yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C11⋊C8—22no—
361C11⋊C8—22no—
362C11⋊C8—41no—
363C11⋊C8—41no—
364C11⋊C8—41no—
365C11⋊C8—41no—
366C11⋊C8—41no—
367C11⋊C8—41no—
368C22×#41C2×D1111yescharacteristic
369C22×M16—111no—
370C22×M16—111no—
371C23×C8—111no—
372C2×C4×D4C2×D1111yescharacteristic
373C2×C4×D4C2×D1111yescharacteristic
374C2×C4×D4C2×D1111yescharacteristic
375#436—224no—
376C2×C4⋊C8—111no—
377C2×C4⋊C8—111no—
378C2×C4⋊C8—111no—
379#408—224no—
380C2×C22⋊C8—111no—
381C2×C22⋊C8—111no—
382C2×C22⋊C8—111no—
383C2×C22⋊C8—111no—
384C2×C22⋊C8—111no—
385C2×C22⋊C8—111no—
386C2×C22⋊C8—111no—
387C2×C22⋊C8—111no—
388C2×C22⋊C8—111no—
389C2×C22⋊C8—111no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—111no—
392C2×C22⋊C8—111no—
393C2×#97—111no—
394C2×C4×C8—111no—
395C2×C4×C8—111no—
396#395Dic1111yescharacteristic
397#394Dic1111yescharacteristic
398#394Dic1111yescharacteristic
399#394Dic1111yescharacteristic
400#393Dic1111yescharacteristic
401#392Dic1111yescharacteristic
402#392Dic1111yescharacteristic
403#392Dic1111yescharacteristic
404C4×C22⋊C4C2×D1111yescharacteristic
405C4×C22⋊C4C2×D1111yescharacteristic
406C4×C22⋊C4C2×D1111yescharacteristic
407#336—111no—
408#336—111no—
409#336—111no—
410#336—111no—
411#336—111no—
412#336—111no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11C2×C4×D411yescharacteristic
442C22×C11#51811yescharacteristic
443C22×C11#51811yescharacteristic
444C22×C11C2×#13111yescharacteristic
445C22×C11C2×#13111yescharacteristic
446C22×C11#56811yescharacteristic
447C22×C11#56811yescharacteristic
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—41no—
452C4×C11—41no—
453C4×C11—41no—
454C4×C11—41no—
455C4×C11—41no—
456C4×C11—41no—
457C4×C11—41no—
458C4×C11#53411yescharacteristic
459C4×C11#53511yescharacteristic
460C4×C11#53811yescharacteristic
461C4×C11#53811yescharacteristic
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—41no—
465C2×#41—41no—
466C2×#41—41no—
467C2×#41—41no—
468C22×Q8C2×Dic1111yescharacteristic
469C22×D4C2×Dic1111yescharacteristic
470C22×D4C2×Dic1111yescharacteristic
471C22×D4C2×Dic1111yescharacteristic
472C22×D4C2×Dic1111yescharacteristic
473C22×D4C2×Dic1111yescharacteristic
474C22×D4C2×Dic1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C2×M16—114no—
480C2×M16—222no—
481C2×M16—441no—
482C2×M16—441no—
483C2×M16—441no—
484C2×M16—441no—
485C22×C8—111no—
486C22×C8—111no—
487C22×C8—111no—
488C22×C8—111no—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8—111no—
492C22×C8—111no—
493C22×C8—222no—
494C22×C8—441no—
495C22×C8—441no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—41no—
501C4×D4—41no—
502C2×C4⋊C4C2×Dic1111yescharacteristic
503C2×C4⋊C4C2×Dic1111yescharacteristic
504C2×C4⋊C4C2×Dic1111yescharacteristic
505C2×C22⋊C4C2×Dic1111yescharacteristic
506C2×C22⋊C4C2×Dic1111yescharacteristic
507C2×C22⋊C4C2×Dic1111yescharacteristic
508C2×C22⋊C4C2×Dic1111yescharacteristic
509C2×C22⋊C4C2×Dic1111yescharacteristic
510C2×C22⋊C4C2×Dic1111yescharacteristic
511C2×C22⋊C4C2×Dic1111yescharacteristic
512C2×C22⋊C4C2×Dic1111yescharacteristic
513C2×C22⋊C4C2×Dic1111yescharacteristic
514C2×C22⋊C4C2×Dic1111yescharacteristic
515C2×C22⋊C4C2×Dic1111yescharacteristic
516C2×C22⋊C4C2×Dic1111yescharacteristic
517C2×C42C22×D1111yescharacteristic
518C2×C42C22×D1111yescharacteristic
519C2×C42C22×D1111yescharacteristic
520C4⋊C8—222no—
521C4⋊C8—441no—
522C4⋊C8—441no—
523C22⋊C8—222no—
524C22⋊C8—222no—
525C22⋊C8—222no—
526C22⋊C8—222no—
527C22⋊C8—222no—
528C22⋊C8—222no—
529C22⋊C8—222no—
530C22⋊C8—441no—
531C22⋊C8—441no—
532C22⋊C8—441no—
533C22⋊C8—441no—
534C22⋊C8—441no—
535C22⋊C8—441no—
536#97—441no—
537C4×C8—222no—
538C4×C8—441no—
539#95C2×Dic1111yescharacteristic
540#95C2×Dic1111yescharacteristic
541#95C2×Dic1111yescharacteristic
542#95C2×Dic1111yescharacteristic
543#95C2×Dic1111yescharacteristic
544#95C2×Dic1111yescharacteristic
545C2×C11—42no—
546C2×C11—81no—
547C2×C11—81no—
548C2×C11—81no—
549C2×C11#232111yescharacteristic
550C2×C11#293311yescharacteristic
551C2×C11#293511yescharacteristic
552C2×C11#297611yescharacteristic
553C2×C11#297811yescharacteristic
554C2×C11#297911yescharacteristic
555C2×C11#298111yescharacteristic
556C24C22×Dic1111yescharacteristic
557C24C22×Dic1111yescharacteristic
558C24C22×Dic1111yescharacteristic
559C24C22×Dic1111yescharacteristic
560#41—44no—
561#41—44no—
562#41—44no—
563#41—44no—
564C2×Q8—22no—
565C2×Q8—41no—
566C2×Q8—41no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4D4×D1112yes—
608C22×C4#434112yes—
609C22×C4C22×Dic1111yescharacteristic
610C22×C4C22×Dic1111yescharacteristic
611C22×C4C22×Dic1111yescharacteristic
612C22×C4C22×Dic1111yescharacteristic
613C22×C4C22×Dic1111yescharacteristic
614C22×C4C22×Dic1111yescharacteristic
615C22×C4C22×Dic1111yescharacteristic
616C22×C4C22×Dic1111yescharacteristic
617C22×C4C22×Dic1111yescharacteristic
618C22×C4C22×Dic1111yescharacteristic
619C22×C4C23×D1111yescharacteristic
620M16—444no—
621M16—444no—
622C2×C8—112no—
623C2×C8—112no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—221no—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8—221no—
634C2×C8—221no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—221no—
645C2×C8—221no—
646C2×C8—444no—
647C4⋊C4—22no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—41no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C11#2203911yescharacteristic, complemented, Sylow
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23D4×Dic1112yes—
697C23C23×Dic1111yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—44no—
704D4—44no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
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—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4D4×Dic1112yes—
749C2×C4#6700112yes—
750C2×C4#6700112yes—
751C2×C4C2×D4×D1111yescharacteristic
752C2×C4C2×#434111yescharacteristic
753C2×C4#6703711yescharacteristic
754C2×C4#6703711yescharacteristic
755C2×C4#6703711yescharacteristic
756C2×C4#6703711yescharacteristic
757C8—222no—
758C8—222no—
759C8—441no—
760C8—441no—
761C8—441no—
762C8—441no—
763C8—441no—
764C8—441no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22C2×D4×Dic1111yescharacteristic
794C22#1062332911yescharacteristic
795C22#1062332911yescharacteristic
796C22C2×#6700111yescharacteristic
797C22C2×#6700111yescharacteristic
798C22#1062335011yescharacteristic
799C22#1062335011yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4#1062312011yescharacteristic
811C4#1062312311yescharacteristic
812C4#1062312411yescharacteristic
813C4#1062312411yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2#1307127711yescharacteristic
819C2#1307734311yescharacteristic
820C2#1307736011yescharacteristic
821C2#1307766411yescharacteristic
822C2#1307767811yescharacteristic
823C2#1307768311yescharacteristic
824C2#1307769211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
Fitting, prime radicalC11×#2388C2
cosocleC22×C4×C11C24
hypercenter#2388D11
hypocenterC11#22039
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. C2×#10622625C2semidirect
2. C2×#10622847C2semidirect
3. #13069415C2semidirect
4. #13069411C2semidirect
5. #13069231C2semidirect
6. #13069224C2semidirect
7. #13069224C2semidirect
8. #13069224C2semidirect
9. #13068914C2semidirect
10. #13068914C2semidirect
11. #13068909C2semidirect
12. #13068796C2semidirect
13. #13068528C2semidirect
14. #13068400C2semidirect
107. C2×#4318D4semidirect
668. C11#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×#106228472
#130694152
#130694112
#130692312
#130692242
#130689142
#130689092
#130687962
#130685282
#130684002
C11×#23882
#2203911