Finite Group Databasebeta

← #14780030

Subgroups — #14780030

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069415C211yesmaximal, characteristic, complemented
2#13069411C211yesmaximal, characteristic, complemented
3#13069231C211yesmaximal, characteristic, complemented
4#13069224C211yesmaximal, characteristic, complemented
5#13069182C211yesmaximal, characteristic, complemented
6#13069175C211yesmaximal, characteristic, complemented
7#13068914C211yesmaximal, characteristic, complemented
8#13068914C211yesmaximal, characteristic, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068909C211yesmaximal, characteristic, complemented
11#13068801C211yesmaximal, characteristic, complemented
12#13068796C211yesmaximal, characteristic, complemented
13#13068684C211yesmaximal, characteristic, complemented
14#13068596C211yesmaximal, characteristic, complemented
15C4×C11×#121C211yesmaximal, characteristic
16C2×C11×#121C411yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C11×#390C411yescharacteristic
24C11×#389C411yescharacteristic
25C11×#388C411yescharacteristic
26C11×#388C411yescharacteristic
27C11×#386C411yescharacteristic
28C11×#386C411yescharacteristic
29C11×#380C411yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
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×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622162C2211yescharacteristic
50#10622162C2211yescharacteristic
51#10622162C2211yescharacteristic
52#10622162C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C22×D4×C11C2×C411yescharacteristic
61C22×D4×C11C2×C411yescharacteristic
62C23×C4×C11C2×C411yescharacteristic
63C23×C4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C11×#121—24no—
68C4×D4×C11—41no—
69C4×D4×C11—41no—
70C4×D4×C11—41no—
71C4×D4×C11—41no—
72C4×D4×C11—41no—
73C4×D4×C11—41no—
74C2×C11×C4⋊C4C2×C411yescharacteristic
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C11×C22⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C42×C11—41no—
90C2×C42×C11—41no—
91C2×C42×C11C2×C411yescharacteristic
92C2×C42×C11C2×C411yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×#4318—41no—
98C2×#4318—41no—
99C2×#4318—41no—
100C22×C11⋊C8—41no—
101C22×C11⋊C8—41no—
102C22×C11⋊C8—41no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C11×#95C2×C411yescharacteristic
112C11×#95C2×C411yescharacteristic
113C11×#95C2×C411yescharacteristic
114C11×#95C2×C411yescharacteristic
115C11×#95C2×C411yescharacteristic
116C11×#95C2×C411yescharacteristic
117C22⋊(C11⋊C8)—41no—
118C22⋊(C11⋊C8)—41no—
119C22⋊(C11⋊C8)—41no—
120C22⋊(C11⋊C8)—41no—
121C22⋊(C11⋊C8)—41no—
122C22⋊(C11⋊C8)—41no—
123C22⋊(C11⋊C8)—41no—
124C22⋊(C11⋊C8)—41no—
125C22⋊(C11⋊C8)—41no—
126C22⋊(C11⋊C8)—41no—
127C4⋊(C11⋊C8)—41no—
128C4⋊(C11⋊C8)—41no—
129C4⋊(C11⋊C8)—41no—
130C4⋊(C11⋊C8)—41no—
131#66867—41no—
132C4×C11⋊C8—41no—
133#23329—111nomaximal, Sylow
134C24×C11C22×C411yescharacteristic
135C24×C11C22×C411yescharacteristic
136C24×C11C22×C411yescharacteristic
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C22×C4×C11—41no—
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C22×C411yescharacteristic
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4—41no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—41no—
193C11×C22⋊C4—41no—
194C11×C22⋊C4—41no—
195C11×C22⋊C4—41no—
196C11×C22⋊C4M1614yescomplemented
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—41no—
206C42×C11—41no—
207#4318—44no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—44no—
233C4×#121D1111yescharacteristic
234#1955—111no—
235#1954—111no—
236#1924—111no—
237#1923—111no—
238#1917—111no—
239#1916—111no—
240#1870—111no—
241#1870—111no—
242#1869—111no—
243#1869—111no—
244#1851—111no—
245#1850—111no—
246#1817—111no—
247#1797—111no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11C2×M1612yes—
268C23×C11#13112yes—
269C23×C11C23×C411yescharacteristic
270D4×C11—44no—
271D4×C11—44no—
272D4×C11—44no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—44no—
304C2×C4×C11—44no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11C2×M1612yes—
318C2×C4×C11C2×M1612yes—
319C2×C4×C11#13112yes—
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C2×C4×C112−1+411yescharacteristic
326C11⋊C8—41no—
327C11⋊C8—41no—
328C11⋊C8—41no—
329C11⋊C8—41no—
330C11⋊C8—41no—
331C11⋊C8—41no—
332C11⋊C8—41no—
333C11⋊C8—41no—
334C22×M16—111no—
335C23×C8—111no—
336C2×#121Dic1111yescharacteristic
337C2×C4×D4C2×D1111yescharacteristic
338C2×C4×D4C2×D1111yescharacteristic
339C2×C4×D4C2×D1111yescharacteristic
340C22×C42C2×D1111yescharacteristic
341C2×C4⋊C8—111no—
342C2×C4⋊C8—111no—
343C2×C4⋊C8—111no—
344C2×C4⋊C8—111no—
345C2×C22⋊C8—111no—
346C2×C22⋊C8—111no—
347C2×C22⋊C8—111no—
348C2×C22⋊C8—111no—
349C2×C22⋊C8—111no—
350C2×C22⋊C8—111no—
351C2×C22⋊C8—111no—
352C2×C22⋊C8—111no—
353C2×C22⋊C8—111no—
354C2×C22⋊C8—111no—
355C2×#97—111no—
356C2×C4×C8—111no—
357#390Dic1111yescharacteristic
358#389Dic1111yescharacteristic
359#388Dic1111yescharacteristic
360#388Dic1111yescharacteristic
361#386Dic1111yescharacteristic
362#386Dic1111yescharacteristic
363#380Dic1111yescharacteristic
364C4×C4⋊C4C2×D1111yescharacteristic
365C4×C22⋊C4C2×D1111yescharacteristic
366C4×C22⋊C4C2×D1111yescharacteristic
367#336—111no—
368#336—111no—
369#336—111no—
370#336—111no—
371#336—111no—
372#336—111no—
373#336—111no—
374#336—111no—
375#336—111no—
376#336—111no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11#51811yescharacteristic
399C22×C11#51811yescharacteristic
400C22×C11#52011yescharacteristic
401C22×C11C22×M1611yescharacteristic
402C22×C11C2×#13111yescharacteristic
403C22×C11C2×#13111yescharacteristic
404C22×C11#56811yescharacteristic
405C4×C11—22no—
406C4×C11—22no—
407C4×C11—22no—
408C4×C11—41no—
409C4×C11—41no—
410C4×C11—41no—
411C4×C11—41no—
412C4×C11—41no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11—41no—
416C4×C11#56011yescharacteristic
417C4×C11#56011yescharacteristic
418C4×C11#56211yescharacteristic
419C4×C11#56211yescharacteristic
420C22×D4C2×Dic1111yescharacteristic
421C22×D4C2×Dic1111yescharacteristic
422C22×D4C2×Dic1111yescharacteristic
423C23×C4C2×Dic1111yescharacteristic
424C23×C4C2×Dic1111yescharacteristic
425C23×C4C22×D1111yescharacteristic
426C23×C4C22×D1111yescharacteristic
427C23×C4C22×D1111yescharacteristic
428C2×M16—441no—
429C2×M16—441no—
430C2×M16—441no—
431C22×C8—111no—
432C22×C8—111no—
433C22×C8—111no—
434C22×C8—111no—
435C22×C8—111no—
436C22×C8—111no—
437C22×C8—111no—
438C22×C8—111no—
439C22×C8—441no—
440C22×C8—441no—
441C22×C8—441no—
442#121—24no—
443C4×D4—41no—
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—41no—
447C4×D4—41no—
448C4×D4—41no—
449C2×C4⋊C4C2×Dic1111yescharacteristic
450C2×C4⋊C4C2×Dic1111yescharacteristic
451C2×C4⋊C4C2×Dic1111yescharacteristic
452C2×C4⋊C4C2×Dic1111yescharacteristic
453C2×C4⋊C4C2×Dic1111yescharacteristic
454C2×C22⋊C4C2×Dic1111yescharacteristic
455C2×C22⋊C4C2×Dic1111yescharacteristic
456C2×C22⋊C4C2×Dic1111yescharacteristic
457C2×C22⋊C4C2×Dic1111yescharacteristic
458C2×C22⋊C4C2×Dic1111yescharacteristic
459C2×C22⋊C4C2×Dic1111yescharacteristic
460C2×C22⋊C4C2×Dic1111yescharacteristic
461C2×C22⋊C4C2×Dic1111yescharacteristic
462C2×C22⋊C4C2×Dic1111yescharacteristic
463C2×C22⋊C4C2×Dic1111yescharacteristic
464C2×C42—41no—
465C2×C42—41no—
466C2×C42C2×Dic1111yescharacteristic
467C2×C42C2×Dic1111yescharacteristic
468C2×C42C22×D1111yescharacteristic
469C2×C42C22×D1111yescharacteristic
470C2×C42C22×D1111yescharacteristic
471C2×C42C22×D1111yescharacteristic
472C4⋊C8—441no—
473C4⋊C8—441no—
474C4⋊C8—441no—
475C4⋊C8—441no—
476C22⋊C8—441no—
477C22⋊C8—441no—
478C22⋊C8—441no—
479C22⋊C8—441no—
480C22⋊C8—441no—
481C22⋊C8—441no—
482C22⋊C8—441no—
483C22⋊C8—441no—
484C22⋊C8—441no—
485C22⋊C8—441no—
486#97—441no—
487C4×C8—441no—
488#95C2×Dic1111yescharacteristic
489#95C2×Dic1111yescharacteristic
490#95C2×Dic1111yescharacteristic
491#95C2×Dic1111yescharacteristic
492#95C2×Dic1111yescharacteristic
493#95C2×Dic1111yescharacteristic
494C2×C11—42no—
495C2×C11—42no—
496C2×C11—81no—
497C2×C11#237711yescharacteristic
498C2×C11#297411yescharacteristic
499C2×C11#297411yescharacteristic
500C2×C11#297611yescharacteristic
501C2×C11#298111yescharacteristic
502C2×C11#298911yescharacteristic
503C2×C11#299411yescharacteristic
504C24C22×Dic1111yescharacteristic
505C24C22×Dic1111yescharacteristic
506C24C22×Dic1111yescharacteristic
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
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—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4C22×Dic1111yescharacteristic
541C22×C4C22×Dic1111yescharacteristic
542C22×C4C22×Dic1111yescharacteristic
543C22×C4C22×Dic1111yescharacteristic
544C22×C4C22×Dic1111yescharacteristic
545C22×C4C22×Dic1111yescharacteristic
546C22×C4C22×Dic1111yescharacteristic
547C22×C4C22×Dic1111yescharacteristic
548C22×C4C22×Dic1111yescharacteristic
549C22×C4C22×Dic1111yescharacteristic
550C22×C4C22×Dic1111yescharacteristic
551C22×C4C23×D1111yescharacteristic
552M16—444no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—221no—
565C2×C8—221no—
566C2×C8—221no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—444no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C22⋊C4—22no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4#431814yescomplemented
593C42—21no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—41no—
602C42—41no—
603C11#2332911yescharacteristic, complemented, Sylow
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×#431812yes—
624C23#6700112yes—
625C23C23×Dic1111yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4C2×#431812yes—
674C2×C4C2×#431812yes—
675C2×C4#6700112yes—
676C2×C4#6703711yescharacteristic
677C2×C4#6703711yescharacteristic
678C2×C4#6703711yescharacteristic
679C2×C4#6703711yescharacteristic
680C2×C4#6704211yescharacteristic
681C2×C4#6704311yescharacteristic
682C8—441no—
683C8—441no—
684C8—441no—
685C8—441no—
686C8—441no—
687C8—441no—
688C8—441no—
689C8—441no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22C22×#431811yescharacteristic
712C22#1062332911yescharacteristic
713C22#1062332911yescharacteristic
714C22C2×#6700111yescharacteristic
715C22C2×#6700111yescharacteristic
716C22#1062335011yescharacteristic
717C22#1062335811yescharacteristic
718C4—22no—
719C4—22no—
720C4—22no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4#1062315111yescharacteristic
730C4#1062315111yescharacteristic
731C4#1062315211yescharacteristic
732C4#1062315211yescharacteristic
733C2—42no—
734C2—42no—
735C2—81no—
736C2#1307177311yescharacteristic
737C2#1307765111yescharacteristic
738C2#1307765111yescharacteristic
739C2#1307766411yescharacteristic
740C2#1307769211yescharacteristic
741C2#1307773311yescharacteristic
742C2#1307777611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×#121C2
prime radicalC2×C11×#121C4
cosocleC22×C4×C11C24
hypercenterC4×#121D11
hypocenterC11#23329
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. #13069415C2semidirect
2. #13069411C2semidirect
3. #13069231C2semidirect
4. #13069224C2semidirect
5. #13069182C2semidirect
6. #13069175C2semidirect
7. #13068914C2semidirect
8. #13068914C2semidirect
9. #13068909C2semidirect
10. #13068909C2semidirect
11. #13068801C2semidirect
12. #13068796C2semidirect
13. #13068684C2semidirect
14. #13068596C2semidirect
196. C11×C22⋊C4M16semidirect
592. C22⋊C4#4318semidirect
603. C11#23329semidirect

Maximal subgroups

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

subgroupindex
#130694152
#130694112
#130692312
#130692242
#130691822
#130691752
#130689142
#130689092
#130688012
#130687962
#130686842
#130685962
C4×C11×#1212
#2332911