Finite Group Databasebeta

← #14780093

Subgroups — #14780093

Order 2816.

828 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
1C4×#66991C211yesmaximal, characteristic
2#13069412C211yesmaximal, characteristic, complemented
3#13069412C211yesmaximal, characteristic, complemented
4#13069232C211yesmaximal, characteristic, complemented
5#13069226C211yesmaximal, characteristic, complemented
6#13069181C211yesmaximal, characteristic, complemented
7#13069179C211yesmaximal, characteristic, complemented
8#13068914C211yesmaximal, characteristic, complemented
9#13068913C211yesmaximal, characteristic, complemented
10#13068911C211yesmaximal, characteristic, complemented
11#13068799C211yesmaximal, characteristic, complemented
12#13068798C211yesmaximal, characteristic, complemented
13#13068683C211yesmaximal, characteristic, complemented
14#13068595C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66991C411yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622834C411yescharacteristic
27C4×C22⋊Dic11C2211yescharacteristic
28C4×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42#10622600C411yescharacteristic
43#10622586C411yescharacteristic
44#10622569C411yescharacteristic
45#10622569C411yescharacteristic
46#10622557C411yescharacteristic
47#10622557C411yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11C2×C411yescharacteristic
63C22×C22⋊D11C2×C411yescharacteristic
64C22×C4×D11C2×C411yescharacteristic
65C22×C4×D11C2×C411yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C2×C11×M16—41no—
68C2×C11×M16—41no—
69C2×C11×M16—41no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C4×D4×C11—41no—
75C4×D4×C11—41no—
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11C2×C411yescharacteristic
81C2×C22⋊Dic11C2×C411yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86#66991—24no—
87C4×C22⋊D11—41no—
88C4×C22⋊D11—41no—
89C4×C22⋊D11—41no—
90C4×C22⋊D11—41no—
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×C4⋊Dic11C2×C411yescharacteristic
94C2×C4⋊Dic11C2×C411yescharacteristic
95C2×Dic11⋊C4C2×C411yescharacteristic
96C2×Dic11⋊C4C2×C411yescharacteristic
97C2×C4×Dic11C2×C411yescharacteristic
98C2×C4×Dic11C2×C411yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×#4318—41no—
103C2×#4318—41no—
104C2×#4318—41no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C42×D11—41no—
110C42×D11—41no—
111C11×C22⋊C8—41no—
112C11×C22⋊C8—41no—
113C11×C22⋊C8—41no—
114C11⋊#95C2×C411yescharacteristic
115C11⋊#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C22⋊(C11⋊C8)—41no—
121C22⋊(C11⋊C8)—41no—
122C22⋊(C11⋊C8)—41no—
123(C2×D11)⋊C8—41no—
124(C2×D11)⋊C8—41no—
125(C2×D11)⋊C8—41no—
126(C2×D11)⋊C8—41no—
127#66879—41no—
128#66879—41no—
129Dic11⋊C8—41no—
130Dic11⋊C8—41no—
131Dic11⋊C8—41no—
132Dic11⋊C8—41no—
133#23334—111nomaximal, Sylow
134C24×C11C22×C411yescharacteristic
135C24×C11C22×C411yescharacteristic
136C23×D11C22×C411yescharacteristic
137C2×D4×C11—22no—
138C2×D4×C11—41no—
139C2×D4×C11—41no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—22no—
158C2×C22⋊D11—22no—
159C2×C22⋊D11—41no—
160C2×C22⋊D11—41no—
161C2×C22⋊D11—41no—
162C2×C22⋊D11—41no—
163C22×Dic11C22×C411yescharacteristic
164C22×Dic11C22×C411yescharacteristic
165C22×Dic11C22×C411yescharacteristic
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—41no—
177C2×C4×D11—41no—
178C2×C4×D11—41no—
179C2×C4×D11—41no—
180C2×C4×D11—41no—
181C2×C4×D11M1614yescomplemented
182C11×M16—44no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C11×C4⋊C4—41no—
196C11×C22⋊C4—41no—
197C11×C22⋊C4—41no—
198C42×C11—21no—
199C42×C11—21no—
200C22⋊Dic11—22no—
201C22⋊Dic11—22no—
202C22⋊Dic11—41no—
203C22⋊Dic11—41no—
204C22⋊Dic11—41no—
205C22⋊Dic11—41no—
206(C2×D11)⋊C4—41no—
207(C2×D11)⋊C4—41no—
208C4⋊Dic11—22no—
209C4⋊Dic11—41no—
210Dic11⋊C4—41no—
211Dic11⋊C4—41no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—41no—
219C4×Dic11—41no—
220#4318—44no—
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—21no—
233C4×#121—111no—
234#1955—111no—
235#1955—111no—
236#1924—111no—
237#1924—111no—
238#1917—111no—
239#1917—111no—
240#1870—111no—
241#1870—111no—
242#1870—111no—
243#1870D1111yescharacteristic, complemented
244#1851—111no—
245#1851—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×C11C23×C411yescharacteristic
263C22×D11—21no—
264C22×D11—21no—
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11C2×M1612yes—
270D4×C11—44no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
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—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11C2×M1612yes—
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C2×C4×C11H(5,𝔽2)11yescharacteristic
296C2×C4×C112−1+411yescharacteristic
297C22⋊D11—44no—
298C22⋊D11—44no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11C2×M1612yes—
320C4×D11—44no—
321C4×D11—44no—
322C4×D11—41no—
323C4×D11—41no—
324C4×D11—41no—
325C4×D11—41no—
326C8×C11—41no—
327C8×C11—41no—
328C8×C11—41no—
329C8×C11—41no—
330C11⋊C8—41no—
331C11⋊C8—41no—
332C11⋊C8—41no—
333C11⋊C8—41no—
334C22×M16—111no—
335C22×M16C2×D1111yescharacteristic
336C2×#121—111no—
337C2×C4×D4—111no—
338C2×C4×D4—111no—
339C2×C4×D4C2×D1111yescharacteristic
340C22×C42—111no—
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⋊C8C2×D1111yescharacteristic
353C2×C22⋊C8C2×D1111yescharacteristic
354C2×C22⋊C8C2×D1111yescharacteristic
355C2×#97—111no—
356C2×#97—111no—
357#390—111no—
358#389—111no—
359#388—111no—
360#388—111no—
361#386—111no—
362#386—111no—
363#380—111no—
364C4×C4⋊C4—111no—
365C4×C22⋊C4—111no—
366C4×C22⋊C4—111no—
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#336C2×D1111yescharacteristic
376#336C2×D1111yescharacteristic
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
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#51811yescharacteristic
392C22×C11#51811yescharacteristic
393C22×C11#52011yescharacteristic
394C22×C11C22×M1611yescharacteristic
395C22×C11#56811yescharacteristic
396C22×C11#56811yescharacteristic
397C22×C11#56811yescharacteristic
398C2×D11—22no—
399C2×D11—22no—
400C2×D11—22no—
401C2×D11—41no—
402C2×D11—41no—
403C2×D11—41no—
404C2×D11—41no—
405C4×C11—22no—
406C4×C11—41no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11#56011yescharacteristic
410C4×C11#56011yescharacteristic
411C4×C11#56211yescharacteristic
412C4×C11#56211yescharacteristic
413Dic11—22no—
414Dic11—41no—
415Dic11—41no—
416Dic11—41no—
417Dic11—41no—
418Dic11—41no—
419Dic11—41no—
420C22×D4—111no—
421C22×D4—111no—
422C22×D4C4×D1111yescharacteristic
423C23×C4—111no—
424C23×C4—111no—
425C23×C4—111no—
426C23×C4C22×D1111yescharacteristic
427C23×C4C22×D1111yescharacteristic
428C2×M16—41no—
429C2×M16—41no—
430C2×M16—41no—
431C2×M16—441no—
432C2×M16—441no—
433C2×M16—441no—
434C22×C8—111no—
435C22×C8—111no—
436C22×C8—111no—
437C22×C8—111no—
438C22×C8C22×D1111yescharacteristic
439C22×C8C22×D1111yescharacteristic
440C22×C8C22×D1111yescharacteristic
441C22×C8C22×D1111yescharacteristic
442#121—224no—
443C4×D4—41no—
444C4×D4—41no—
445C4×D4—441no—
446C4×D4—441no—
447C4×D4—441no—
448C4×D4—441no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—111no—
451C2×C4⋊C4—111no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4C4×D1111yescharacteristic
454C2×C22⋊C4—111no—
455C2×C22⋊C4—111no—
456C2×C22⋊C4—111no—
457C2×C22⋊C4—111no—
458C2×C22⋊C4—111no—
459C2×C22⋊C4—111no—
460C2×C22⋊C4—111no—
461C2×C22⋊C4—111no—
462C2×C22⋊C4C4×D1111yescharacteristic
463C2×C22⋊C4C4×D1111yescharacteristic
464C2×C42—111no—
465C2×C42—111no—
466C2×C42—111no—
467C2×C42—111no—
468C2×C42—111no—
469C2×C42—441no—
470C2×C42—441no—
471C2×C42C22×D1111yescharacteristic
472C4⋊C8—441no—
473C4⋊C8—441no—
474C4⋊C8—441no—
475C4⋊C8—441no—
476C22⋊C8—41no—
477C22⋊C8—41no—
478C22⋊C8—41no—
479C22⋊C8—441no—
480C22⋊C8—441no—
481C22⋊C8—441no—
482C22⋊C8—441no—
483C22⋊C8—441no—
484C22⋊C8—441no—
485C22⋊C8—441no—
486#97—441no—
487#97—441no—
488#95—111no—
489#95—111no—
490#95—111no—
491#95—111no—
492#95—111no—
493#95—111no—
494C2×C11—81no—
495C2×C11—81no—
496C2×C11#237711yescharacteristic
497C2×C11#297311yescharacteristic
498C2×C11#297511yescharacteristic
499C2×C11#297811yescharacteristic
500C2×C11#298011yescharacteristic
501C2×C11#298911yescharacteristic
502C2×C11#299511yescharacteristic
503D11—42no—
504C24—111no—
505C24C2×C4×D1111yescharacteristic
506C24C2×C4×D1111yescharacteristic
507C2×D4—22no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—222no—
511C2×D4—222no—
512C2×D4—441no—
513C2×D4—441no—
514C2×D4—441no—
515C2×D4—441no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
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—111no—
529C22×C4—114no—
530C22×C4—111no—
531C22×C4—111no—
532C22×C4—111no—
533C22×C4—111no—
534C22×C4—111no—
535C22×C4—111no—
536C22×C4—221no—
537C22×C4—221no—
538C22×C4—221no—
539C22×C4—221no—
540C22×C4—221no—
541C22×C4—221no—
542C22×C4—441no—
543C22×C4—441no—
544C22×C4—441no—
545C22×C4—441no—
546C22×C4—441no—
547C22×C4C2×C4×D1111yescharacteristic
548C22×C4C2×C4×D1111yescharacteristic
549C22×C4C2×C4×D1111yescharacteristic
550C22×C4C2×C4×D1111yescharacteristic
551C22×C4C23×D1111yescharacteristic
552M16—44no—
553M16—444no—
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×C8—21no—
565C2×C8—21no—
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—221no—
578C4⋊C4—41no—
579C4⋊C4—222no—
580C4⋊C4—441no—
581C4⋊C4—441no—
582C4⋊C4—441no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—222no—
586C22⋊C4—222no—
587C22⋊C4—441no—
588C22⋊C4—441no—
589C22⋊C4—441no—
590C22⋊C4—441no—
591C22⋊C4—441no—
592C22⋊C4—441no—
593C42—21no—
594C42—21no—
595C42—221no—
596C42—221no—
597C42—221no—
598C42—221no—
599C42—221no—
600C42—221no—
601C42—441no—
602C42—441no—
603C11#2333411yescharacteristic, 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—112no—
619C23—221no—
620C23—221no—
621C23—221no—
622C23—221no—
623C23—221no—
624C23—221no—
625C23C22×C4×D1111yescharacteristic
626D4—44no—
627D4—444no—
628D4—444no—
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—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—112no—
649C2×C4—221no—
650C2×C4—221no—
651C2×C4—221no—
652C2×C4—221no—
653C2×C4—221no—
654C2×C4—221no—
655C2×C4—221no—
656C2×C4—221no—
657C2×C4—221no—
658C2×C4—221no—
659C2×C4—221no—
660C2×C4—221no—
661C2×C4—221no—
662C2×C4—221no—
663C2×C4—221no—
664C2×C4—221no—
665C2×C4—221no—
666C2×C4—221no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—444no—
670C2×C4—444no—
671C2×C4—441no—
672C2×C4—441no—
673C2×C4—441no—
674C2×C4—441no—
675C2×C4M16×D1112yes—
676C2×C4#6703711yescharacteristic
677C2×C4#6703711yescharacteristic
678C2×C4#6703711yescharacteristic
679C2×C4#6703711yescharacteristic
680C2×C4#6704211yescharacteristic
681C2×C4#6704311yescharacteristic
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—441no—
687C8—441no—
688C8—441no—
689C8—441no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—222no—
705C22—222no—
706C22—222no—
707C22—441no—
708C22—441no—
709C22—441no—
710C22—441no—
711C22#1062301711yescharacteristic
712C22#1062307611yescharacteristic
713C22#1062307711yescharacteristic
714C22C2×M16×D1111yescharacteristic
715C22#1062327611yescharacteristic
716C22#1062328111yescharacteristic
717C22#1062328111yescharacteristic
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—222no—
723C4—441no—
724C4—441no—
725C4—441no—
726C4—441no—
727C4—441no—
728C4—441no—
729C4#1062312611yescharacteristic
730C4#1062315111yescharacteristic
731C4#1062315211yescharacteristic
732C4#1062319811yescharacteristic
733C2—81no—
734C2—81no—
735C2—442no—
736C2#1307176811yescharacteristic
737C2#1307764311yescharacteristic
738C2#1307765411yescharacteristic
739C2#1307767411yescharacteristic
740C2#1307768411yescharacteristic
741C2#1307773111yescharacteristic
742C2#1307778211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC2×#66991C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#23334
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #13069412C2semidirect
3. #13069412C2semidirect
4. #13069232C2semidirect
5. #13069226C2semidirect
6. #13069181C2semidirect
7. #13069179C2semidirect
8. #13068914C2semidirect
9. #13068913C2semidirect
10. #13068911C2semidirect
11. #13068799C2semidirect
12. #13068798C2semidirect
13. #13068683C2semidirect
14. #13068595C2semidirect
15. C11×#1870C2semidirect
181. C2×C4×D11M16semidirect
243. #1870D11semidirect
603. C11#23334semidirect

Maximal subgroups

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

subgroupindex
C4×#669912
#130694122
#130692322
#130692262
#130691812
#130691792
#130689142
#130689132
#130689112
#130687992
#130687982
#130686832
#130685952
C11×#18702
#2333411