Finite Group Databasebeta

← #14780337

Subgroups — #14780337

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071895C211yesmaximal, characteristic
2#13068914C211yesmaximal, characteristic, complemented
3#13068913C211yesmaximal, characteristic, complemented
4#13068913C211yesmaximal, characteristic, complemented
5#13068912C211yesmaximal, characteristic, complemented
6#13068911C211yesmaximal, characteristic, complemented
7#13068911C211yesmaximal, characteristic, complemented
8#13068910C211yesmaximal, characteristic, complemented
9#13068910C211yesmaximal, characteristic, complemented
10#13068907C211yesmaximal, characteristic, complemented
11#13068905C211yesmaximal, characteristic, complemented
12#13068905C211yesmaximal, characteristic, complemented
13#13068760C211yesmaximal, characteristic, complemented
14#13068760C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24C22×C8×D11C2211yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29#10622836C411yescharacteristic
30#10622836C411yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40#10622605C411yescharacteristic
41#10622605C411yescharacteristic
42#10622573C411yescharacteristic
43#10622573C411yescharacteristic
44#10622562C411yescharacteristic
45#10622562C411yescharacteristic
46#10622545C2211yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
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×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C2×C11×M16—41no—
70C2×C11×M16—41no—
71C2×C11×M16—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C4×D4×C11—41no—
77C4×D4×C11—41no—
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C4×C22⋊D11—41no—
87C4×C22⋊D11—41no—
88C4×C22⋊D11—41no—
89C4×C22⋊D11—41no—
90C4×C22⋊D11—41no—
91C4×C22⋊D11—41no—
92C4×C22⋊D11—41no—
93C4×C22⋊D11—41no—
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×C4⋊Dic11C2×C411yescharacteristic
101C2×Dic11⋊C4C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×#4318—41no—
108C2×#4318—41no—
109C2×#4318—41no—
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C2×#4313—41no—
115C2×#4313—41no—
116C2×#4313—41no—
117C2×C8×D11—41no—
118C2×C8×D11—41no—
119C2×C8×D11—41no—
120C4×D44—41no—
121C4×D44—41no—
122C11×C22⋊C8—41no—
123C11×C22⋊C8—41no—
124C11×C22⋊C8—41no—
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C22⋊(C11⋊C8)—41no—
130C22⋊(C11⋊C8)—41no—
131C22⋊(C11⋊C8)—41no—
132(C2×D11)⋊C8—41no—
133(C2×D11)⋊C8—41no—
134(C2×D11)⋊C8—41no—
135(C2×D11)⋊C8—41no—
136(C2×D11)⋊C8—41no—
137(C2×D11)⋊C8—41no—
138#23359—111nomaximal, Sylow
139C24×C11C22×C411yescharacteristic
140C24×C11C22×C411yescharacteristic
141C23×D11C22×C411yescharacteristic
142C23×D11C22×C411yescharacteristic
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
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×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—22no—
164C2×C22⋊D11—22no—
165C2×C22⋊D11—41no—
166C2×C22⋊D11—41no—
167C2×C22⋊D11—41no—
168C2×C22⋊D11—41no—
169C2×C22⋊D11—41no—
170C2×C22⋊D11—41no—
171C2×C22⋊D11—41no—
172C2×C22⋊D11—41no—
173C2×C22⋊D11—41no—
174C2×C22⋊D11—41no—
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C22×Dic11C22×C411yescharacteristic
180C22×Dic11C22×C411yescharacteristic
181C2×D44—22no—
182C2×D44—41no—
183C2×D44—41no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C11×M16—44no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C11×C4⋊C4—41no—
210C11×C22⋊C4—41no—
211C11×C22⋊C4—41no—
212C42×C11—21no—
213C42×C11—21no—
214C22⋊Dic11—41no—
215C22⋊Dic11—41no—
216C22⋊Dic11—41no—
217C22⋊Dic11—41no—
218(C2×D11)⋊C4—41no—
219(C2×D11)⋊C4—41no—
220(C2×D11)⋊C4—41no—
221(C2×D11)⋊C4—41no—
222(C2×D11)⋊C4—41no—
223(C2×D11)⋊C4—41no—
224C4⋊Dic11—41no—
225Dic11⋊C4—41no—
226Dic11⋊C4—41no—
227Dic11⋊C4—41no—
228Dic11⋊C4—41no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C4×Dic11—21no—
232C4×Dic11—21no—
233#4318—44no—
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—
246#4313—44no—
247C8×D11—44no—
248#2397—111no—
249#1870—111no—
250#1870—111no—
251#1870—111no—
252#1870—111no—
253#1870—111no—
254#1870—111no—
255#1870—111no—
256#1870—111no—
257#1870D1111yescharacteristic, complemented
258#1869—111no—
259#1869—111no—
260#1869—111no—
261#1840—111no—
262#1840—111no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11C23×C411yescharacteristic
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11#13112yes—
292D4×C11—44no—
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—21no—
304C2×C4×C11—21no—
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×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C22⋊D11—44no—
320C22⋊D11—44no—
321C22⋊D11—44no—
322C22⋊D11—44no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341D44—44no—
342C4×D11—41no—
343C4×D11—41no—
344C4×D11—41no—
345C4×D11—41no—
346C4×D11—41no—
347C4×D11—41no—
348C4×D11—41no—
349C4×D11—41no—
350C8×C11—41no—
351C8×C11—41no—
352C8×C11—41no—
353C8×C11—41no—
354C11⋊C8—41no—
355C11⋊C8—41no—
356C11⋊C8—41no—
357C11⋊C8—41no—
358C22×M16—111no—
359C22×M16—111no—
360C22×M16C2×D1111yescharacteristic
361C23×C8—111no—
362C2×C4×D4—111no—
363C2×C4×D4—111no—
364C2×C4×D4—111no—
365C2×C4×D4—111no—
366C2×C4×D4—111no—
367C2×C4×D4C2×D1111yescharacteristic
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370C2×C22⋊C8—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8—111no—
373C2×C22⋊C8—111no—
374C2×C22⋊C8—111no—
375C2×C22⋊C8—111no—
376C2×C22⋊C8—111no—
377C2×C22⋊C8C2×D1111yescharacteristic
378C2×C22⋊C8C2×D1111yescharacteristic
379C2×C22⋊C8C2×D1111yescharacteristic
380#399—111no—
381#399—111no—
382#399—111no—
383#399—111no—
384#392—111no—
385#392—111no—
386#392—111no—
387#392—111no—
388#376—111no—
389#336—111no—
390#336—111no—
391#336—111no—
392#336—111no—
393#336—111no—
394#336—111no—
395#336—111no—
396#336—111no—
397#336—111no—
398#336—111no—
399#336C2×D1111yescharacteristic
400#336C2×D1111yescharacteristic
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11#51811yescharacteristic
416C22×C11#51811yescharacteristic
417C22×C11#51811yescharacteristic
418C22×C11C2×#13111yescharacteristic
419C22×C11#56811yescharacteristic
420C22×C11#56811yescharacteristic
421C22×C11#56811yescharacteristic
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—41no—
426C2×D11—41no—
427C2×D11—41no—
428C2×D11—41no—
429C2×D11—41no—
430C2×D11—41no—
431C2×D11—41no—
432C2×D11—41no—
433C2×D11—41no—
434C2×D11—41no—
435C2×D11—41no—
436C4×C11—41no—
437C4×C11—41no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11#56011yescharacteristic
441C4×C11#56011yescharacteristic
442C4×C11#56011yescharacteristic
443C4×C11#56011yescharacteristic
444Dic11—41no—
445Dic11—41no—
446Dic11—41no—
447Dic11—41no—
448Dic11—41no—
449Dic11—41no—
450C22×D4—111no—
451C22×D4—111no—
452C22×D4—111no—
453C22×D4—111no—
454C22×D4—111no—
455C22×D4C4×D1111yescharacteristic
456C23×C4—111no—
457C23×C4—111no—
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1111yescharacteristic
460C2×M16—41no—
461C2×M16—41no—
462C2×M16—41no—
463C2×M16—441no—
464C2×M16—441no—
465C2×M16—441no—
466C2×M16—441no—
467C2×M16—441no—
468C2×M16—441no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—111no—
472C22×C8—111no—
473C22×C8—441no—
474C22×C8—441no—
475C22×C8—441no—
476C22×C8C22×D1111yescharacteristic
477C22×C8C22×D1111yescharacteristic
478C22×C8C22×D1111yescharacteristic
479C22×C8C22×D1111yescharacteristic
480C4×D4—41no—
481C4×D4—41no—
482C4×D4—441no—
483C4×D4—441no—
484C4×D4—441no—
485C4×D4—441no—
486C4×D4—441no—
487C4×D4—441no—
488C4×D4—441no—
489C4×D4—441no—
490C4×D4—441no—
491C4×D4—441no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4C4×D1111yescharacteristic
498C2×C22⋊C4—111no—
499C2×C22⋊C4—111no—
500C2×C22⋊C4—111no—
501C2×C22⋊C4—111no—
502C2×C22⋊C4—111no—
503C2×C22⋊C4—111no—
504C2×C22⋊C4—111no—
505C2×C22⋊C4—111no—
506C2×C22⋊C4—111no—
507C2×C22⋊C4—111no—
508C2×C22⋊C4C4×D1111yescharacteristic
509C2×C22⋊C4C4×D1111yescharacteristic
510C2×C42—111no—
511C2×C42—111no—
512C2×C42C22×D1111yescharacteristic
513C22⋊C8—41no—
514C22⋊C8—41no—
515C22⋊C8—41no—
516C22⋊C8—441no—
517C22⋊C8—441no—
518C22⋊C8—441no—
519C22⋊C8—441no—
520C22⋊C8—441no—
521C22⋊C8—441no—
522C22⋊C8—441no—
523C22⋊C8—441no—
524C22⋊C8—441no—
525#95—111no—
526#95—111no—
527#95—111no—
528#95—111no—
529C2×C11—81no—
530C2×C11—81no—
531C2×C11#238011yescharacteristic
532C2×C11#297611yescharacteristic
533C2×C11#297611yescharacteristic
534C2×C11#297611yescharacteristic
535C2×C11#297811yescharacteristic
536C2×C11#297811yescharacteristic
537C2×C11#297811yescharacteristic
538D11—42no—
539D11—81no—
540C24—111no—
541C24—111no—
542C24C2×C4×D1111yescharacteristic
543C24C2×C4×D1111yescharacteristic
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—222no—
548C2×D4—222no—
549C2×D4—222no—
550C2×D4—441no—
551C2×D4—441no—
552C2×D4—441no—
553C2×D4—441no—
554C2×D4—441no—
555C2×D4—441no—
556C2×D4—441no—
557C2×D4—441no—
558C2×D4—441no—
559C2×D4—441no—
560C2×D4—441no—
561C2×D4—441no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—111no—
577C22×C4—111no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4C2×C4×D1111yescharacteristic
593C22×C4C2×C4×D1111yescharacteristic
594C22×C4C2×C4×D1111yescharacteristic
595C22×C4C2×C4×D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597M16—44no—
598M16—444no—
599M16—444no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—221no—
615C2×C8—221no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—444no—
625C4⋊C4—41no—
626C4⋊C4—441no—
627C4⋊C4—441no—
628C4⋊C4—441no—
629C4⋊C4—441no—
630C4⋊C4—441no—
631C22⋊C4—41no—
632C22⋊C4—41no—
633C22⋊C4—441no—
634C22⋊C4—441no—
635C22⋊C4—441no—
636C22⋊C4—441no—
637C22⋊C4—441no—
638C22⋊C4—441no—
639C22⋊C4—441no—
640C22⋊C4—441no—
641C22⋊C4—441no—
642C22⋊C4—441no—
643C42—21no—
644C42—21no—
645C42—221no—
646C42—221no—
647C42—221no—
648C42—221no—
649C11#2335911yescharacteristic, complemented, Sylow
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—112no—
665C23—221no—
666C23—221no—
667C23—221no—
668C23—221no—
669C23—221no—
670C23—221no—
671C23—221no—
672C23—221no—
673C23—221no—
674C23—221no—
675C23—221no—
676C23—221no—
677C23—221no—
678C23C22×C4×D1111yescharacteristic
679D4—44no—
680D4—444no—
681D4—444no—
682D4—444no—
683D4—444no—
684D4—444no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—221no—
706C2×C4—221no—
707C2×C4—221no—
708C2×C4—221no—
709C2×C4—221no—
710C2×C4—221no—
711C2×C4—221no—
712C2×C4—221no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—221no—
716C2×C4—221no—
717C2×C4—221no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—221no—
722C2×C4—221no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4#6703711yescharacteristic
732C2×C4#6703711yescharacteristic
733C2×C4#6703711yescharacteristic
734C2×C4#6703711yescharacteristic
735C2×C4#6704211yescharacteristic
736C2×C4#6704211yescharacteristic
737C8—41no—
738C8—41no—
739C8—41no—
740C8—41no—
741C8—441no—
742C8—441no—
743C8—441no—
744C8—441no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—222no—
760C22—222no—
761C22—222no—
762C22—441no—
763C22—441no—
764C22—441no—
765C22—441no—
766C22—441no—
767C22—441no—
768C22—441no—
769C22—441no—
770C22—441no—
771C22—441no—
772C22—441no—
773C22#1062301711yescharacteristic
774C22#1062307611yescharacteristic
775C22#1062307611yescharacteristic
776C22#1062327611yescharacteristic
777C22#1062327611yescharacteristic
778C22D11×#13111yescharacteristic
779C22#1062328111yescharacteristic
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—441no—
785C4—441no—
786C4—441no—
787C4—441no—
788C4—441no—
789C4—441no—
790C4#1062312611yescharacteristic
791C4#1062315111yescharacteristic
792C4#1062315111yescharacteristic
793C4#1062319711yescharacteristic
794C2—81no—
795C2—81no—
796C2—442no—
797C2—881no—
798C2#1307179111yescharacteristic
799C2#1307765911yescharacteristic
800C2#1307766011yescharacteristic
801C2#1307766311yescharacteristic
802C2#1307767311yescharacteristic
803C2#1307767511yescharacteristic
804C2#1307767611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radical#13071895C2
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#23359
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #13068914C2semidirect
3. #13068913C2semidirect
4. #13068913C2semidirect
5. #13068912C2semidirect
6. #13068911C2semidirect
7. #13068911C2semidirect
8. #13068910C2semidirect
9. #13068910C2semidirect
10. #13068907C2semidirect
11. #13068905C2semidirect
12. #13068905C2semidirect
13. #13068760C2semidirect
14. #13068760C2semidirect
15. C11×#1870C2semidirect
257. #1870D11semidirect
649. C11#23359semidirect

Maximal subgroups

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

subgroupindex
#130718952
#130689142
#130689132
#130689122
#130689112
#130689102
#130689072
#130689052
#130687602
C11×#18702
#2335911