Finite Group Databasebeta

← C2×#13078976 #15623016

Subgroups — C2×#13078976 #15623016

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623260C211yesmaximal, characteristic, complemented
2C2×#10623255C211yesmaximal, characteristic
3#13078976C2116yesmaximal, direct product factor
4C2×#10622695C211yesmaximal, characteristic, complemented
5C2×#10622410C211yesmaximal, characteristic, complemented
6C2×#10622702C211yesmaximal, characteristic, complemented
7C2×#10622408C211yesmaximal, characteristic, complemented
8C2×#10622413C211yesmaximal, characteristic, complemented
9C2×#10622310C211yesmaximal, characteristic, complemented
10C2×#10622405C211yesmaximal, characteristic, complemented
11C2×#10622416C211yesmaximal, characteristic
12C2×#10622415C211yesmaximal, characteristic, complemented
13C2×#10622417C211yesmaximal, characteristic
14C2×D11×#103C211yesmaximal, characteristic, complemented
15C2×#10622302C211yesmaximal, characteristic, complemented
16C2×C11×#487C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×#66999—21no—
23C2×#66997—21no—
24C2×#66997C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27#10623260—24no—
28#10623260C2218yescomplemented
29#10623255—24no—
30#10623255C2218yes—
31C2×#66949—21no—
32C2×#66949—21no—
33C2×#66949—21no—
34C2×#66947—21no—
35C2×#66947—21no—
36C2×#66945C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66943C2211yescharacteristic
39C2×#66942—21no—
40C2×#66941C2211yescharacteristic
41C2×#66928C2211yescharacteristic
42C2×#66925C2211yescharacteristic
43C2×#66923C2211yescharacteristic
44C11×#487C2218yescomplemented
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C4×C8×C11C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×#66880C2211yescharacteristic
58C2×#66879C2211yescharacteristic
59C2×C8×Dic11C2211yescharacteristic
60#10622702C2218yescomplemented
61#10622695C2218yescomplemented
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66867C2211yescharacteristic
67#10622417C2218yes—
68#10622416C2218yes—
69#10622415C2218yescomplemented
70D11×#103C2218yescomplemented
71#10622413C2218yescomplemented
72#10622410C2218yescomplemented
73#10622408C2218yescomplemented
74#10622405C2218yescomplemented
75#10622310C2218yescomplemented
76#10622302C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C2×#4343—22no—
81C2×#4343—24no—
82C2×#4343—24no—
83C2×#4343C2314yes—
84C2×Q8×D11—22no—
85C2×Q8×D11—24no—
86C2×Q8×D11—24no—
87C2×Q8×D11C2314yes—
88C22×D44—21no—
89C22×D44C2311yescharacteristic
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11C2311yescharacteristic
94C22×Dic22—21no—
95C22×Dic22—21no—
96C22×Dic22C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C11×C4⋊Q8—22no—
100C11×C4⋊Q8—22no—
101C11×C4⋊Q8C2314yes—
102C11×C4⋊Q8C2314yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109#67000—22no—
110#67000C2314yes—
111#66999—28no—
112#66997—28no—
113#66997—22no—
114#66997C2314yes—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4D411yescharacteristic
121C2×(C2×D11)⋊C4D411yescharacteristic
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4D411yescharacteristic
133C2×Dic11⋊C4D411yescharacteristic
134C2×C4×Dic11—21no—
135C2×C4×Dic11C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C2×#4313—24no—
139C2×#4313C2314yes—
140C2×C8×D11—24no—
141C2×C8×D11C2314yes—
142#66949—28no—
143#66949—28no—
144#66949—28no—
145#66947—28no—
146#66947—28no—
147#66945—22no—
148#66945C2314yes—
149C4⋊C4×D11—22no—
150C4⋊C4×D11C2314yes—
151#66943—22no—
152#66943C2314yes—
153#66942—28no—
154#66941—22no—
155#66941C2314yes—
156#66928—22no—
157#66928C2314yes—
158#66925D414yes—
159#66925C2314yes—
160#66923—22no—
161#66923C2314yes—
162C11×#103C2314yes—
163C11×#103C2314yes—
164C11×#103C2314yes—
165C11×#103C2314yes—
166C4×C8×C11C2314yes—
167#66899C2314yes—
168#66899C2314yes—
169#66899C2314yes—
170#66899C2314yes—
171#66885C2314yes—
172#66885C2314yes—
173#66880C2314yes—
174#66880C2314yes—
175#66879C2314yes—
176C8×Dic11C2314yes—
177#66874C2314yes—
178#66874C2314yes—
179#66873C2314yes—
180#66873C2314yes—
181#66867C2314yes—
182C2×#3137—111nomaximal, Sylow
183C23×D11—21no—
184C23×D11C2×D411yescharacteristic
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—24no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11—22no—
192C2×Q8×C11—82no—
193C2×Q8×C11C2412yes—
194C2×Q8×C11C2412yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208#4343—28no—
209#4343—28no—
210#4343—48no—
211Q8×D11—28no—
212Q8×D11—28no—
213Q8×D11—48no—
214C2×D44—24no—
215C2×D44—21no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—44no—
219C2×D44C2412yes—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×C4×D11—82no—
226C2×C4×D11C2×D412yes—
227C2×C4×D11#4114yes—
228C2×C4×D11#4114yes—
229C2×C4×D11C2412yes—
230C2×Dic22—24no—
231C2×Dic22—24no—
232C2×Dic22—21no—
233C2×Dic22—22no—
234C2×Dic22—22no—
235C2×Dic22—44no—
236C2×Dic22—82no—
237C2×Dic22C2412yes—
238C2×C8×C11—22no—
239C2×C8×C11—22no—
240C2×C8×C11C2412yes—
241C2×C8×C11C2412yes—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4C2412yes—
248C11×C4⋊C4C2412yes—
249C42×C11C2×D412yes—
250C42×C11C2412yes—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4C2×D414yes—
257(C2×D11)⋊C4C2×D414yes—
258C4⋊Dic11—24no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11C2412yes—
262C4⋊Dic11C2412yes—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4C2×D414yes—
271Dic11⋊C4C2×D414yes—
272C4×Dic11—24no—
273C4×Dic11C2×D412yes—
274C4×Dic11C2412yes—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279#4313—28no—
280C8×D11—28no—
281C2×#544—111no—
282C2×#536—111no—
283#3137—1116no—
284C2×#491—111no—
285C2×#491—111no—
286C2×#489—111no—
287C2×#489—111no—
288C2×#488—111no—
289C2×#488—111no—
290C2×#487—111no—
291C2×#487D1111yescharacteristic, complemented
292C2×#417—111no—
293C2×#419—111no—
294C2×#416—111no—
295C22×#103—111no—
296C2×#405—111no—
297C23×C11C22×D411yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11#12414yes—
305C22×D11C22×D412yes—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—22no—
310Q8×C11—42no—
311Q8×C11—42no—
312Q8×C11—84no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C2×#4112yes—
327C2×C4×C11C2×#4112yes—
328C2×C4×C11C2511yescharacteristic
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11#12414yes—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340C2×Dic11C22×D412yes—
341D44—22no—
342D44—22no—
343D44—48no—
344D44—42no—
345C4×D11—48no—
346C4×D11—48no—
347C4×D11—84no—
348C4×D11#12418yes—
349C4×D11C2×#4114yes—
350C4×D11C2×#4114yes—
351Dic22—22no—
352Dic22—22no—
353Dic22—42no—
354Dic22—48no—
355Dic22—84no—
356C8×C11—22no—
357C8×C11—22no—
358C11⋊C8—22no—
359C11⋊C8—22no—
360C22×#41—111no—
361C23×Q8—111no—
362C22×M16—111no—
363C23×C8—111no—
364#544—118no—
365#544—224no—
366#536—118no—
367#536—224no—
368C2×C4⋊Q8—111no—
369C2×C4⋊Q8—111no—
370C2×C4⋊Q8—221no—
371C2×C4⋊Q8C2×D1111yescharacteristic
372C2×C4⋊Q8C2×D1111yescharacteristic
373C2×#125—111no—
374C2×#125—111no—
375C2×#125—221no—
376C2×#124—111no—
377C2×#124—111no—
378C2×#123—221no—
379C2×#123—221no—
380C2×C22⋊Q8—221no—
381C2×C22⋊Q8—221no—
382C2×C22⋊Q8—221no—
383C2×C22⋊Q8—221no—
384C2×#117—111no—
385C2×#117—111no—
386C22×C4⋊C4—111no—
387#491—118no—
388#491—118no—
389#489—118no—
390#489—118no—
391#488—118no—
392#488—118no—
393#487—118no—
394#487C2×D1118yescomplemented
395#419—118no—
396#417—118no—
397#416—118no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—118no—
407C2×#103C2×D1111yescharacteristic
408C2×#103C2×D1111yescharacteristic
409C2×#103C2×D1111yescharacteristic
410C2×#103C2×D1111yescharacteristic
411C2×#102—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415#405—118no—
416C2×#97—111no—
417C2×#97—111no—
418C2×C4×C8—111no—
419C2×C4×C8C2×D1111yescharacteristic
420C22×C11C2×#12412yes—
421C22×C11#57712yes—
422C22×C11#57812yes—
423C22×C11C23×D411yescharacteristic
424C2×D11—28no—
425C2×D11—22no—
426C2×D11—22no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—84no—
431C2×D11C2×#12414yes—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11C2×#12412yes—
439C4×C11C22×#4111yescharacteristic
440C4×C11C22×#4111yescharacteristic
441Dic11—22no—
442Dic11—22no—
443Dic11—42no—
444Dic11—42no—
445Dic11—42no—
446Dic11C2×#12414yes—
447C2×#41—114no—
448C2×#41—222no—
449C2×#41—224no—
450C2×#41—224no—
451C22×Q8—21no—
452C22×Q8—114no—
453C22×Q8—111no—
454C22×Q8—221no—
455C22×Q8—221no—
456C22×Q8—222no—
457C22×Q8—224no—
458C22×Q8—224no—
459C22×Q8C22×D1111yescharacteristic
460C22×Q8C22×D1111yescharacteristic
461C22×D4—111no—
462C22×D4—221no—
463C23×C4—111no—
464C23×C4—221no—
465C23×C4—221no—
466C23×C4—221no—
467C2×M16—114no—
468C2×M16—224no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—114no—
472C22×C8—224no—
473C22×C8C22×D1111yescharacteristic
474C22×C8C22×D1111yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8—22no—
477C4⋊Q8—114no—
478C4⋊Q8—114no—
479C4⋊Q8—222no—
480C4⋊Q8—222no—
481C4⋊Q8—228no—
482C4⋊Q8C22×D1114yes—
483C4⋊Q8C22×D1114yes—
484#125—114no—
485#125—114no—
486#125—222no—
487#125—228no—
488#125—222no—
489#124—114no—
490#124—114no—
491#124—222no—
492#124—222no—
493#123—228no—
494#123—228no—
495C22⋊Q8—228no—
496C22⋊Q8—228no—
497C22⋊Q8—228no—
498C22⋊Q8—228no—
499#117—114no—
500#117—114no—
501#117—114no—
502#117—222no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—114no—
511C2×C4⋊C4—222no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C4⋊C4C22×D1111yescharacteristic
522C2×C22⋊C4—111no—
523C2×C22⋊C4—111no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C42—111no—
530C2×C42—221no—
531C2×C42C22×D1111yescharacteristic
532#103—114no—
533#103—114no—
534#103—114no—
535#103—114no—
536#103—114no—
537#103—114no—
538#103—114no—
539#103—114no—
540#103C22×D1114yes—
541#103C22×D1114yes—
542#103C22×D1114yes—
543#103C22×D1114yes—
544#102—114no—
545#102—114no—
546#102—114no—
547#102—114no—
548#97—114no—
549#97—114no—
550C4×C8—114no—
551C4×C8C22×D1114yes—
552C2×C11#313714yescomplemented
553C2×C11C22×#12411yescharacteristic
554C2×C11C2×#57711yescharacteristic
555C2×C11C2×#57811yescharacteristic
556D11—24no—
557D11—82no—
558C24—111no—
559C24—221no—
560#41—228no—
561#41—228no—
562#41—448no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—82no—
571C2×Q8—112no—
572C2×Q8—224no—
573C2×Q8—224no—
574C2×Q8—228no—
575C2×Q8—228no—
576C2×Q8—221no—
577C2×Q8—222no—
578C2×Q8—222no—
579C2×Q8—444no—
580C2×Q8—448no—
581C2×Q8—882no—
582C2×Q8C23×D1112yes—
583C2×Q8C23×D1112yes—
584C2×D4—112no—
585C2×D4—224no—
586C2×D4—221no—
587C2×D4—222no—
588C2×D4—222no—
589C2×D4—444no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—111no—
595C22×C4—112no—
596C22×C4—114no—
597C22×C4—114no—
598C22×C4—112no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—224no—
602C22×C4—224no—
603C22×C4—224no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—444no—
608C22×C4—444no—
609C22×C4—882no—
610C22×C4D4×D1111yescharacteristic
611C22×C4D4×D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613M16—228no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—112no—
617C2×C8—112no—
618C2×C8—228no—
619C2×C8—222no—
620C2×C8—222no—
621C2×C8C23×D1112yes—
622C2×C8C23×D1112yes—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—114no—
629C4⋊C4—114no—
630C4⋊C4—112no—
631C4⋊C4—112no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4—224no—
637C4⋊C4—224no—
638C4⋊C4—221no—
639C4⋊C4—221no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4C23×D1112yes—
643C4⋊C4C23×D1112yes—
644C22⋊C4—114no—
645C22⋊C4—114no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C22⋊C4—224no—
650C22⋊C4—224no—
651C42—112no—
652C42—112no—
653C42—224no—
654C42D4×D1112yes—
655C42C23×D1112yes—
656C11C2×#313711yescharacteristic, complemented, Sylow
657C23—112no—
658C23—114no—
659C23—222no—
660C23—222no—
661C23—222no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23C2×D4×D1111yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—42no—
672Q8—84no—
673Q8—222no—
674Q8—222no—
675Q8—448no—
676Q8—442no—
677Q8—884no—
678D4—222no—
679D4—222no—
680D4—448no—
681D4—442no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—112no—
693C2×C4—114no—
694C2×C4—114no—
695C2×C4—114no—
696C2×C4—118no—
697C2×C4—112no—
698C2×C4—112no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—448no—
705C2×C4—448no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—884no—
710C2×C4C2×D4×D1112yes—
711C2×C4C2×D4×D1112yes—
712C2×C4C2×D4×D1111yescharacteristic
713C2×C4#41×D1112yes—
714C2×C4#41×D1112yes—
715C2×C4C24×D1111yescharacteristic
716C8—22no—
717C8—22no—
718C8—222no—
719C8—222no—
720C22—114no—
721C22—228no—
722C22—222no—
723C22—222no—
724C22—442no—
725C22—442no—
726C22—442no—
727C22—884no—
728C22D11×#12412yes—
729C22#1062329312yes—
730C22#1062329712yes—
731C22C22×D4×D1111yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—114no—
739C4—222no—
740C4—222no—
741C4—442no—
742C4—442no—
743C4—442no—
744C4D11×#12412yes—
745C4C2×#41×D1111yescharacteristic
746C4C2×#41×D1111yescharacteristic
747C2—224no—
748C2—882no—
749C2#1307897614yesdirect product factor
750C2C2×D11×#12411yescharacteristic
751C2C2×#1062329311yescharacteristic
752C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
hypercenterC2×#487D11
hypocenterC11C2×#3137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
1. C2×#10623260C2semidirect
3. #13078976C2direct (N × H)
4. C2×#10622695C2semidirect
5. C2×#10622410C2semidirect
6. C2×#10622702C2semidirect
7. C2×#10622408C2semidirect
8. C2×#10622413C2semidirect
9. C2×#10622310C2semidirect
10. C2×#10622405C2semidirect
12. C2×#10622415C2semidirect
14. C2×D11×#103C2semidirect
15. C2×#10622302C2semidirect
16. C2×C11×#487C2semidirect
28. #10623260C22semidirect
44. C11×#487C22semidirect
60. #10622702C22semidirect
61. #10622695C22semidirect
69. #10622415C22semidirect
70. D11×#103C22semidirect
71. #10622413C22semidirect
72. #10622410C22semidirect
73. #10622408C22semidirect
74. #10622405C22semidirect
75. #10622310C22semidirect
76. #10622302C22semidirect
291. C2×#487D11semidirect
394. #487C2×D11semidirect
552. C2×C11#3137semidirect
656. C11C2×#3137semidirect
749. C2#13078976direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232602
C2×#106232552
#130789762
C2×#106226952
C2×#106224102
C2×#106227022
C2×#106224082
C2×#106224132
C2×#106223102
C2×#106224052
C2×#106224162
C2×#106224152
C2×#106224172
C2×D11×#1032
C2×#106223022
C2×C11×#4872
C2×#313711