Finite Group Databasebeta

← C2×#13082527 #15662148

Subgroups — C2×#13082527 #15662148

Order 2816.

7758 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082527C2132yesmaximal, direct product factor
2C2×#10623115C212yesmaximal, complemented
3C2×#10623094C212yesmaximal, complemented
4C2×#10623110C212yesmaximal, complemented
5C2×#10623096C214yesmaximal, complemented
6C2×#10623083C214yesmaximal, complemented
7C2×#10623082C212yesmaximal, complemented
8C2×#10623065C214yesmaximal, complemented
9C2×#10623364C212yesmaximal, complemented
10C2×#10623001C212yesmaximal, complemented
11C2×#10623008C212yesmaximal, complemented
12C2×#10623008C211yesmaximal, characteristic, complemented
13C22×#66922C211yesmaximal, characteristic, complemented
14C2×#10623054C212yesmaximal, complemented
15C2×C4×C11×#41C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×#4339C2212yes—
18C22×#4339C2214yes—
19C23×Dic22C2212yes—
20C4×C11×#41C22116yescomplemented
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2212yes—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2212yes—
27C2×C11×#117C2212yes—
28C2×C11×#117C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C22×C42×C11C2212yes—
31#10623364C22132yescomplemented
32C2×#66999C2214yes—
33C2×#66992C2218yes—
34C2×#66991C2214yes—
35C2×#66983C2212yes—
36C2×#66983C2214yes—
37C2×#66983C2214yes—
38C2×#66983C2212yes—
39C2×#66979C2214yes—
40C22×C4⋊Dic11C2212yes—
41C22×C4⋊Dic11C2212yes—
42C2×#66977C2214yes—
43C2×#66977C2214yes—
44#10623115C22132yescomplemented
45#10623110C22132yescomplemented
46#10623096C22164yescomplemented
47#10623094C22132yescomplemented
48#10623083C22164yescomplemented
49#10623082C22132yescomplemented
50#10623065C22164yescomplemented
51#10623054C22132yescomplemented
52C2×#66951C2218yes—
53C2×#66949C2218yes—
54C2×#66945C2214yes—
55C2×C4⋊C4×D11C2214yes—
56C2×#66938C2218yes—
57C2×#66936C2218yes—
58C2×(C22⋊D11)⋊C4C2218yes—
59#10623008C22132yescomplemented
60#10623008C22116yescomplemented
61C2×#66928C2214yes—
62C2×#66928C2212yes—
63C2×#66927C2211yescharacteristic
64C2×C4×D44C2214yes—
65C2×C4×D44C2212yes—
66C2×C4×D44C2212yes—
67C2×C4×D44C2214yes—
68#10623001C22132yescomplemented
69C2×#66923C2214yes—
70C2×#66922C2212yes—
71C2×#66922C2212yes—
72C2×#66922C2212yes—
73C2×#66922C2212yes—
74C2×#66922C2211yescharacteristic
75C2×#66922C22116yescomplemented
76C2×C4×Dic22C2214yes—
77C2×C4×Dic22C2214yes—
78C2×C11×#41—28no—
79C2×C11×#41C2318yes—
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2312yes—
83C23×C4×C11C2312yes—
84C23×C4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2312yes—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2318yes—
91C23×Dic11C2314yes—
92C2×#4339—216no—
93C2×#4339—416no—
94C2×#4339C23116yes—
95C2×#4339C23132yes—
96C22×D44C2312yes—
97C22×D44C2312yes—
98C22×D44C2312yes—
99C22×C4×D11C2314yes—
100C22×C4×D11C2318yes—
101C22×Dic22—48no—
102C22×Dic22C2312yes—
103C22×Dic22C2314yes—
104C22×Dic22C2314yes—
105C22×Dic22C23116yes—
106C4×Q8×C11C2318yes—
107C4×Q8×C11C2318yes—
108C4×D4×C11C2318yes—
109C4×D4×C11C23116yes—
110C4×D4×C11C2318yes—
111C4×D4×C11C23116yes—
112C11×#117C2318yes—
113C11×#117C23116yes—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2312yes—
120C2×C11×C22⋊C4C2312yes—
121C2×C42×C11C2312yes—
122C2×C42×C11C2312yes—
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2318yes—
128C2×C42×C11C2312yes—
129C2×C42×C11C23116yes—
130C2×C22⋊Dic11C2318yes—
131#66999C23132yes—
132#66992C23164yes—
133#66991C23132yes—
134#66983C23132yes—
135#66983C23116yes—
136#66983C23132yes—
137#66983C23116yes—
138C2×(C2×D11)⋊C4C2318yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2318yes—
142#66979C23132yes—
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2314yes—
145C2×C4⋊Dic11C2314yes—
146C2×C4⋊Dic11C2314yes—
147C2×C4⋊Dic11C2314yes—
148C2×C4⋊Dic11C2312yes—
149C2×C4⋊Dic11C23116yes—
150C2×C4⋊Dic11C23116yes—
151#66977C23132yes—
152#66977C23132yes—
153C2×Dic11⋊C4C2318yes—
154C2×Dic11⋊C4C2318yes—
155C2×C4×Dic11C2318yes—
156#66951C23164yes—
157#66949C23164yes—
158#66945C23132yes—
159C4⋊C4×D11C23132yes—
160#66938C23164yes—
161#66936C23164yes—
162(C22⋊D11)⋊C4C23164yes—
163#66928C23116yes—
164#66928C23132yes—
165#66927C2318yes—
166C4×D44C23132yes—
167C4×D44C23116yes—
168C4×D44C23116yes—
169C4×D44C23132yes—
170#66923C23132yes—
171#66922C23116yes—
172#66922C23116yes—
173#66922C23116yes—
174#66922C23116yes—
175#66922C2318yes—
176C4×Dic22C23132yes—
177C4×Dic22C23132yes—
178C2×#3511—111nomaximal, Sylow
179C24×C11C2412yes—
180C24×C11C2411yescharacteristic
181C23×D11C2414yes—
182C11×#41—232no—
183C2×Q8×C11—24no—
184C2×Q8×C11C2414yes—
185C2×D4×C11—28no—
186C2×D4×C11—24no—
187C2×D4×C11C2414yes—
188C2×D4×C11C2418yes—
189C22×C4×C11—28no—
190C22×C4×C11—24no—
191C22×C4×C11—28no—
192C22×C4×C11—24no—
193C22×C4×C11—28no—
194C22×C4×C11#4118yescomplemented
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2418yes—
199C22×C4×C11C2418yes—
200C22×C4×C11C2411yescharacteristic
201C22×C4×C11C2414yes—
202C22×C4×C11C2418yes—
203C22×C4×C11C2411yescharacteristic
204C22×C4×C11C2414yes—
205C22×C4×C11C2411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2414yes—
208C22×C4×C11C2411yescharacteristic
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—216no—
211C2×C22⋊D11—416no—
212C2×C22⋊D11C24116yes—
213C2×C22⋊D11C24132yes—
214C22×Dic11—48no—
215C22×Dic11C2414yes—
216C22×Dic11C2418yes—
217C22×Dic11C24116yes—
218#4339—264no—
219#4339—464no—
220C2×D44—28no—
221C2×D44—28no—
222C2×D44—28no—
223C2×D44C2418yes—
224C2×D44C2418yes—
225C2×D44C2418yes—
226C2×C4×D11—216no—
227C2×C4×D11—416no—
228C2×C4×D11C24116yes—
229C2×C4×D11C24132yes—
230C2×Dic22—28no—
231C2×Dic22—216no—
232C2×Dic22—432no—
233C2×Dic22—48no—
234C2×Dic22C2418yes—
235C2×Dic22C24116yes—
236C2×Dic22C24116yes—
237C11×C4⋊C4C2414yes—
238C11×C4⋊C4C2414yes—
239C11×C4⋊C4C2418yes—
240C11×C4⋊C4C2418yes—
241C11×C22⋊C4C2418yes—
242C11×C22⋊C4C2418yes—
243C11×C22⋊C4C2418yes—
244C42×C11C2418yes—
245C42×C11C2418yes—
246C42×C11C2414yes—
247C42×C11C2414yes—
248C42×C11C2414yes—
249C42×C11C2414yes—
250C42×C11C2418yes—
251C22⋊Dic11C24132yes—
252(C2×D11)⋊C4C24132yes—
253(C2×D11)⋊C4C24116yes—
254(C2×D11)⋊C4C24116yes—
255(C2×D11)⋊C4C24132yes—
256C4⋊Dic11C2418yes—
257C4⋊Dic11C24116yes—
258C4⋊Dic11C24116yes—
259C4⋊Dic11C24116yes—
260C4⋊Dic11C24116yes—
261C4⋊Dic11C2418yes—
262Dic11⋊C4C24132yes—
263Dic11⋊C4C24132yes—
264C4×Dic11C24132yes—
265#3511—1132no—
266C2×#556—112no—
267C2×#555—112no—
268C2×#554—112no—
269C2×#553—114no—
270C2×#548—114no—
271C2×#547—112no—
272C2×#542—114no—
273C2×#537—112no—
274C2×#533—112no—
275C2×#532—112no—
276C2×#532—111no—
277C22×C4⋊Q8—111no—
278C2×#520—112no—
279C2×C4×#41D1111yescharacteristic, complemented
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—24no—
283C23×C11—24no—
284C23×C11—24no—
285C23×C11C2×#4114yes—
286C23×C11C2514yes—
287C23×C11C2512yes—
288C23×C11C2511yescharacteristic
289C22×D11—28no—
290C22×D11—28no—
291C22×D11—28no—
292C22×D11C2518yes—
293Q8×C11—28no—
294D4×C11—216no—
295D4×C11—28no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—22no—
301C2×C4×C11—216no—
302C2×C4×C11—28no—
303C2×C4×C11—216no—
304C2×C4×C11—28no—
305C2×C4×C11—216no—
306C2×C4×C11C2×#4114yes—
307C2×C4×C11C2×#4114yes—
308C2×C4×C11C2×#41116yescomplemented
309C2×C4×C11H(5,𝔽2)14yes—
310C2×C4×C112−1+414yes—
311C2×C4×C11C2514yes—
312C2×C4×C11C2514yes—
313C2×C4×C11C2514yes—
314C2×C4×C11C2512yes—
315C2×C4×C11C2512yes—
316C2×C4×C11C2512yes—
317C2×C4×C11C2512yes—
318C2×C4×C11C2512yes—
319C2×C4×C11C2512yes—
320C22⋊D11—232no—
321C22⋊D11—432no—
322C2×Dic11—28no—
323C2×Dic11—216no—
324C2×Dic11—416no—
325C2×Dic11C2518yes—
326C2×Dic11C25116yes—
327D44—216no—
328D44—216no—
329D44—216no—
330C4×D11—232no—
331C4×D11—432no—
332Dic22—216no—
333Dic22—232no—
334Dic22—416no—
335C22×#41—112no—
336C22×#41—114no—
337C22×#41C2×D1111yescharacteristic
338C23×Q8—112no—
339#556—1132no—
340#555—1132no—
341#554—1132no—
342#553—1164no—
343#548—1164no—
344#547—1132no—
345#542—1164no—
346#537—1132no—
347#533—1132no—
348#532—1116no—
349#532—1132no—
350C2×C4⋊Q8—112no—
351C2×C4⋊Q8—112no—
352C2×C4⋊Q8—112no—
353C2×C4⋊Q8—112no—
354C2×C4⋊Q8—111no—
355C2×C4⋊Q8—1116no—
356C2×#127—111no—
357C2×#126—118no—
358C2×#125—114no—
359C2×#124—118no—
360C2×#124—112no—
361C2×#124—114no—
362C2×#123—118no—
363C2×C22⋊Q8—114no—
364C2×C22⋊Q8—114no—
365C2×C22⋊Q8—114no—
366C2×C22⋊Q8—118no—
367C2×#121—114no—
368C2×#121—118no—
369C2×#121—114no—
370C2×#121—112no—
371C2×#121—112no—
372C2×#121—114no—
373#520—1132no—
374C4×#41C2×D11116yescomplemented
375C2×C4×Q8—114no—
376C2×C4×Q8—114no—
377C2×C4×Q8C2×D1111yescharacteristic
378C2×C4×Q8C2×D1111yescharacteristic
379C2×C4×D4—118no—
380C2×C4×D4—114no—
381C2×C4×D4—112no—
382C2×C4×D4—114no—
383C2×C4×D4—112no—
384C2×C4×D4C2×D1111yescharacteristic
385C2×C4×D4C2×D1112yes—
386C2×C4×D4C2×D1112yes—
387C2×C4×D4C2×D1111yescharacteristic
388C2×#117—114no—
389C2×#117—114no—
390C2×#117C2×D1111yescharacteristic
391C2×#117C2×D1112yes—
392C22×C4⋊C4—112no—
393C22×C4⋊C4—112no—
394C22×C4⋊C4—114no—
395C22×C42C2×D1111yescharacteristic
396C22×C42C2×D1112yes—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—28no—
400C22×C11—24no—
401C22×C11—24no—
402C22×C11—24no—
403C22×C11—48no—
404C22×C11C22×#4114yes—
405C22×C11C22×#4112yes—
406C22×C11C2×H(5,𝔽2)12yes—
407C22×C11C2×2−1+412yes—
408C22×C11C2611yescharacteristic
409C2×D11—28no—
410C2×D11—28no—
411C2×D11—28no—
412C2×D11—416no—
413C4×C11—24no—
414C4×C11—22no—
415C4×C11—24no—
416C4×C11—24no—
417C4×C11—22no—
418C4×C11C22×#4114yes—
419C4×C11C22×#4114yes—
420C4×C11C2×H(5,𝔽2)14yes—
421C4×C11C2×2−1+414yes—
422Dic11—28no—
423Dic11—216no—
424C2×#41—28no—
425C2×#41—1116no—
426C2×#41—1132no—
427C2×#41—2216no—
428C2×#41—4416no—
429C2×#41C22×D1118yes—
430C22×Q8—112no—
431C22×Q8—114no—
432C22×Q8—114no—
433C22×Q8—1116no—
434C22×Q8—448no—
435C22×Q8C22×D1111yescharacteristic
436C22×D4—114no—
437C22×D4—118no—
438C22×D4—112no—
439C22×D4—112no—
440C22×D4—112no—
441C22×D4C22×D1112yes—
442C22×D4C22×D1111yescharacteristic
443C23×C4—114no—
444C23×C4—114no—
445C23×C4—118no—
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1112yes—
448C23×C4C22×D1112yes—
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1112yes—
451C23×C4C22×D1111yescharacteristic
452C4⋊Q8—1116no—
453C4⋊Q8—1116no—
454C4⋊Q8—1116no—
455C4⋊Q8—1116no—
456C4⋊Q8—118no—
457#127—118no—
458#126—1164no—
459#125—1132no—
460#124—1164no—
461#124—1116no—
462#124—1132no—
463#123—1164no—
464C22⋊Q8—1132no—
465C22⋊Q8—1132no—
466C22⋊Q8—1132no—
467C22⋊Q8—1164no—
468#121—1132no—
469#121—1164no—
470#121—1132no—
471#121—1116no—
472#121—1116no—
473#121—1132no—
474C4×Q8—1132no—
475C4×Q8—1132no—
476C4×Q8C22×D1118yes—
477C4×Q8C22×D1118yes—
478C4×D4—1164no—
479C4×D4—1132no—
480C4×D4—1116no—
481C4×D4—1132no—
482C4×D4—1116no—
483C4×D4C22×D1118yes—
484C4×D4C22×D11116yes—
485C4×D4C22×D11116yes—
486C4×D4C22×D1118yes—
487#117—1132no—
488#117—1132no—
489#117C22×D1118yes—
490#117C22×D11116yes—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4—118no—
495C2×C4⋊C4—1116no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—1116no—
498C2×C4⋊C4—112no—
499C2×C4⋊C4—112no—
500C2×C4⋊C4—118no—
501C2×C4⋊C4—1132no—
502C2×C4⋊C4C22×D1111yescharacteristic
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C4⋊C4C22×D1112yes—
505C2×C4⋊C4C22×D1112yes—
506C2×C22⋊C4—118no—
507C2×C22⋊C4—118no—
508C2×C22⋊C4—118no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4C22×D1112yes—
512C2×C22⋊C4C22×D1112yes—
513C2×C22⋊C4C22×D1112yes—
514C2×C42—118no—
515C2×C42C22×D1112yes—
516C2×C42C22×D1111yescharacteristic
517C2×C42C22×D1112yes—
518C2×C42C22×D1111yescharacteristic
519C2×C42C22×D1111yescharacteristic
520C2×C42C22×D1112yes—
521C2×C42C22×D1118yes—
522C2×C42C22×D11116yes—
523C2×C42C22×D1111yescharacteristic
524C2×C11—24no—
525C2×C11—44no—
526C2×C11#351114yescomplemented
527C2×C11C23×#4111yescharacteristic
528C2×C11C22×H(5,𝔽2)11yescharacteristic
529C2×C11C22×2−1+411yescharacteristic
530D11—48no—
531C24—114no—
532C24C23×D1112yes—
533C24C23×D1111yescharacteristic
534#41—232no—
535#41—2264no—
536#41—4464no—
537C2×Q8—24no—
538C2×Q8—118no—
539C2×Q8—1116no—
540C2×Q8—1116no—
541C2×Q8—228no—
542C2×Q8—2216no—
543C2×Q8—448no—
544C2×Q8—4432no—
545C2×Q8C23×D1114yes—
546C2×D4—28no—
547C2×D4—24no—
548C2×D4—1116no—
549C2×D4—1132no—
550C2×D4—118no—
551C2×D4—118no—
552C2×D4—118no—
553C2×D4—2216no—
554C2×D4—228no—
555C2×D4—228no—
556C2×D4—228no—
557C2×D4—4416no—
558C2×D4C23×D1118yes—
559C2×D4C23×D1114yes—
560C22×C4—28no—
561C22×C4—24no—
562C22×C4—28no—
563C22×C4—24no—
564C22×C4—28no—
565C22×C4—114no—
566C22×C4—118no—
567C22×C4—1116no—
568C22×C4—1116no—
569C22×C4—1132no—
570C22×C4—2216no—
571C22×C4—4416no—
572C22×C4—448no—
573C22×C4#433918yescomplemented
574C22×C4C23×D1114yes—
575C22×C4C23×D1118yes—
576C22×C4C23×D1118yes—
577C22×C4C23×D1114yes—
578C22×C4C23×D1118yes—
579C22×C4C23×D1112yes—
580C22×C4C23×D1111yescharacteristic
581C22×C4C23×D1111yescharacteristic
582C22×C4C23×D1112yes—
583C22×C4C23×D1112yes—
584C22×C4C23×D1111yescharacteristic
585C22×C4C23×D1111yescharacteristic
586C22×C4C23×D1114yes—
587C22×C4C23×D1111yescharacteristic
588C22×C4C23×D1111yescharacteristic
589C4⋊C4—1116no—
590C4⋊C4—1116no—
591C4⋊C4—1116no—
592C4⋊C4—1132no—
593C4⋊C4—1116no—
594C4⋊C4—118no—
595C4⋊C4—118no—
596C4⋊C4—1132no—
597C4⋊C4C23×D1114yes—
598C4⋊C4C23×D1114yes—
599C4⋊C4C23×D1118yes—
600C4⋊C4C23×D1118yes—
601C22⋊C4—1132no—
602C22⋊C4—1132no—
603C22⋊C4—1132no—
604C22⋊C4—1116no—
605C22⋊C4—1116no—
606C22⋊C4C23×D1118yes—
607C22⋊C4C23×D1118yes—
608C22⋊C4C23×D1118yes—
609C42—1132no—
610C42C23×D1114yes—
611C42C23×D1118yes—
612C42C23×D1114yes—
613C42C23×D1118yes—
614C42C23×D1114yes—
615C42C23×D1114yes—
616C42C23×D1118yes—
617C11C2×#351111yescharacteristic, complemented, Sylow
618C23—22no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—118no—
624C23—228no—
625C23—228no—
626C23—228no—
627C23C2×#433914yes—
628C23C24×D1114yes—
629C23C24×D1112yes—
630C23C24×D1111yescharacteristic
631Q8—28no—
632Q8—2216no—
633Q8—2232no—
634Q8—4416no—
635D4—216no—
636D4—28no—
637D4—2232no—
638D4—2216no—
639D4—2216no—
640D4—2216no—
641D4—4432no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—216no—
648C2×C4—28no—
649C2×C4—216no—
650C2×C4—28no—
651C2×C4—216no—
652C2×C4—118no—
653C2×C4—1116no—
654C2×C4—228no—
655C2×C4—2216no—
656C2×C4—2232no—
657C2×C4—4432no—
658C2×C4—4416no—
659C2×C4C2×#433914yes—
660C2×C4C2×#433914yes—
661C2×C4C2×#4339116yescomplemented
662C2×C4#6704214yes—
663C2×C4#6704314yes—
664C2×C4C24×D1114yes—
665C2×C4C24×D1112yes—
666C2×C4C24×D1112yes—
667C2×C4C24×D1114yes—
668C2×C4C24×D1114yes—
669C2×C4C24×D1112yes—
670C2×C4C24×D1112yes—
671C2×C4C24×D1112yes—
672C2×C4C24×D1112yes—
673C22—22no—
674C22—22no—
675C22—28no—
676C22—24no—
677C22—24no—
678C22—24no—
679C22—48no—
680C22—228no—
681C22—228no—
682C22—228no—
683C22—4416no—
684C22C22×#433914yes—
685C22C22×#433912yes—
686C22C2×#6704212yes—
687C22C2×#6704312yes—
688C22C25×D1111yescharacteristic
689C4—24no—
690C4—24no—
691C4—22no—
692C4—24no—
693C4—22no—
694C4—228no—
695C4—2216no—
696C4C22×#433914yes—
697C4C22×#433914yes—
698C4C2×#6704214yes—
699C4C2×#6704314yes—
700C2—24no—
701C2—44no—
702C2—448no—
703C2#1308252714yesdirect product factor
704C2C23×#433911yescharacteristic
705C2C22×#6704211yescharacteristic
706C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C4×C11×#41C2
socleC23×C11C25
hypercenterC2×C4×#41D11
hypocenterC11C2×#3511
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13082527C2direct (N × H)
2. C2×#10623115C2semidirect
3. C2×#10623094C2semidirect
4. C2×#10623110C2semidirect
5. C2×#10623096C2semidirect
6. C2×#10623083C2semidirect
7. C2×#10623082C2semidirect
8. C2×#10623065C2semidirect
9. C2×#10623364C2semidirect
10. C2×#10623001C2semidirect
11. C2×#10623008C2semidirect
12. C2×#10623008C2semidirect
13. C22×#66922C2semidirect
14. C2×#10623054C2semidirect
15. C2×C4×C11×#41C2semidirect
20. C4×C11×#41C22semidirect
31. #10623364C22semidirect
44. #10623115C22semidirect
45. #10623110C22semidirect
46. #10623096C22semidirect
47. #10623094C22semidirect
48. #10623083C22semidirect
49. #10623082C22semidirect
50. #10623065C22semidirect
51. #10623054C22semidirect
59. #10623008C22semidirect
60. #10623008C22semidirect
68. #10623001C22semidirect
75. C2×#66922C22semidirect
194. C22×C4×C11#41semidirect
279. C2×C4×#41D11semidirect
308. C2×C4×C11C2×#41semidirect
374. C4×#41C2×D11semidirect
526. C2×C11#3511semidirect
573. C22×C4#4339semidirect
617. C11C2×#3511semidirect
661. C2×C4C2×#4339semidirect
703. C2#13082527direct (N × H)

Maximal subgroups

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

subgroupindex
#130825272
C2×#106231152
C2×#106230942
C2×#106231102
C2×#106230962
C2×#106230832
C2×#106230822
C2×#106230652
C2×#106233642
C2×#106230012
C2×#106230082
C22×#669222
C2×#106230542
C2×C4×C11×#412
C2×#351111