Finite Group Databasebeta

← C2×#13119926 #16033014

Subgroups — C2×#13119926 #16033014

Order 3328.

2726 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
1C22×#88143C211yesmaximal, characteristic, complemented
2C22×#88178C211yesmaximal, characteristic
3#13119926C2116yesmaximal, direct product factor
4C2×#11718610C211yesmaximal, characteristic
5C2×#11718318C211yesmaximal, characteristic, complemented
6C2×#11718609C211yesmaximal, characteristic
7C2×#11718640C211yesmaximal, characteristic, complemented
8C2×#11718307C211yesmaximal, characteristic, complemented
9C2×#11718646C211yesmaximal, characteristic, complemented
10C2×#11718633C211yesmaximal, characteristic, complemented
11C2×#11718605C211yesmaximal, characteristic
12C2×#11718605C211yesmaximal, characteristic
13C2×#11718314C211yesmaximal, characteristic, complemented
14C2×#11718310C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic13C211yesmaximal, characteristic
16C2×C13×#385C211yesmaximal, characteristic
17C24×C4×C13C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C2×#88178—28no—
31C2×#88178C2218yes—
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C2×#88143—28no—
45C2×#88143C2218yescomplemented
46C13×#385C2218yes—
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C4×C22⋊Dic13C2218yes—
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718646C2218yescomplemented
59#11718640C2218yescomplemented
60#11718633C2218yescomplemented
61#11718610C2218yes—
62#11718609C2218yes—
63#11718605C2218yes—
64#11718605C2218yes—
65#11718318C2218yescomplemented
66#11718314C2218yescomplemented
67#11718310C2218yescomplemented
68#11718307C2218yescomplemented
69C25×C13C2311yescharacteristic
70C23×C4×C13—24no—
71C23×C4×C13—24no—
72C23×C4×C13—42no—
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2314yes—
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C22×Dic26—24no—
89C22×Dic26—24no—
90C22×Dic26—42no—
91C22×Dic26C2314yes—
92C2×C13×C4⋊C4—24no—
93C2×C13×C4⋊C4—24no—
94C2×C13×C4⋊C4C2314yes—
95C2×C13×C4⋊C4C2314yes—
96C2×C13×C22⋊C4—24no—
97C2×C13×C22⋊C4—42no—
98C2×C13×C22⋊C4C2314yes—
99C2×C13×C22⋊C4C2314yes—
100C2×C22⋊Dic13—24no—
101C2×C22⋊Dic13—24no—
102C2×C22⋊Dic13—24no—
103C2×C22⋊Dic13Q818yescomplemented
104C2×C22⋊Dic13C2314yes—
105C2×C22⋊Dic13C2314yes—
106C2×C22⋊Dic13C2314yes—
107C2×C22⋊Dic13C2314yes—
108C2×C4⋊Dic13—24no—
109C2×C4⋊Dic13—24no—
110C2×C4⋊Dic13—24no—
111C2×C4⋊Dic13C2314yes—
112C2×C4⋊Dic13C2314yes—
113C2×C4⋊Dic13C2314yes—
114#88178—232no—
115C2×#6101—24no—
116C2×#6101—24no—
117C2×#6101—24no—
118C2×#6101—24no—
119C2×#6101—24no—
120C2×#6101—24no—
121C2×#6101—42no—
122C2×#6101D418yes—
123C2×#6101C2314yes—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×#6101C2314yes—
127C2×#6101C2314yes—
128C2×#6101C2314yes—
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×C4×Dic13—24no—
132C2×C4×Dic13—24no—
133C2×C4×Dic13—42no—
134C2×C4×Dic13—42no—
135C2×C4×Dic13C2314yes—
136C2×C4×Dic13C2314yes—
137C2×C4×Dic13C2314yes—
138C2×C4×Dic13C2314yes—
139#88143—232no—
140C13×#95C2314yes—
141C13×#95C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2556—131nomaximal, Sylow
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13C2×Q814yes—
158C24×C13C2412yes—
159C24×C13C2411yescharacteristic
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—28no—
176C22×C4×C13—28no—
177C22×C4×C13—44no—
178C22×C4×C13—416no—
179C22×C4×C13C2×D414yes—
180C22×C4×C13#4114yes—
181C22×C4×C13#4114yes—
182C22×C4×C13C2412yes—
183C22×C4×C13C2412yes—
184C22×C4×C13C2412yes—
185C22×C4×C13C2412yes—
186C22×C4×C13C2412yes—
187C22×C4×C13C2412yes—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13C2×D414yes—
208C22×Dic13C2×D414yes—
209C22×Dic13C2×Q814yes—
210C22×Dic13C2×Q814yes—
211C22×Dic13#4114yes—
212C22×Dic13C2412yes—
213C22×Dic13C2412yes—
214C22×Dic13C2412yes—
215C22×Dic13C2412yes—
216C22×Dic13C2412yes—
217C22×Dic13C2412yes—
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C2×Dic26—28no—
221C2×Dic26—28no—
222C2×Dic26—44no—
223C2×Dic26—416no—
224C13×C4⋊C4—28no—
225C13×C4⋊C4—28no—
226C13×C22⋊C4—28no—
227C13×C22⋊C4—44no—
228C22⋊Dic13—28no—
229C22⋊Dic13—28no—
230C22⋊Dic13—28no—
231C22⋊Dic13C2×Q8116yescomplemented
232C4⋊Dic13—28no—
233C4⋊Dic13—28no—
234C4⋊Dic13—28no—
235#6101—28no—
236#6101—28no—
237#6101—28no—
238#6101—28no—
239#6101—28no—
240#6101—28no—
241#6101—44no—
242#6101C2×D4116yes—
243C4×Dic13—28no—
244C4×Dic13—28no—
245C4×Dic13—44no—
246C4×Dic13—44no—
247C22×#125—131no—
248C22×C22⋊Q8—131no—
249#2556—1316no—
250C2×#399—131no—
251C2×#398—131no—
252C2×#396—131no—
253C2×#395—131no—
254C2×#391—131no—
255C2×#389—131no—
256C2×#389—131no—
257C2×#388—131no—
258C2×#388—131no—
259C2×#387—131no—
260C2×#385D1311yescharacteristic
261C2×C4×C4⋊C4—131no—
262C2×C4×C22⋊C4—131no—
263C23×C13—28no—
264C23×C13—28no—
265C23×C13—28no—
266C23×C13—22no—
267C23×C13—22no—
268C23×C13—22no—
269C23×C13—22no—
270C23×C13—22no—
271C23×C13—22no—
272C23×C13—44no—
273C23×C13—44no—
274C23×C13—44no—
275C23×C13—44no—
276C23×C13C22×D412yes—
277C23×C13C22×Q814yes—
278C23×C13C22×Q812yes—
279C23×C13C2×#4112yes—
280C23×C13C2×#4112yes—
281C23×C13C2×#4112yes—
282C23×C13H(5,𝔽2)12yes—
283C23×C132−1+412yes—
284C23×C13C2511yescharacteristic
285C2×C4×C13—28no—
286C2×C4×C13—28no—
287C2×C4×C13—28no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—416no—
304C2×C4×C13—44no—
305C2×C4×C13—44no—
306C2×C4×C13—44no—
307C2×C4×C13C22×D414yes—
308C2×C4×C13C2×#4114yes—
309C2×C4×C13C2×#4114yes—
310C2×Dic13—28no—
311C2×Dic13—28no—
312C2×Dic13—28no—
313C2×Dic13—28no—
314C2×Dic13—28no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—44no—
335C2×Dic13—44no—
336C2×Dic13—44no—
337C2×Dic13C22×D414yes—
338C2×Dic13C22×D414yes—
339C2×Dic13C22×Q814yes—
340C2×Dic13C22×Q814yes—
341C2×Dic13C2×#4114yes—
342Dic26—416no—
343C23×Q8—131no—
344C24×C4C2×D1311yescharacteristic
345C2×#125—138no—
346C2×#125—268no—
347C2×C22⋊Q8—138no—
348C2×C22⋊Q8—268no—
349C22×C4⋊C4—131no—
350C22×C4⋊C4—131no—
351C22×C4⋊C4—131no—
352C22×C4⋊C4—131no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4—131no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—131no—
357C22×C4⋊C4—131no—
358C22×C4⋊C4—131no—
359C22×C4⋊C4—131no—
360C22×C4⋊C4C2×D1311yescharacteristic
361C22×C4⋊C4C2×D1311yescharacteristic
362C22×C22⋊C4—131no—
363C22×C22⋊C4—131no—
364C22×C22⋊C4—131no—
365C22×C22⋊C4—131no—
366C22×C22⋊C4C2×D1311yescharacteristic
367C22×C22⋊C4C2×D1311yescharacteristic
368C22×C42—131no—
369C22×C42—131no—
370C22×C42—131no—
371C22×C42—131no—
372#399—138no—
373#398—138no—
374#396—138no—
375#395—138no—
376#391—138no—
377#389—138no—
378#389—138no—
379#388—138no—
380#388—138no—
381#387—138no—
382#385C2×D1318yes—
383C4×C4⋊C4—138no—
384C4×C22⋊C4—138no—
385C2×#95—131no—
386C2×#95—131no—
387C2×#95—131no—
388C2×#95—131no—
389C2×#95—131no—
390C2×#95—131no—
391C2×#95—131no—
392C2×#95—131no—
393C2×#95C2×D1311yescharacteristic
394C2×#95C2×D1311yescharacteristic
395C22×C13—24no—
396C22×C13—24no—
397C22×C13—24no—
398C22×C13—42no—
399C22×C13—42no—
400C22×C13—42no—
401C22×C13—42no—
402C22×C13—416no—
403C22×C13#53214yes—
404C22×C13#53314yes—
405C22×C13#53914yes—
406C22×C13#54614yes—
407C22×C13D4×Q814yes—
408C22×C13#55214yes—
409C22×C13#55414yes—
410C22×C13C23×D411yescharacteristic
411C22×C13C23×Q811yescharacteristic
412C22×C13C22×#4111yescharacteristic
413C22×C13C22×#4111yescharacteristic
414C22×C13C22×#4111yescharacteristic
415C22×C13C2×H(5,𝔽2)11yescharacteristic
416C22×C13C2×2−1+411yescharacteristic
417C4×C13—24no—
418C4×C13—24no—
419C4×C13—24no—
420C4×C13—42no—
421C4×C13—42no—
422C4×C13—42no—
423Dic13—24no—
424Dic13—24no—
425Dic13—24no—
426Dic13—24no—
427Dic13—24no—
428Dic13—42no—
429Dic13—42no—
430Dic13—42no—
431C25C22×D1311yescharacteristic
432C22×Q8—134no—
433C22×Q8—264no—
434C22×Q8—264no—
435C22×Q8—522no—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—42no—
439C23×C4—131no—
440C23×C4—131no—
441C23×C4—131no—
442C23×C4—131no—
443C23×C4—131no—
444C23×C4—131no—
445C23×C4—131no—
446C23×C4—131no—
447C23×C4C22×D1311yescharacteristic
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1311yescharacteristic
450C23×C4C22×D1314yes—
451C23×C4C22×D1311yescharacteristic
452C23×C4C22×D1311yescharacteristic
453C23×C4C22×D1311yescharacteristic
454#125—2632no—
455C22⋊Q8—2632no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—138no—
459C2×C4⋊C4—134no—
460C2×C4⋊C4—134no—
461C2×C4⋊C4—134no—
462C2×C4⋊C4—134no—
463C2×C4⋊C4—134no—
464C2×C4⋊C4—134no—
465C2×C4⋊C4—134no—
466C2×C4⋊C4—134no—
467C2×C4⋊C4—134no—
468C2×C4⋊C4—134no—
469C2×C4⋊C4—134no—
470C2×C4⋊C4—264no—
471C2×C4⋊C4—264no—
472C2×C4⋊C4—264no—
473C2×C4⋊C4—264no—
474C2×C4⋊C4—264no—
475C2×C4⋊C4—264no—
476C2×C4⋊C4—264no—
477C2×C4⋊C4—264no—
478C2×C4⋊C4—264no—
479C2×C4⋊C4—522no—
480C2×C4⋊C4C22×D1314yes—
481C2×C4⋊C4C22×D1314yes—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—138no—
485C2×C22⋊C4—134no—
486C2×C22⋊C4—134no—
487C2×C22⋊C4—134no—
488C2×C22⋊C4—134no—
489C2×C22⋊C4—264no—
490C2×C22⋊C4—264no—
491C2×C22⋊C4—264no—
492C2×C22⋊C4C22×D1314yes—
493C2×C22⋊C4C22×D1314yes—
494C2×C42—134no—
495C2×C42—134no—
496C2×C42—134no—
497C2×C42—134no—
498C2×C42—264no—
499C2×C42—264no—
500C2×C42—522no—
501C2×C42—522no—
502#95—134no—
503#95—134no—
504#95—134no—
505#95—134no—
506#95—134no—
507#95—134no—
508#95—134no—
509#95—134no—
510#95C22×D1314yes—
511#95C22×D1314yes—
512C2×C13—44no—
513C2×C13#255618yescomplemented
514C2×C13C2×#53211yescharacteristic
515C2×C13C2×#53311yescharacteristic
516C2×C13C2×#53911yescharacteristic
517C2×C13C2×#54611yescharacteristic
518C2×C13C2×D4×Q811yescharacteristic
519C2×C13C2×#55211yescharacteristic
520C2×C13C2×#55411yescharacteristic
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24Q8×D1314yes—
528C24C23×D1312yes—
529C24C23×D1311yescharacteristic
530C2×Q8—268no—
531C2×Q8—268no—
532C2×Q8—524no—
533C2×Q8—5216no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—44no—
552C22×C4—416no—
553C22×C4—134no—
554C22×C4—134no—
555C22×C4—134no—
556C22×C4—134no—
557C22×C4—134no—
558C22×C4—132no—
559C22×C4—132no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—132no—
563C22×C4—132no—
564C22×C4—132no—
565C22×C4—132no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—262no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4#612714yes—
586C22×C4D4×D1314yes—
587C22×C4#612914yes—
588C22×C4C23×D1312yes—
589C22×C4C23×D1312yes—
590C22×C4C23×D1312yes—
591C22×C4C23×D1312yes—
592C22×C4C23×D1312yes—
593C22×C4C23×D1312yes—
594C4⋊C4—28no—
595C4⋊C4—28no—
596C4⋊C4—1316no—
597C4⋊C4—268no—
598C4⋊C4—268no—
599C4⋊C4—268no—
600C4⋊C4—268no—
601C4⋊C4—268no—
602C4⋊C4—268no—
603C4⋊C4—268no—
604C4⋊C4—268no—
605C4⋊C4—268no—
606C4⋊C4—524no—
607C22⋊C4—28no—
608C22⋊C4—44no—
609C22⋊C4—1316no—
610C22⋊C4—268no—
611C22⋊C4—268no—
612C22⋊C4—268no—
613C42—268no—
614C42—268no—
615C42—524no—
616C42—524no—
617C13C2×#255611yescharacteristic, complemented, Sylow
618C23—28no—
619C23—28no—
620C23—28no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23C2×#612712yes—
632C23C2×D4×D1312yes—
633C23C2×#612912yes—
634C23#8825112yes—
635C23C2×Q8×D1314yes—
636C23C2×Q8×D1312yes—
637C23#41×D1312yes—
638C23#8825712yes—
639C23C24×D1311yescharacteristic
640Q8—5216no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—416no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—134no—
664C2×C4—134no—
665C2×C4—134no—
666C2×C4—134no—
667C2×C4—134no—
668C2×C4—268no—
669C2×C4—268no—
670C2×C4—268no—
671C2×C4—268no—
672C2×C4—268no—
673C2×C4—262no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—262no—
677C2×C4—262no—
678C2×C4—262no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—524no—
693C2×C4—524no—
694C2×C4—524no—
695C2×C4C2×#612714yes—
696C2×C4C2×D4×D1314yes—
697C2×C4C2×#612914yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—416no—
705C22—42no—
706C22#1171921614yes—
707C22#1171924614yes—
708C22#1171925314yes—
709C22#1171929614yes—
710C22#1171932714yes—
711C22#1171933714yes—
712C22#1171936514yes—
713C22C22×#612711yescharacteristic
714C22C22×D4×D1311yescharacteristic
715C22C22×#612911yescharacteristic
716C22C2×#8825111yescharacteristic
717C22C22×Q8×D1311yescharacteristic
718C22C2×#41×D1311yescharacteristic
719C22C2×#8825711yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—264no—
727C4—264no—
728C4—264no—
729C4—264no—
730C4—264no—
731C4—522no—
732C4—522no—
733C4—522no—
734C2—44no—
735C2#1311992618yesdirect product factor
736C2C2×#1171925311yescharacteristic
737C2C2×#1171932711yescharacteristic
738C2C2×#1171936511yescharacteristic
739C2C2×#1171929611yescharacteristic
740C2C2×#1171933711yescharacteristic
741C2C2×#1171924611yescharacteristic
742C2C2×#1171921611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#385D13
hypocenterC13C2×#2556
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#88143C2semidirect
3. #13119926C2direct (N × H)
5. C2×#11718318C2semidirect
7. C2×#11718640C2semidirect
8. C2×#11718307C2semidirect
9. C2×#11718646C2semidirect
10. C2×#11718633C2semidirect
13. C2×#11718314C2semidirect
14. C2×#11718310C2semidirect
45. C2×#88143C22semidirect
58. #11718646C22semidirect
59. #11718640C22semidirect
60. #11718633C22semidirect
65. #11718318C22semidirect
66. #11718314C22semidirect
67. #11718310C22semidirect
68. #11718307C22semidirect
103. C2×C22⋊Dic13Q8semidirect
231. C22⋊Dic13C2×Q8semidirect
513. C2×C13#2556semidirect
617. C13C2×#2556semidirect
735. C2#13119926direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881432
C22×#881782
#131199262
C2×#117186102
C2×#117183182
C2×#117186092
C2×#117186402
C2×#117183072
C2×#117186462
C2×#117186332
C2×#117186052
C2×#117183142
C2×#117183102
C2×C4×C22⋊Dic132
C2×C13×#3852
C2×#255613