Finite Group Databasebeta

← C2×#13118434 #16030937

Subgroups — C2×#13118434 #16030937

Order 3328.

3246 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88142C211yesmaximal, characteristic, complemented
2C22×#88150C211yesmaximal, characteristic
3C22×#88150C211yesmaximal, characteristic
4C22×C4×Dic26C211yesmaximal, characteristic, complemented
5#13118434C2116yesmaximal, direct product factor
6C2×#11718645C211yesmaximal, characteristic, complemented
7C2×#11718641C211yesmaximal, characteristic, complemented
8C2×#11718655C211yesmaximal, characteristic
9C2×#11718655C211yesmaximal, characteristic
10C2×#11718307C211yesmaximal, characteristic, complemented
11C2×#11718308C211yesmaximal, characteristic, complemented
12C2×#11718633C211yesmaximal, characteristic, complemented
13C2×#11718601C211yesmaximal, characteristic
14C2×#11718330C211yesmaximal, characteristic
15C2×#11718327C211yesmaximal, characteristic
16C2×C13×#389C211yesmaximal, characteristic, complemented
17C23×C4×D13C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C23×Dic26C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C2×#88150—28no—
45C2×#88150—28no—
46C2×#88150C2218yes—
47C2×#88150C2218yes—
48C2×#88142—28no—
49C2×#88142C2218yescomplemented
50C2×C4×Dic26—28no—
51C2×C4×Dic26C2218yescomplemented
52C13×#389C2218yescomplemented
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61#11718655C2218yes—
62#11718655C2218yes—
63#11718645C2218yescomplemented
64#11718641C2218yescomplemented
65#11718633C2218yescomplemented
66#11718601C2218yes—
67#11718330C2218yes—
68#11718327C2218yes—
69#11718308C2218yescomplemented
70#11718307C2218yescomplemented
71C24×D13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C22×C4×D13—24no—
87C22×C4×D13—24no—
88C22×C4×D13—24no—
89C22×C4×D13C2314yes—
90C22×Dic26—24no—
91C22×Dic26—24no—
92C22×Dic26—24no—
93C22×Dic26—24no—
94C22×Dic26—24no—
95C22×Dic26D418yes—
96C22×Dic26C2314yes—
97C22×Dic26C2314yes—
98C2×C13×C4⋊C4—24no—
99C2×C13×C4⋊C4—24no—
100C2×C13×C4⋊C4—24no—
101C2×C13×C4⋊C4—24no—
102C2×C13×C4⋊C4C2314yes—
103C2×C13×C4⋊C4C2314yes—
104C2×C13×C4⋊C4C2314yes—
105C2×C13×C4⋊C4C2314yes—
106C2×C42×C13—24no—
107C2×C42×C13C2314yes—
108C2×#6103—24no—
109C2×#6103—24no—
110C2×#6103—24no—
111C2×#6103—24no—
112C2×#6103—24no—
113C2×#6103Q818yescomplemented
114C2×#6103C2314yes—
115C2×#6103C2314yes—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×C4⋊Dic13—24no—
121C2×C4⋊Dic13—24no—
122C2×C4⋊Dic13C2314yes—
123C2×C4⋊Dic13C2314yes—
124C2×#6101—24no—
125C2×#6101—24no—
126C2×#6101—24no—
127C2×#6101—24no—
128C2×#6101—24no—
129C2×#6101—24no—
130C2×#6101—24no—
131C2×#6101D418yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×#6101C2314yes—
137C2×#6101C2314yes—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×C4×Dic13—24no—
141C2×C4×Dic13—24no—
142C2×C4×Dic13—24no—
143C2×C4×Dic13C2314yes—
144C2×C4×Dic13C2314yes—
145C2×C4×Dic13C2314yes—
146#88150—232no—
147#88150—232no—
148#88142—232no—
149C4×Dic26—232no—
150C13×#95C2314yes—
151C13×#95C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2429—131nomaximal, Sylow
159C24×C13C2411yescharacteristic
160C23×D13—22no—
161C23×D13—22no—
162C23×D13—22no—
163C23×D13—22no—
164C23×D13—22no—
165C23×D13—22no—
166C23×D13C2×Q814yes—
167C23×D13C2412yes—
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—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13C2×D414yes—
186C22×C4×C13C2×D414yes—
187C22×C4×C13C2×Q814yes—
188C22×C4×C13#4114yes—
189C22×C4×C13C2412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
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×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13C2×D414yes—
212C22×Dic13C2×D414yes—
213C22×Dic13C2×D414yes—
214C22×Dic13C2×D414yes—
215C22×Dic13C2×Q814yes—
216C22×Dic13#4114yes—
217C22×Dic13C2412yes—
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C22×Dic13C2412yes—
221C22×Dic13C2412yes—
222C22×Dic13C2412yes—
223C22×Dic13C2412yes—
224C2×C4×D13—28no—
225C2×C4×D13—28no—
226C2×C4×D13—28no—
227C2×C4×D13—416no—
228C2×Dic26—232no—
229C2×Dic26—28no—
230C2×Dic26—28no—
231C2×Dic26—28no—
232C2×Dic26—28no—
233C2×Dic26—28no—
234C2×Dic26—416no—
235C2×Dic26C2×D4116yes—
236C13×C4⋊C4—28no—
237C13×C4⋊C4—28no—
238C13×C4⋊C4—28no—
239C13×C4⋊C4—28no—
240C42×C13—28no—
241#6103—28no—
242#6103—28no—
243#6103—28no—
244#6103—28no—
245#6103—28no—
246#6103C2×Q8116yescomplemented
247C4⋊Dic13—28no—
248C4⋊Dic13—28no—
249#6101—28no—
250#6101—28no—
251#6101—28no—
252#6101—28no—
253#6101—28no—
254#6101—28no—
255#6101—28no—
256#6101C2×D4116yes—
257C4×Dic13—28no—
258C4×Dic13—28no—
259C4×Dic13—28no—
260C22×C4⋊Q8—131no—
261C22×C22⋊Q8—131no—
262C22×C22⋊Q8—131no—
263C22×C4×Q8—131no—
264#2429—1316no—
265C2×#398—131no—
266C2×#398—131no—
267C2×#396—131no—
268C2×#396—131no—
269C2×#391—131no—
270C2×#389—131no—
271C2×#389—131no—
272C2×#389D1311yescharacteristic, complemented
273C2×#388—131no—
274C2×#388—131no—
275C2×C4×C22⋊C4—131no—
276C23×C13C22×D412yes—
277C23×C13C22×D412yes—
278C23×C13C22×Q812yes—
279C23×C13C2×#4112yes—
280C23×C13C2×#4112yes—
281C23×C132−1+412yes—
282C23×C132−1+412yes—
283C23×C13C2511yescharacteristic
284C22×D13—28no—
285C22×D13—28no—
286C22×D13—28no—
287C22×D13—22no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—22no—
292C22×D13—22no—
293C22×D13—44no—
294C22×D13—44no—
295C22×D13—44no—
296C22×D13—44no—
297C22×D13C22×Q814yes—
298C2×C4×C13—28no—
299C2×C4×C13—28no—
300C2×C4×C13—28no—
301C2×C4×C13—28no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—44no—
320C2×C4×C13—44no—
321C2×C4×C13—44no—
322C2×C4×C13C22×D414yes—
323C2×C4×C13C22×D414yes—
324C2×C4×C13C22×Q814yes—
325C2×C4×C13C2×#4114yes—
326C2×Dic13—28no—
327C2×Dic13—28no—
328C2×Dic13—28no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—44no—
345C2×Dic13—44no—
346C2×Dic13—44no—
347C2×Dic13#121116yes—
348C2×Dic13C22×D414yes—
349C2×Dic13C22×D414yes—
350C2×Dic13C22×D414yes—
351C2×Dic13C22×D414yes—
352C2×Dic13C22×Q814yes—
353C2×Dic13C2×#4114yes—
354C4×D13—416no—
355Dic26—232no—
356Dic26—416no—
357C23×Q8—131no—
358C23×Q8—131no—
359C24×C4—131no—
360C2×C4⋊Q8—138no—
361C2×C4⋊Q8—268no—
362C2×C22⋊Q8—138no—
363C2×C22⋊Q8—138no—
364C2×C22⋊Q8—268no—
365C2×C22⋊Q8—268no—
366C2×C4×Q8—138no—
367C2×C4×Q8—268no—
368C22×C4⋊C4—131no—
369C22×C4⋊C4—131no—
370C22×C4⋊C4—131no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—131no—
374C22×C4⋊C4—131no—
375C22×C4⋊C4—131no—
376C22×C4⋊C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4C2×D1311yescharacteristic
379C22×C4⋊C4C2×D1311yescharacteristic
380C22×C4⋊C4C2×D1311yescharacteristic
381C22×C4⋊C4C2×D1311yescharacteristic
382C22×C22⋊C4—131no—
383C22×C22⋊C4—131no—
384C22×C22⋊C4—131no—
385C22×C22⋊C4—131no—
386C22×C22⋊C4—131no—
387C22×C22⋊C4—131no—
388C22×C42—131no—
389C22×C42—131no—
390C22×C42—131no—
391C22×C42C2×D1311yescharacteristic
392#398—138no—
393#398—138no—
394#396—138no—
395#396—138no—
396#391—138no—
397#389—138no—
398#389—138no—
399#389C2×D1318yescomplemented
400#388—138no—
401#388—138no—
402C4×C22⋊C4—138no—
403C2×#95—131no—
404C2×#95—131no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95C2×D1311yescharacteristic
410C2×#95C2×D1311yescharacteristic
411C22×C13C2×#12114yes—
412C22×C13#53314yes—
413C22×C13#54114yes—
414C22×C13#54714yes—
415C22×C13#54814yes—
416C22×C13D4×Q814yes—
417C22×C13D4×Q814yes—
418C22×C13C23×D411yescharacteristic
419C22×C13C23×D411yescharacteristic
420C22×C13C23×Q811yescharacteristic
421C22×C13C22×#4111yescharacteristic
422C22×C13C22×#4111yescharacteristic
423C22×C13C2×2−1+411yescharacteristic
424C22×C13C2×2−1+411yescharacteristic
425C2×D13—24no—
426C2×D13—24no—
427C2×D13—24no—
428C2×D13—42no—
429C2×D13—416no—
430C2×D13—42no—
431C2×D13—42no—
432C2×D13—42no—
433C4×C13—24no—
434C4×C13—24no—
435C4×C13—24no—
436C4×C13—24no—
437C4×C13—42no—
438C4×C13—42no—
439C4×C13—42no—
440Dic13—24no—
441Dic13—24no—
442Dic13—24no—
443Dic13—42no—
444Dic13—42no—
445Dic13—42no—
446Dic13C2×#12118yes—
447C25—131no—
448C22×Q8—138no—
449C22×Q8—134no—
450C22×Q8—134no—
451C22×Q8—264no—
452C22×Q8—264no—
453C22×Q8—264no—
454C22×Q8—264no—
455C22×Q8—264no—
456C23×C4—131no—
457C23×C4—131no—
458C23×C4—131no—
459C23×C4—131no—
460C23×C4—131no—
461C23×C4—131no—
462C23×C4—131no—
463C23×C4—134no—
464C23×C4—264no—
465C23×C4—264no—
466C23×C4—264no—
467C23×C4C22×D1311yescharacteristic
468C23×C4C22×D1311yescharacteristic
469C23×C4C22×D1311yescharacteristic
470C23×C4C22×D1311yescharacteristic
471C23×C4C22×D1311yescharacteristic
472C23×C4C22×D1311yescharacteristic
473C23×C4C22×D1311yescharacteristic
474C4⋊Q8—2632no—
475C22⋊Q8—2632no—
476C22⋊Q8—2632no—
477C4×Q8—2632no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—138no—
483C2×C4⋊C4—134no—
484C2×C4⋊C4—134no—
485C2×C4⋊C4—134no—
486C2×C4⋊C4—134no—
487C2×C4⋊C4—134no—
488C2×C4⋊C4—134no—
489C2×C4⋊C4—134no—
490C2×C4⋊C4—134no—
491C2×C4⋊C4—134no—
492C2×C4⋊C4—134no—
493C2×C4⋊C4—264no—
494C2×C4⋊C4—264no—
495C2×C4⋊C4—264no—
496C2×C4⋊C4—264no—
497C2×C4⋊C4—264no—
498C2×C4⋊C4—264no—
499C2×C4⋊C4—264no—
500C2×C4⋊C4—264no—
501C2×C4⋊C4—264no—
502C2×C4⋊C4C22×D1314yes—
503C2×C4⋊C4C22×D1314yes—
504C2×C4⋊C4C22×D1314yes—
505C2×C4⋊C4C22×D1314yes—
506C2×C22⋊C4—138no—
507C2×C22⋊C4—134no—
508C2×C22⋊C4—134no—
509C2×C22⋊C4—134no—
510C2×C22⋊C4—134no—
511C2×C22⋊C4—134no—
512C2×C22⋊C4—134no—
513C2×C22⋊C4—264no—
514C2×C22⋊C4—264no—
515C2×C22⋊C4—264no—
516C2×C22⋊C4—264no—
517C2×C22⋊C4—264no—
518C2×C42—24no—
519C2×C42—134no—
520C2×C42—134no—
521C2×C42—134no—
522C2×C42—264no—
523C2×C42—264no—
524C2×C42—264no—
525C2×C42C22×D1314yes—
526#95—134no—
527#95—134no—
528#95—134no—
529#95—134no—
530#95—134no—
531#95—134no—
532#95C22×D1314yes—
533#95C22×D1314yes—
534C2×C13#242918yescomplemented
535C2×C13C22×#12111yescharacteristic
536C2×C13C2×#53311yescharacteristic
537C2×C13C2×#54111yescharacteristic
538C2×C13C2×#54711yescharacteristic
539C2×C13C2×#54811yescharacteristic
540C2×C13C2×D4×Q811yescharacteristic
541C2×C13C2×D4×Q811yescharacteristic
542D13—44no—
543C24—134no—
544C24—132no—
545C24—262no—
546C24—262no—
547C24—262no—
548C24—262no—
549C24—262no—
550C24—262no—
551C24C23×D1311yescharacteristic
552C2×Q8—1316no—
553C2×Q8—268no—
554C2×Q8—2632no—
555C2×Q8—268no—
556C2×Q8—268no—
557C2×Q8—268no—
558C2×Q8—268no—
559C2×Q8—5216no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—134no—
578C22×C4—134no—
579C22×C4—134no—
580C22×C4—132no—
581C22×C4—134no—
582C22×C4—134no—
583C22×C4—134no—
584C22×C4—132no—
585C22×C4—132no—
586C22×C4—132no—
587C22×C4—132no—
588C22×C4—132no—
589C22×C4—132no—
590C22×C4—268no—
591C22×C4—268no—
592C22×C4—268no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—5216no—
609C22×C4#612714yes—
610C22×C4D4×D1314yes—
611C22×C4D4×D1314yes—
612C22×C4Q8×D1314yes—
613C22×C4C23×D1312yes—
614C22×C4C23×D1312yes—
615C22×C4C23×D1312yes—
616C22×C4C23×D1312yes—
617C22×C4C23×D1312yes—
618C22×C4C23×D1312yes—
619C22×C4C23×D1312yes—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—1316no—
625C4⋊C4—268no—
626C4⋊C4—268no—
627C4⋊C4—268no—
628C4⋊C4—268no—
629C4⋊C4—268no—
630C4⋊C4—268no—
631C4⋊C4—268no—
632C4⋊C4—268no—
633C4⋊C4—268no—
634C22⋊C4—1316no—
635C22⋊C4—268no—
636C22⋊C4—268no—
637C22⋊C4—268no—
638C22⋊C4—268no—
639C22⋊C4—268no—
640C42—28no—
641C42—268no—
642C42—268no—
643C42—268no—
644C13C2×#242911yescharacteristic, complemented, Sylow
645C23—134no—
646C23—268no—
647C23—268no—
648C23—268no—
649C23—262no—
650C23—262no—
651C23—262no—
652C23—262no—
653C23—262no—
654C23—262no—
655C23—524no—
656C23—524no—
657C23—524no—
658C23—524no—
659C23C2×#612712yes—
660C23C2×D4×D1312yes—
661C23C2×D4×D1312yes—
662C23C2×Q8×D1312yes—
663C23#8825412yes—
664C23#41×D1312yes—
665C23#8825712yes—
666C23C24×D1311yescharacteristic
667Q8—2632no—
668Q8—5216no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—28no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—1316no—
694C2×C4—134no—
695C2×C4—134no—
696C2×C4—134no—
697C2×C4—134no—
698C2×C4—134no—
699C2×C4—134no—
700C2×C4—268no—
701C2×C4—268no—
702C2×C4—268no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—262no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—5216no—
719C2×C4—524no—
720C2×C4—524no—
721C2×C4—524no—
722C2×C4C2×#612714yes—
723C2×C4C2×D4×D1314yes—
724C2×C4C2×D4×D1314yes—
725C2×C4C2×Q8×D1314yes—
726C22—264no—
727C22—264no—
728C22—264no—
729C22—522no—
730C22—522no—
731C22—522no—
732C22—522no—
733C22—5216no—
734C22#1171921214yes—
735C22#1171925714yes—
736C22#1171928314yes—
737C22D13×#12114yes—
738C22#1171933714yes—
739C22#1171940114yes—
740C22#1171943214yes—
741C22C22×#612711yescharacteristic
742C22C22×D4×D1311yescharacteristic
743C22C22×D4×D1311yescharacteristic
744C22C22×Q8×D1311yescharacteristic
745C22C2×#8825411yescharacteristic
746C22C2×#41×D1311yescharacteristic
747C22C2×#8825711yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—138no—
756C4—264no—
757C4—264no—
758C4—264no—
759C4—522no—
760C4—522no—
761C4—522no—
762C2—524no—
763C2#1311843418yesdirect product factor
764C2C2×D13×#12111yescharacteristic
765C2C2×#1171928311yescharacteristic
766C2C2×#1171940111yescharacteristic
767C2C2×#1171921211yescharacteristic
768C2C2×#1171925711yescharacteristic
769C2C2×#1171933711yescharacteristic
770C2C2×#1171943211yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#389C2
socleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#389D13
hypocenterC13C2×#2429
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#88142C2semidirect
4. C22×C4×Dic26C2semidirect
5. #13118434C2direct (N × H)
6. C2×#11718645C2semidirect
7. C2×#11718641C2semidirect
10. C2×#11718307C2semidirect
11. C2×#11718308C2semidirect
12. C2×#11718633C2semidirect
16. C2×C13×#389C2semidirect
49. C2×#88142C22semidirect
51. C2×C4×Dic26C22semidirect
52. C13×#389C22semidirect
63. #11718645C22semidirect
64. #11718641C22semidirect
65. #11718633C22semidirect
69. #11718308C22semidirect
70. #11718307C22semidirect
113. C2×#6103Q8semidirect
246. #6103C2×Q8semidirect
272. C2×#389D13semidirect
399. #389C2×D13semidirect
534. C2×C13#2429semidirect
644. C13C2×#2429semidirect
763. C2#13118434direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881422
C22×#881502
C22×C4×Dic262
#131184342
C2×#117186452
C2×#117186412
C2×#117186552
C2×#117183072
C2×#117183082
C2×#117186332
C2×#117186012
C2×#117183302
C2×#117183272
C2×C13×#3892
C2×#242913