Finite Group Databasebeta

← C2×#13117645 #16021834

Subgroups — C2×#13117645 #16021834

Order 3328.

3046 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88190C211yesmaximal, characteristic
2#13117645C2116yesmaximal, direct product factor
3C2×#11718307C211yesmaximal, characteristic, complemented
4C2×#11718307C211yesmaximal, characteristic, complemented
5C2×#11718606C211yesmaximal, characteristic, complemented
6C2×#11718606C211yesmaximal, characteristic, complemented
7C2×#11718605C211yesmaximal, characteristic, complemented
8C2×#11718605C211yesmaximal, characteristic, complemented
9C2×#11718881C211yesmaximal, characteristic
10C2×#11718871C211yesmaximal, characteristic, complemented
11C2×#11718607C211yesmaximal, characteristic, complemented
12C2×#11718312C211yesmaximal, characteristic, complemented
13C2×#11718310C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#386C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C23×Dic26C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C2×#88190C4116yescomplemented
32C2×#88190C2218yes—
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C13×#386C2218yes—
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45#11718881C2218yes—
46#11718871C2218yescomplemented
47C4×C22⋊Dic13C2218yescomplemented
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718607C2218yescomplemented
59#11718606C2218yescomplemented
60#11718606C2218yescomplemented
61#11718605C2218yescomplemented
62#11718605C2218yescomplemented
63C22⋊C4×Dic13C2218yescomplemented
64#11718312C2218yescomplemented
65#11718310C2218yescomplemented
66#11718307C2218yescomplemented
67#11718307C2218yescomplemented
68C25×C13C2311yescharacteristic
69C25×C13C2311yescharacteristic
70C22×D4×C13—42no—
71C22×D4×C13—42no—
72C22×D4×C13C2×C418yes—
73C22×D4×C13C2314yes—
74C23×C4×C13—24no—
75C23×C4×C13—42no—
76C23×C4×C13—42no—
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2314yes—
83C23×Dic13—24no—
84C23×Dic13—42no—
85C23×Dic13—42no—
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2314yes—
95C22×Dic26—42no—
96C22×Dic26—42no—
97C22×Dic26C2×C418yescomplemented
98C22×Dic26C2314yes—
99C2×C13×C22⋊C4—24no—
100C2×C13×C22⋊C4—42no—
101C2×C13×C22⋊C4—42no—
102C2×C13×C22⋊C4C2314yes—
103C2×C13×C22⋊C4C2314yes—
104C2×C13×C22⋊C4C2314yes—
105C2×C22⋊Dic13—24no—
106C2×C22⋊Dic13—42no—
107C2×C22⋊Dic13—42no—
108C2×C22⋊Dic13C2×C418yescomplemented
109C2×C22⋊Dic13C2×C418yescomplemented
110C2×C22⋊Dic13C2×C418yescomplemented
111C2×C22⋊Dic13C2×C418yescomplemented
112C2×C22⋊Dic13C2314yes—
113C2×C22⋊Dic13C2314yes—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×C22⋊Dic13C2314yes—
119#88190C2×C4164yescomplemented
120C2×#6101—24no—
121C2×#6101—24no—
122C2×#6101—42no—
123C2×#6101—42no—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×#6101C2314yes—
127C2×#6101C2314yes—
128C2×C4×Dic13—42no—
129C2×C4×Dic13—42no—
130C2×C4×Dic13—42no—
131C2×C4×Dic13—42no—
132C2×C4×Dic13C2×C418yescomplemented
133C2×C4×Dic13C2314yes—
134C2×C4×Dic13C2314yes—
135C2×C4×Dic13C2314yes—
136C2×C4×Dic13C2314yes—
137C2×C4×Dic13C2314yes—
138C13×#95C2314yes—
139C13×#95C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2337—131nomaximal, Sylow
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13—22no—
158C24×C13—22no—
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13C22×C414yes—
164C24×C13C22×C414yes—
165C24×C13C2412yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
168C2×D4×C13—416no—
169C2×D4×C13—44no—
170C2×D4×C13—44no—
171C2×D4×C13C22×C4116yes—
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×C13—28no—
186C22×C4×C13—44no—
187C22×C4×C13—44no—
188C22×C4×C13—416no—
189C22×C4×C13C22×C414yes—
190C22×C4×C13#4114yes—
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×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—28no—
216C22×Dic13—44no—
217C22×Dic13—44no—
218C22×Dic13—416no—
219C22×Dic13C22×C414yes—
220C22×Dic13C22×C414yes—
221C22×Dic13C22×C414yes—
222C22×Dic13C22×C414yes—
223C22×Dic13#4114yes—
224C22×Dic13C2412yes—
225C22×Dic13C2412yes—
226C22×Dic13C2412yes—
227C22×Dic13C2412yes—
228C22×Dic13C2412yes—
229C22×Dic13C2412yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C2×Dic26—416no—
233C2×Dic26—44no—
234C2×Dic26—44no—
235C2×Dic26C22×C4116yescomplemented
236C13×C22⋊C4—28no—
237C13×C22⋊C4—44no—
238C13×C22⋊C4—44no—
239C22⋊Dic13—28no—
240C22⋊Dic13—44no—
241C22⋊Dic13—44no—
242C22⋊Dic13C22×C4116yescomplemented
243C22⋊Dic13C22×C4116yescomplemented
244C22⋊Dic13C22×C4116yescomplemented
245C22⋊Dic13C22×C4116yescomplemented
246#6101—28no—
247#6101—28no—
248#6101—44no—
249#6101—44no—
250C4×Dic13—44no—
251C4×Dic13—44no—
252C4×Dic13—44no—
253C4×Dic13—44no—
254C4×Dic13C22×C4116yescomplemented
255C22×#124—131no—
256#2337—1316no—
257C2×#391—131no—
258C2×#391—131no—
259C2×#388—131no—
260C2×#388—131no—
261C2×#388—131no—
262C2×#388—131no—
263C2×#386—131no—
264C2×#386D1311yescharacteristic
265C2×#385—131no—
266C2×#385—131no—
267C2×#383—131no—
268C2×C4×C4⋊C4—131no—
269C2×C4×C22⋊C4—131no—
270C2×C4×C22⋊C4—131no—
271C23×C13—28no—
272C23×C13—28no—
273C23×C13—28no—
274C23×C13—28no—
275C23×C13—28no—
276C23×C13—28no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—44no—
290C23×C13—44no—
291C23×C13—44no—
292C23×C13—44no—
293C23×C13—44no—
294C23×C13—44no—
295C23×C13—44no—
296C23×C13—44no—
297C23×C13C23×C414yes—
298C23×C13C23×C414yes—
299C23×C13C23×C412yes—
300C23×C13C2×#4112yes—
301C23×C13C2×#4112yes—
302C23×C13H(5,𝔽2)12yes—
303C23×C13H(5,𝔽2)12yes—
304C23×C13H(5,𝔽2)12yes—
305C23×C132−1+412yes—
306C23×C13C2511yescharacteristic
307D4×C13—416no—
308C2×C4×C13—28no—
309C2×C4×C13—28no—
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—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—416no—
324C2×C4×C13—44no—
325C2×C4×C13—44no—
326C2×C4×C13—44no—
327C2×C4×C13C23×C414yes—
328C2×C4×C13C2×#4114yes—
329C2×Dic13—28no—
330C2×Dic13—28no—
331C2×Dic13—28no—
332C2×Dic13—28no—
333C2×Dic13—28no—
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—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—416no—
354C2×Dic13—44no—
355C2×Dic13—44no—
356C2×Dic13—44no—
357C2×Dic13C23×C414yes—
358C2×Dic13C23×C414yes—
359C2×Dic13C23×C414yes—
360C2×Dic13C23×C414yes—
361C2×Dic13C2×#4114yes—
362Dic26—416no—
363C23×Q8—131no—
364C23×D4C2×D1311yescharacteristic
365C24×C4—131no—
366C24×C4C2×D1311yescharacteristic
367C2×#124—1316no—
368C2×#124—138no—
369C22×C4⋊C4—131no—
370C22×C4⋊C4—131no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C22⋊C4—131no—
374C22×C22⋊C4—131no—
375C22×C22⋊C4—131no—
376C22×C22⋊C4—131no—
377C22×C22⋊C4—131no—
378C22×C22⋊C4—131no—
379C22×C22⋊C4—131no—
380C22×C22⋊C4C2×D1311yescharacteristic
381C22×C22⋊C4C2×D1311yescharacteristic
382C22×C22⋊C4C2×D1311yescharacteristic
383C22×C42—131no—
384C22×C42—131no—
385C22×C42—131no—
386C22×C42—131no—
387C22×C42—131no—
388#391—138no—
389#391—138no—
390#388—138no—
391#388—138no—
392#388—138no—
393#388—138no—
394#386—138no—
395#386C2×D1318yes—
396#385—138no—
397#385—138no—
398#383—138no—
399C4×C4⋊C4—138no—
400C4×C22⋊C4—138no—
401C4×C22⋊C4—138no—
402C2×#95—131no—
403C2×#95—131no—
404C2×#95—131no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95—131no—
411C2×#95—131no—
412C2×#95C2×D1311yescharacteristic
413C2×#95C2×D1311yescharacteristic
414C22×C13—24no—
415C22×C13—24no—
416C22×C13—24no—
417C22×C13—24no—
418C22×C13—24no—
419C22×C13—24no—
420C22×C13—416no—
421C22×C13—416no—
422C22×C13—42no—
423C22×C13—42no—
424C22×C13—42no—
425C22×C13—42no—
426C22×C13—42no—
427C22×C13—42no—
428C22×C13—42no—
429C22×C13—42no—
430C22×C13C4×#4114yes—
431C22×C13#51814yes—
432C22×C13#52014yes—
433C22×C13#53814yes—
434C22×C13#53814yes—
435C22×C13#54214yes—
436C22×C13#54214yes—
437C22×C13C24×C411yescharacteristic
438C22×C13C22×#4111yescharacteristic
439C22×C13C22×#4111yescharacteristic
440C22×C13C2×H(5,𝔽2)11yescharacteristic
441C22×C13C2×H(5,𝔽2)11yescharacteristic
442C22×C13C2×H(5,𝔽2)11yescharacteristic
443C22×C13C2×2−1+411yescharacteristic
444C4×C13—24no—
445C4×C13—24no—
446C4×C13—42no—
447C4×C13—42no—
448C4×C13—42no—
449Dic13—24no—
450Dic13—24no—
451Dic13—24no—
452Dic13—24no—
453Dic13—24no—
454Dic13—42no—
455Dic13—42no—
456Dic13—42no—
457C25C22×D1311yescharacteristic
458C25C22×D1311yescharacteristic
459C22×Q8—138no—
460C22×Q8—134no—
461C22×Q8—522no—
462C22×Q8—522no—
463C22×D4—42no—
464C22×D4—42no—
465C22×D4C4×D1318yes—
466C22×D4C22×D1314yes—
467C23×C4—24no—
468C23×C4—42no—
469C23×C4—42no—
470C23×C4—131no—
471C23×C4—131no—
472C23×C4—131no—
473C23×C4—131no—
474C23×C4—131no—
475C23×C4—131no—
476C23×C4—131no—
477C23×C4—131no—
478C23×C4—134no—
479C23×C4—264no—
480C23×C4—522no—
481C23×C4—522no—
482C23×C4C22×D1311yescharacteristic
483C23×C4C22×D1311yescharacteristic
484C23×C4C22×D1311yescharacteristic
485C23×C4C22×D1311yescharacteristic
486C23×C4C22×D1311yescharacteristic
487C23×C4C22×D1314yes—
488#124—1364no—
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—522no—
496C2×C4⋊C4—522no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—138no—
501C2×C22⋊C4—138no—
502C2×C22⋊C4—138no—
503C2×C22⋊C4—138no—
504C2×C22⋊C4—134no—
505C2×C22⋊C4—134no—
506C2×C22⋊C4—134no—
507C2×C22⋊C4—134no—
508C2×C22⋊C4—134no—
509C2×C22⋊C4—134no—
510C2×C22⋊C4—134no—
511C2×C22⋊C4—264no—
512C2×C22⋊C4—522no—
513C2×C22⋊C4—522no—
514C2×C22⋊C4C22×D1314yes—
515C2×C22⋊C4C22×D1314yes—
516C2×C22⋊C4C22×D1314yes—
517C2×C42—138no—
518C2×C42—134no—
519C2×C42—134no—
520C2×C42—134no—
521C2×C42—134no—
522C2×C42—134no—
523C2×C42—522no—
524C2×C42—522no—
525C2×C42—522no—
526C2×C42—522no—
527#95—134no—
528#95—134no—
529#95—134no—
530#95—134no—
531#95—134no—
532#95—134no—
533#95—134no—
534#95—134no—
535#95—134no—
536#95—134no—
537#95C22×D1314yes—
538#95C22×D1314yes—
539C2×C13—44no—
540C2×C13—44no—
541C2×C13#233718yescomplemented
542C2×C13C2×C4×#4111yescharacteristic
543C2×C13C2×#51811yescharacteristic
544C2×C13C2×#52011yescharacteristic
545C2×C13C2×#53811yescharacteristic
546C2×C13C2×#53811yescharacteristic
547C2×C13C2×#54211yescharacteristic
548C2×C13C2×#54211yescharacteristic
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24C2×C4×D1314yes—
562C24C2×C4×D1314yes—
563C24C23×D1312yes—
564C24C23×D1312yes—
565C24C23×D1311yescharacteristic
566C2×Q8—1316no—
567C2×Q8—5216no—
568C2×Q8—524no—
569C2×Q8—524no—
570C2×D4—416no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4C2×C4×D13116yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—28no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—416no—
591C22×C4—134no—
592C22×C4—134no—
593C22×C4—134no—
594C22×C4—134no—
595C22×C4—134no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—132no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—132no—
602C22×C4—132no—
603C22×C4—132no—
604C22×C4—268no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—524no—
625C22×C4—524no—
626C22×C4—5216no—
627C22×C4C2×C4×D1314yes—
628C22×C4#612914yes—
629C22×C4C23×D1312yes—
630C22×C4C23×D1312yes—
631C22×C4C23×D1312yes—
632C22×C4C23×D1312yes—
633C22×C4C23×D1312yes—
634C4⋊C4—268no—
635C4⋊C4—268no—
636C4⋊C4—524no—
637C4⋊C4—524no—
638C22⋊C4—28no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—1316no—
642C22⋊C4—1316no—
643C22⋊C4—1316no—
644C22⋊C4—1316no—
645C22⋊C4—268no—
646C22⋊C4—524no—
647C22⋊C4—524no—
648C42—1316no—
649C42—524no—
650C42—524no—
651C42—524no—
652C42—524no—
653C13C2×#233711yescharacteristic, complemented, Sylow
654C23—28no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23C22×C4×D1314yes—
681C23C22×C4×D1314yes—
682C23C22×C4×D1312yes—
683C23C2×#612912yes—
684C23#8825112yes—
685C23#8825112yes—
686C23#8825112yes—
687C23#41×D1312yes—
688C23#8825712yes—
689C23C24×D1311yescharacteristic
690Q8—5216no—
691D4—416no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—416no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—134no—
712C2×C4—134no—
713C2×C4—134no—
714C2×C4—134no—
715C2×C4—134no—
716C2×C4—268no—
717C2×C4—268no—
718C2×C4—268no—
719C2×C4—268no—
720C2×C4—268no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—5216no—
741C2×C4—524no—
742C2×C4—524no—
743C2×C4—524no—
744C2×C4C22×C4×D1314yes—
745C2×C4C2×#612914yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—416no—
757C22—416no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22#1171919114yes—
763C22C4×#612914yes—
764C22#1171925114yes—
765C22#1171929814yes—
766C22#1171930814yes—
767C22#1171931814yes—
768C22#1171936714yes—
769C22C23×C4×D1311yescharacteristic
770C22C22×#612911yescharacteristic
771C22C2×#8825111yescharacteristic
772C22C2×#8825111yescharacteristic
773C22C2×#8825111yescharacteristic
774C22C2×#41×D1311yescharacteristic
775C22C2×#8825711yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—264no—
782C4—264no—
783C4—264no—
784C4—264no—
785C4—264no—
786C4—522no—
787C4—522no—
788C4—522no—
789C2—44no—
790C2—44no—
791C2#1311764518yesdirect product factor
792C2C2×C4×#612911yescharacteristic
793C2C2×#1171919111yescharacteristic
794C2C2×#1171925111yescharacteristic
795C2C2×#1171931811yescharacteristic
796C2C2×#1171929811yescharacteristic
797C2C2×#1171930811yescharacteristic
798C2C2×#1171936711yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#386C2
socleC24×C13C24
prime radicalC23×D4×C13C22
cosocleC23×C13C25
hypercenterC2×#386D13
hypocenterC13C2×#2337
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. #13117645C2direct (N × H)
3. C2×#11718307C2semidirect
4. C2×#11718307C2semidirect
5. C2×#11718606C2semidirect
6. C2×#11718606C2semidirect
7. C2×#11718605C2semidirect
8. C2×#11718605C2semidirect
10. C2×#11718871C2semidirect
11. C2×#11718607C2semidirect
12. C2×#11718312C2semidirect
13. C2×#11718310C2semidirect
14. C2×C22⋊C4×Dic13C2semidirect
15. C2×C4×C22⋊Dic13C2semidirect
31. C2×#88190C4semidirect
46. #11718871C22semidirect
47. C4×C22⋊Dic13C22semidirect
58. #11718607C22semidirect
59. #11718606C22semidirect
60. #11718606C22semidirect
61. #11718605C22semidirect
62. #11718605C22semidirect
63. C22⋊C4×Dic13C22semidirect
64. #11718312C22semidirect
65. #11718310C22semidirect
66. #11718307C22semidirect
67. #11718307C22semidirect
97. C22×Dic26C2×C4semidirect
108. C2×C22⋊Dic13C2×C4semidirect
109. C2×C22⋊Dic13C2×C4semidirect
110. C2×C22⋊Dic13C2×C4semidirect
111. C2×C22⋊Dic13C2×C4semidirect
119. #88190C2×C4semidirect
132. C2×C4×Dic13C2×C4semidirect
235. C2×Dic26C22×C4semidirect
242. C22⋊Dic13C22×C4semidirect
243. C22⋊Dic13C22×C4semidirect
244. C22⋊Dic13C22×C4semidirect
245. C22⋊Dic13C22×C4semidirect
254. C4×Dic13C22×C4semidirect
541. C2×C13#2337semidirect
653. C13C2×#2337semidirect
791. C2#13117645direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881902
#131176452
C2×#117183072
C2×#117186062
C2×#117186052
C2×#117188812
C2×#117188712
C2×#117186072
C2×#117183122
C2×#117183102
C2×C22⋊C4×Dic132
C2×C4×C22⋊Dic132
C2×C13×#3862
C2×#233713