Finite Group Databasebeta

← C2×#13118642 #16030400

Subgroups — C2×#13118642 #16030400

Order 3328.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88200C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D13C211yesmaximal, characteristic
3C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
4#13118642C2116yesmaximal, direct product factor
5C2×#11718610C211yesmaximal, characteristic, complemented
6C2×#11718644C211yesmaximal, characteristic, complemented
7C2×#11718609C211yesmaximal, characteristic, complemented
8C2×#11718890C211yesmaximal, characteristic, complemented
9C2×#11718633C211yesmaximal, characteristic, complemented
10C2×#11718642C211yesmaximal, characteristic, complemented
11C2×#11718617C211yesmaximal, characteristic
12C2×#11718617C211yesmaximal, characteristic
13C2×#11718871C211yesmaximal, characteristic, complemented
14C2×#11718650C211yesmaximal, characteristic, complemented
15C2×#11718650C211yesmaximal, characteristic, complemented
16C22×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
17C23×Q8×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C2×C13×C22⋊Q8—28no—
24C2×C13×C22⋊Q8C2218yescomplemented
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C2×#88200—28no—
34C2×#88200C2218yescomplemented
35C2×C4×C22⋊D13—28no—
36C2×C4×C22⋊D13C2218yes—
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×C4⋊Dic13C2211yescharacteristic
41C22×C4⋊Dic13C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×#6101C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×C4×Dic13C2211yescharacteristic
50C2×C4⋊C4×D13—28no—
51C2×C4⋊C4×D13C2218yescomplemented
52#11718890C2218yescomplemented
53#11718871C2218yescomplemented
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62#11718650C2218yescomplemented
63#11718650C2218yescomplemented
64#11718644C2218yescomplemented
65#11718642C2218yescomplemented
66#11718633C2218yescomplemented
67#11718617C2218yes—
68#11718617C2218yes—
69#11718610C2218yescomplemented
70#11718609C2218yescomplemented
71C25×C13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C22×Q8×C13—24no—
74C22×Q8×C13—24no—
75C22×Q8×C13—42no—
76C22×Q8×C13C2314yes—
77C23×C4×C13—24no—
78C23×C4×C13—24no—
79C23×C4×C13—42no—
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2314yes—
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C22×C22⋊D13—24no—
88C22×C22⋊D13—24no—
89C22×C22⋊D13Q818yescomplemented
90C22×C22⋊D13C2314yes—
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C22×C4×D13—24no—
99C22×C4×D13—24no—
100C22×C4×D13—24no—
101C22×C4×D13—24no—
102C22×C4×D13—24no—
103C22×C4×D13—24no—
104C22×C4×D13—24no—
105C22×C4×D13—42no—
106C22×C4×D13—42no—
107C22×C4×D13C2314yes—
108C22×C4×D13C2314yes—
109C22×C4×D13C2314yes—
110C13×C22⋊Q8—232no—
111C2×C13×C4⋊C4—24no—
112C2×C13×C4⋊C4—24no—
113C2×C13×C4⋊C4D418yescomplemented
114C2×C13×C4⋊C4C2314yes—
115C2×C13×C4⋊C4C2314yes—
116C2×C13×C4⋊C4C2314yes—
117C2×C13×C22⋊C4—24no—
118C2×C13×C22⋊C4—24no—
119C2×C13×C22⋊C4C2314yes—
120C2×C13×C22⋊C4C2314yes—
121C2×C22⋊Dic13—24no—
122C2×C22⋊Dic13—24no—
123C2×C22⋊Dic13—42no—
124C2×C22⋊Dic13C2314yes—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127#88200—232no—
128C4×C22⋊D13—232no—
129C2×#6103—24no—
130C2×#6103—24no—
131C2×#6103D418yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×C4⋊Dic13—24no—
136C2×C4⋊Dic13—24no—
137C2×C4⋊Dic13C2314yes—
138C2×C4⋊Dic13C2314yes—
139C2×#6101—24no—
140C2×#6101—24no—
141C2×#6101—24no—
142C2×#6101—24no—
143C2×#6101—24no—
144C2×#6101—24no—
145C2×#6101—42no—
146C2×#6101C2314yes—
147C2×#6101C2314yes—
148C2×#6101C2314yes—
149C2×#6101C2314yes—
150C2×#6101C2314yes—
151C2×#6101C2314yes—
152C2×#6101C2314yes—
153C2×C4×Dic13—24no—
154C2×C4×Dic13C2314yes—
155C4⋊C4×D13—232no—
156#88071C2314yes—
157#88071C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164C2×#2449—131nomaximal, Sylow
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13C2×Q814yes—
172C24×C13C2412yes—
173C24×C13C2411yescharacteristic
174C23×D13—22no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13C2×D414yes—
179C23×D13C2×Q814yes—
180C23×D13#4114yes—
181C23×D13C2412yes—
182C2×Q8×C13—28no—
183C2×Q8×C13—28no—
184C2×Q8×C13—44no—
185C2×Q8×C13—416no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—28no—
201C22×C4×C13—28no—
202C22×C4×C13—44no—
203C22×C4×C13—416no—
204C22×C4×C13C2×D414yes—
205C22×C4×C13C2×D414yes—
206C22×C4×C13C2×D414yes—
207C22×C4×C13C2×D414yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C2×C22⋊D13—232no—
215C2×C22⋊D13—28no—
216C2×C22⋊D13—28no—
217C2×C22⋊D13C2×Q8116yescomplemented
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13C2×D414yes—
237C22×Dic13C2×Q814yes—
238C22×Dic13#4114yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C2×C4×D13—232no—
247C2×C4×D13—28no—
248C2×C4×D13—28no—
249C2×C4×D13—28no—
250C2×C4×D13—28no—
251C2×C4×D13—28no—
252C2×C4×D13—28no—
253C2×C4×D13—28no—
254C2×C4×D13—44no—
255C2×C4×D13—44no—
256C2×C4×D13—416no—
257C2×C4×D13—416no—
258C13×C4⋊C4—28no—
259C13×C4⋊C4—28no—
260C13×C4⋊C4C2×D4116yescomplemented
261C13×C22⋊C4—28no—
262C13×C22⋊C4—28no—
263C22⋊Dic13—28no—
264C22⋊Dic13—28no—
265C22⋊Dic13—44no—
266#6103—28no—
267#6103—28no—
268#6103C2×D4116yes—
269C4⋊Dic13—28no—
270C4⋊Dic13—28no—
271#6101—28no—
272#6101—28no—
273#6101—28no—
274#6101—28no—
275#6101—28no—
276#6101—28no—
277#6101—44no—
278C4×Dic13—28no—
279C22×C22⋊Q8—131no—
280C22×C22⋊Q8D1311yescharacteristic, complemented
281C22×C4×D4—131no—
282C23×C4⋊C4—131no—
283#2449—1316no—
284C2×#399—131no—
285C2×#398—131no—
286C2×#396—131no—
287C2×#395—131no—
288C2×#389—131no—
289C2×#387—131no—
290C2×#386—131no—
291C2×#386—131no—
292C2×#385—131no—
293C2×#385—131no—
294C2×#385—131no—
295C23×C13—28no—
296C23×C13—28no—
297C23×C13—28no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—44no—
305C23×C13—44no—
306C23×C13—44no—
307C23×C13—44no—
308C23×C13C22×D412yes—
309C23×C13C22×D412yes—
310C23×C13C22×Q814yes—
311C23×C13C22×Q812yes—
312C23×C13C2×#4112yes—
313C23×C13C2×#4112yes—
314C23×C13H(5,𝔽2)12yes—
315C23×C132−1+412yes—
316C23×C13C2511yescharacteristic
317C22×D13—28no—
318C22×D13—28no—
319C22×D13—28no—
320C22×D13—28no—
321C22×D13—28no—
322C22×D13—28no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13C22⋊Q8116yescomplemented
328C22×D13C22×D414yes—
329C22×D13C22×Q814yes—
330C22×D13C2×#4114yes—
331Q8×C13—416no—
332C2×C4×C13—28no—
333C2×C4×C13—28no—
334C2×C4×C13—28no—
335C2×C4×C13—28no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—416no—
351C2×C4×C13—44no—
352C2×C4×C13—44no—
353C2×C4×C13C22×D414yes—
354C2×C4×C13C22×D414yes—
355C2×C4×C13C22×D414yes—
356C2×C4×C13C22×D414yes—
357C22⋊D13—232no—
358C2×Dic13—28no—
359C2×Dic13—28no—
360C2×Dic13—28no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—44no—
380C2×Dic13—44no—
381C2×Dic13—44no—
382C2×Dic13—44no—
383C2×Dic13C22×D414yes—
384C2×Dic13C22×Q814yes—
385C2×Dic13C2×#4114yes—
386C4×D13—232no—
387C4×D13—416no—
388C4×D13—416no—
389C23×Q8C2×D1311yescharacteristic
390C23×D4—131no—
391C24×C4—131no—
392C24×C4—131no—
393C24×C4—131no—
394C24×C4C2×D1311yescharacteristic
395C2×C22⋊Q8—28no—
396C2×C22⋊Q8—138no—
397C2×C22⋊Q8—268no—
398C2×C22⋊Q8C2×D1318yescomplemented
399C2×C4×D4—138no—
400C2×C4×D4—268no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
407C22×C4⋊C4—131no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4—131no—
410C22×C4⋊C4—138no—
411C22×C4⋊C4—268no—
412C22×C4⋊C4C2×D1311yescharacteristic
413C22×C4⋊C4C2×D1311yescharacteristic
414C22×C4⋊C4C2×D1311yescharacteristic
415C22×C22⋊C4—131no—
416C22×C22⋊C4—131no—
417C22×C22⋊C4—131no—
418C22×C22⋊C4—131no—
419C22×C22⋊C4—131no—
420C22×C22⋊C4—131no—
421C22×C22⋊C4C2×D1311yescharacteristic
422C22×C22⋊C4C2×D1311yescharacteristic
423C22×C42—131no—
424#399—138no—
425#398—138no—
426#396—138no—
427#395—138no—
428#389—138no—
429#387—138no—
430#386—138no—
431#386—138no—
432#385—138no—
433#385—138no—
434#385—138no—
435C2×#95—131no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C22×C13—24no—
444C22×C13—24no—
445C22×C13—24no—
446C22×C13—42no—
447C22×C13—42no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—416no—
451C22×C13C2×C22⋊Q814yes—
452C22×C13#52514yes—
453C22×C13#53914yes—
454C22×C13D4214yes—
455C22×C13#54714yes—
456C22×C13D4×Q814yes—
457C22×C13#55414yes—
458C22×C13C23×D411yescharacteristic
459C22×C13C23×D411yescharacteristic
460C22×C13C23×Q811yescharacteristic
461C22×C13C22×#4111yescharacteristic
462C22×C13C22×#4111yescharacteristic
463C22×C13C2×H(5,𝔽2)11yescharacteristic
464C22×C13C2×2−1+411yescharacteristic
465C2×D13—24no—
466C2×D13—24no—
467C2×D13—24no—
468C2×D13—24no—
469C2×D13—24no—
470C2×D13—24no—
471C2×D13—232no—
472C2×D13C2×C22⋊Q818yescomplemented
473C4×C13—24no—
474C4×C13—24no—
475C4×C13—24no—
476C4×C13—24no—
477C4×C13—42no—
478C4×C13—42no—
479Dic13—24no—
480Dic13—24no—
481Dic13—24no—
482Dic13—42no—
483Dic13—42no—
484Dic13—42no—
485Dic13—42no—
486C25—131no—
487C25C22×D1311yescharacteristic
488C22×Q8—24no—
489C22×Q8—24no—
490C22×Q8—42no—
491C22×Q8C22×D1314yes—
492C22×D4—138no—
493C22×D4—134no—
494C22×D4—264no—
495C22×D4—264no—
496C23×C4—24no—
497C23×C4—24no—
498C23×C4—42no—
499C23×C4—131no—
500C23×C4—131no—
501C23×C4—131no—
502C23×C4—131no—
503C23×C4—131no—
504C23×C4—131no—
505C23×C4—131no—
506C23×C4—134no—
507C23×C4—134no—
508C23×C4—134no—
509C23×C4—264no—
510C23×C4—264no—
511C23×C4—264no—
512C23×C4—264no—
513C23×C4—264no—
514C23×C4—264no—
515C23×C4—264no—
516C23×C4—522no—
517C23×C4—522no—
518C23×C4C22×D1311yescharacteristic
519C23×C4C22×D1311yescharacteristic
520C23×C4C22×D1314yes—
521C23×C4C22×D1311yescharacteristic
522C23×C4C22×D1311yescharacteristic
523C23×C4C22×D1311yescharacteristic
524C23×C4C22×D1311yescharacteristic
525C22⋊Q8—232no—
526C22⋊Q8—2632no—
527C4×D4—2632no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—134no—
531C2×C4⋊C4—134no—
532C2×C4⋊C4—134no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—264no—
540C2×C4⋊C4—264no—
541C2×C4⋊C4—264no—
542C2×C4⋊C4—264no—
543C2×C4⋊C4—264no—
544C2×C4⋊C4—264no—
545C2×C4⋊C4—264no—
546C2×C4⋊C4—264no—
547C2×C4⋊C4—2632no—
548C2×C4⋊C4—522no—
549C2×C4⋊C4C22⋊D1318yescomplemented
550C2×C4⋊C4C22×D1314yes—
551C2×C4⋊C4C22×D1314yes—
552C2×C4⋊C4C22×D1314yes—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—138no—
556C2×C22⋊C4—134no—
557C2×C22⋊C4—134no—
558C2×C22⋊C4—134no—
559C2×C22⋊C4—134no—
560C2×C22⋊C4—134no—
561C2×C22⋊C4—134no—
562C2×C22⋊C4—264no—
563C2×C22⋊C4—264no—
564C2×C22⋊C4—264no—
565C2×C22⋊C4—264no—
566C2×C22⋊C4—522no—
567C2×C22⋊C4C22×D1314yes—
568C2×C22⋊C4C22×D1314yes—
569C2×C42—134no—
570C2×C42—264no—
571#95—134no—
572#95—134no—
573#95—134no—
574#95—134no—
575#95—134no—
576#95—134no—
577#95—134no—
578#95—134no—
579C2×C13—44no—
580C2×C13#244918yescomplemented
581C2×C13C22×C22⋊Q811yescharacteristic
582C2×C13C2×#52511yescharacteristic
583C2×C13C2×#53911yescharacteristic
584C2×C13C2×D4211yescharacteristic
585C2×C13C2×#54711yescharacteristic
586C2×C13C2×D4×Q811yescharacteristic
587C2×C13C2×#55411yescharacteristic
588D13—28no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—134no—
596C24—134no—
597C24—134no—
598C24—132no—
599C24—262no—
600C24—262no—
601C24—262no—
602C24—262no—
603C24Q8×D1314yes—
604C24C23×D1312yes—
605C24C23×D1311yescharacteristic
606C2×Q8—28no—
607C2×Q8—28no—
608C2×Q8—44no—
609C2×Q8—416no—
610C2×D4—1316no—
611C2×D4—268no—
612C2×D4—2632no—
613C2×D4—268no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—28no—
629C22×C4—28no—
630C22×C4—44no—
631C22×C4—416no—
632C22×C4—134no—
633C22×C4—134no—
634C22×C4—134no—
635C22×C4—132no—
636C22×C4—132no—
637C22×C4—132no—
638C22×C4—132no—
639C22×C4—132no—
640C22×C4—132no—
641C22×C4—132no—
642C22×C4—268no—
643C22×C4—268no—
644C22×C4—2632no—
645C22×C4—268no—
646C22×C4—268no—
647C22×C4—262no—
648C22×C4—262no—
649C22×C4—262no—
650C22×C4—262no—
651C22×C4—262no—
652C22×C4—262no—
653C22×C4—268no—
654C22×C4—262no—
655C22×C4—262no—
656C22×C4—262no—
657C22×C4—262no—
658C22×C4—262no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—262no—
663C22×C4—262no—
664C22×C4—262no—
665C22×C4—262no—
666C22×C4—268no—
667C22×C4—268no—
668C22×C4—524no—
669C22×C4—524no—
670C22×C4—5216no—
671C22×C4—5216no—
672C22×C4D4×D1314yes—
673C22×C4C2×C22⋊D1314yes—
674C22×C4C2×C22⋊D1314yes—
675C22×C4C2×C22⋊D1314yes—
676C22×C4C23×D1312yes—
677C22×C4C23×D1312yes—
678C22×C4C23×D1312yes—
679C22×C4C23×D1312yes—
680C22×C4C23×D1312yes—
681C22×C4C23×D1312yes—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—268no—
685C4⋊C4—268no—
686C4⋊C4—268no—
687C4⋊C4—268no—
688C4⋊C4—268no—
689C4⋊C4—268no—
690C4⋊C4—268no—
691C4⋊C4—268no—
692C4⋊C4—524no—
693C4⋊C4C2×C22⋊D13116yescomplemented
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—1316no—
697C22⋊C4—268no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—268no—
701C22⋊C4—524no—
702C42—268no—
703C13C2×#244911yescharacteristic, complemented, Sylow
704C23—28no—
705C23—28no—
706C23—28no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—1316no—
718C23—134no—
719C23—134no—
720C23—134no—
721C23—268no—
722C23—268no—
723C23—268no—
724C23—268no—
725C23—268no—
726C23—268no—
727C23—262no—
728C23—262no—
729C23—262no—
730C23—262no—
731C23C2×D4×D1312yes—
732C23#8825112yes—
733C23C2×Q8×D1314yes—
734C23C2×Q8×D1312yes—
735C23#8825412yes—
736C23#41×D1312yes—
737C23#41×D1312yes—
738C23C22×C22⋊D1312yes—
739C23C24×D1311yescharacteristic
740Q8—416no—
741D4—2632no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—416no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—134no—
764C2×C4—134no—
765C2×C4—134no—
766C2×C4—2632no—
767C2×C4—268no—
768C2×C4—268no—
769C2×C4—268no—
770C2×C4—262no—
771C2×C4—262no—
772C2×C4—262no—
773C2×C4—262no—
774C2×C4—262no—
775C2×C4—262no—
776C2×C4—262no—
777C2×C4—262no—
778C2×C4—262no—
779C2×C4—262no—
780C2×C4—262no—
781C2×C4—262no—
782C2×C4—262no—
783C2×C4—262no—
784C2×C4—262no—
785C2×C4—262no—
786C2×C4—262no—
787C2×C4—262no—
788C2×C4—5216no—
789C2×C4—5216no—
790C2×C4—524no—
791C2×C4—524no—
792C2×C4—524no—
793C2×C4—524no—
794C2×C4C2×D4×D1314yes—
795C2×C4C22×C22⋊D1314yes—
796C2×C4C22×C22⋊D1314yes—
797C2×C4C22×C22⋊D1314yes—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—416no—
805C22—42no—
806C22—138no—
807C22—264no—
808C22—264no—
809C22—264no—
810C22—264no—
811C22—264no—
812C22—2632no—
813C22—264no—
814C22D13×C22⋊Q814yes—
815C22#1171933614yes—
816C22#1171934114yes—
817C22#1171934314yes—
818C22D4×C22⋊D1314yes—
819C22Q8×C22⋊D1314yes—
820C22#1171953314yes—
821C22C22×D4×D1311yescharacteristic
822C22C2×#8825111yescharacteristic
823C22C22×Q8×D1311yescharacteristic
824C22C2×#8825411yescharacteristic
825C22C2×#41×D1311yescharacteristic
826C22C2×#41×D1311yescharacteristic
827C22C23×C22⋊D1311yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—42no—
833C4—42no—
834C4—264no—
835C4—264no—
836C4—264no—
837C4—522no—
838C4—522no—
839C4—522no—
840C4—522no—
841C2—44no—
842C2—268no—
843C2#1311864218yesdirect product factor
844C2C2×D13×C22⋊Q811yescharacteristic
845C2C2×#1171953311yescharacteristic
846C2C2×#1171934311yescharacteristic
847C2C2×D4×C22⋊D1311yescharacteristic
848C2C2×#1171933611yescharacteristic
849C2C2×Q8×C22⋊D1311yescharacteristic
850C2C2×#1171934111yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×C22⋊Q8C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC22×C22⋊Q8D13
hypocenterC13C2×#2449
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#88200C2semidirect
3. C22×C4⋊C4×D13C2semidirect
4. #13118642C2direct (N × H)
5. C2×#11718610C2semidirect
6. C2×#11718644C2semidirect
7. C2×#11718609C2semidirect
8. C2×#11718890C2semidirect
9. C2×#11718633C2semidirect
10. C2×#11718642C2semidirect
13. C2×#11718871C2semidirect
14. C2×#11718650C2semidirect
15. C2×#11718650C2semidirect
16. C22×C13×C22⋊Q8C2semidirect
24. C2×C13×C22⋊Q8C22semidirect
34. C2×#88200C22semidirect
51. C2×C4⋊C4×D13C22semidirect
52. #11718890C22semidirect
53. #11718871C22semidirect
62. #11718650C22semidirect
63. #11718650C22semidirect
64. #11718644C22semidirect
65. #11718642C22semidirect
66. #11718633C22semidirect
69. #11718610C22semidirect
70. #11718609C22semidirect
89. C22×C22⋊D13Q8semidirect
113. C2×C13×C4⋊C4D4semidirect
217. C2×C22⋊D13C2×Q8semidirect
260. C13×C4⋊C4C2×D4semidirect
280. C22×C22⋊Q8D13semidirect
327. C22×D13C22⋊Q8semidirect
398. C2×C22⋊Q8C2×D13semidirect
472. C2×D13C2×C22⋊Q8semidirect
549. C2×C4⋊C4C22⋊D13semidirect
580. C2×C13#2449semidirect
693. C4⋊C4C2×C22⋊D13semidirect
703. C13C2×#2449semidirect
843. C2#13118642direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882002
C22×C4×C22⋊D132
C22×C4⋊C4×D132
#131186422
C2×#117186102
C2×#117186442
C2×#117186092
C2×#117188902
C2×#117186332
C2×#117186422
C2×#117186172
C2×#117188712
C2×#117186502
C22×C13×C22⋊Q82
C2×#244913