Finite Group Databasebeta

← C2×#13126883 #16739521

Subgroups — C2×#13126883 #16739521

Order 3328.

2094 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
1C2×#11719218C211yesmaximal, characteristic
2C2×Q8×C22⋊D13C211yesmaximal, characteristic
3#13126883C2116yesmaximal, direct product factor
4C2×#11718458C211yesmaximal, characteristic, complemented
5C2×#11718475C211yesmaximal, characteristic, complemented
6C2×#11718632C211yesmaximal, characteristic, complemented
7C2×#11718457C211yesmaximal, characteristic, complemented
8C2×#11718477C211yesmaximal, characteristic, complemented
9C2×#11718777C211yesmaximal, characteristic, complemented
10C2×#11718454C211yesmaximal, characteristic, complemented
11C2×#11718469C211yesmaximal, characteristic, complemented
12C2×#11718889C211yesmaximal, characteristic, complemented
13C2×#11718450C211yesmaximal, characteristic, complemented
14C2×#11718772C211yesmaximal, characteristic
15C2×#11718463C211yesmaximal, characteristic, complemented
16C22×C13×#103C211yesmaximal, characteristic, complemented
17C23×Q8×C13C2211yescharacteristic
18C22×Q8×D13C2211yescharacteristic
19C23×C8×C13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21Q8×C22⋊D13—24no—
22Q8×C22⋊D13C2218yes—
23C2×#88200—21no—
24C2×#88200C2211yescharacteristic
25C2×Q8×Dic13C2211yescharacteristic
26C2×#88198—21no—
27C2×#88198C2211yescharacteristic
28C22×#6107C2211yescharacteristic
29C22×#6107C2211yescharacteristic
30C2×#88183—21no—
31C2×C4×C22⋊D13—21no—
32C2×C4×C22⋊D13C2211yescharacteristic
33C2×#88180—21no—
34C2×#88178—21no—
35C2×#88178C2211yescharacteristic
36C2×#88178C2211yescharacteristic
37C22×Dic52C2211yescharacteristic
38C22×#6094C2211yescharacteristic
39#11719218—24no—
40#11719218C2218yes—
41C2×#88152—21no—
42C2×#88151C2211yescharacteristic
43C2×#88146C2211yescharacteristic
44C2×#88144C2211yescharacteristic
45C2×#88143—21no—
46C2×#88141C2211yescharacteristic
47C2×C13×#103C2211yescharacteristic
48C2×C13×#103C2211yescharacteristic
49C2×C13×#103C2211yescharacteristic
50C2×C13×#103C2211yescharacteristic
51C2×C13×#103C2218yescomplemented
52#11718889C2218yescomplemented
53C2×#88075C2211yescharacteristic
54C2×#88075C2211yescharacteristic
55C2×C22⋊#1055C2211yescharacteristic
56#11718777C2218yescomplemented
57#11718772C2218yes—
58C2×#88060C2211yescharacteristic
59C2×#88058C2211yescharacteristic
60C2×#88056C2211yescharacteristic
61C2×#88056C2211yescharacteristic
62C2×#88055C2211yescharacteristic
63C2×#88054C2211yescharacteristic
64#11718632C2218yescomplemented
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69#11718477C2218yescomplemented
70#11718475C2218yescomplemented
71#11718469C2218yescomplemented
72#11718463C2218yescomplemented
73#11718458C2218yescomplemented
74#11718457C2218yescomplemented
75#11718454C2218yescomplemented
76#11718450C2218yescomplemented
77C22×Q8×C13—21no—
78C22×Q8×C13—22no—
79C22×Q8×C13—24no—
80C22×Q8×C13—42no—
81C22×Q8×C13C2311yescharacteristic
82C22×Q8×C13C2314yes—
83C22×Q8×C13C2311yescharacteristic
84C23×C4×C13—21no—
85C23×C4×C13—21no—
86C23×C4×C13C2311yescharacteristic
87C22×C22⋊D13D411yescharacteristic
88C2×Q8×D13—22no—
89C2×Q8×D13—24no—
90C2×Q8×D13—42no—
91C2×Q8×D13C2314yes—
92C22×C4×D13—21no—
93C22×C4×D13C2311yescharacteristic
94C22×Dic26—21no—
95C22×Dic26C2311yescharacteristic
96C22×Dic26C2311yescharacteristic
97C22×C8×C13—42no—
98C22×C8×C13C2311yescharacteristic
99C22×C8×C13C2311yescharacteristic
100C22×C8×C13C2314yes—
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C4⋊C4C2311yescharacteristic
105C2×C13×C4⋊C4C2314yes—
106C2×C22⋊Dic13—21no—
107C2×C22⋊Dic13—21no—
108C2×C22⋊Dic13D411yescharacteristic
109#88200—22no—
110#88200—28no—
111#88200C2314yes—
112Q8×Dic13—22no—
113Q8×Dic13C2314yes—
114#88198—28no—
115#88198—22no—
116#88198C2314yes—
117C2×#6107—24no—
118C2×#6107—42no—
119C2×#6107C2314yes—
120C2×#6107C2314yes—
121#88183—28no—
122C4×C22⋊D13—28no—
123C4×C22⋊D13D414yes—
124C4×C22⋊D13C2314yes—
125C2×#6103—21no—
126C2×#6103—21no—
127C2×#6103—21no—
128C2×#6103D411yescharacteristic
129#88180—28no—
130C2×C4⋊Dic13—21no—
131C2×C4⋊Dic13—21no—
132C2×C4⋊Dic13—21no—
133C2×C4⋊Dic13C2311yescharacteristic
134C2×C4⋊Dic13C2311yescharacteristic
135#88178—22no—
136#88178—22no—
137#88178—28no—
138#88178C2314yes—
139#88178C2314yes—
140C2×#6101—21no—
141C2×#6101—21no—
142C2×#6101—21no—
143C2×#6101—21no—
144C2×#6101—21no—
145C2×#6101—21no—
146C2×#6101—21no—
147C2×#6101D411yescharacteristic
148C2×C4×Dic13—21no—
149C2×C4×Dic13—21no—
150C2×C4×Dic13—21no—
151C2×C4×Dic13C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153C22×#1055C2311yescharacteristic
154C2×Dic52—42no—
155C2×Dic52C2314yes—
156C2×#6094—42no—
157C2×#6094C2314yes—
158#88152—28no—
159#88151—22no—
160#88151C2314yes—
161#88146—22no—
162#88146C2314yes—
163#88144—22no—
164#88144C2314yes—
165#88143—28no—
166#88141—22no—
167#88141C2314yes—
168C13×#103C2314yes—
169C13×#103C2314yes—
170C13×#103C2314yes—
171C13×#103C2314yes—
172#88075C2314yes—
173#88075C2314yes—
174C22⋊#1055C2314yes—
175#88060C2314yes—
176#88058C2314yes—
177#88056C2314yes—
178#88056C2314yes—
179#88055C2314yes—
180#88054C2314yes—
181#88050C2314yes—
182#88050C2314yes—
183#88048C2314yes—
184#88048C2314yes—
185C2×#3312—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C23×D13C2×D411yescharacteristic
188C2×Q8×C13—21no—
189C2×Q8×C13—24no—
190C2×Q8×C13—21no—
191C2×Q8×C13—22no—
192C2×Q8×C13—28no—
193C2×Q8×C13—22no—
194C2×Q8×C13—22no—
195C2×Q8×C13—44no—
196C2×Q8×C13—44no—
197C2×Q8×C13—48no—
198C2×Q8×C13#4114yes—
199C2×Q8×C13C2412yes—
200C2×Q8×C13C2412yes—
201C22×C4×C13—21no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—24no—
208C22×C4×C13—24no—
209C22×C4×C13—44no—
210C22×C4×C13—44no—
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D412yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2411yescharacteristic
215C2×C22⋊D13—24no—
216C2×C22⋊D13C2×D414yes—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13C2×D411yescharacteristic
222C22×Dic13C2×D411yescharacteristic
223C22×Dic13C2×D411yescharacteristic
224Q8×D13—28no—
225Q8×D13—44no—
226Q8×D13—48no—
227C2×C4×D13—22no—
228C2×C4×D13—22no—
229C2×C4×D13—24no—
230C2×C4×D13—44no—
231C2×C4×D13C2×D412yes—
232C2×C4×D13C2412yes—
233C2×Dic26—22no—
234C2×Dic26—22no—
235C2×Dic26—22no—
236C2×Dic26—22no—
237C2×Dic26—21no—
238C2×Dic26—21no—
239C2×Dic26—24no—
240C2×Dic26—44no—
241C2×Dic26C2412yes—
242C2×Dic26C2412yes—
243C2×C8×C13—22no—
244C2×C8×C13—22no—
245C2×C8×C13—44no—
246C2×C8×C13C2412yes—
247C2×C8×C13C2412yes—
248C13×C4⋊C4—21no—
249C13×C4⋊C4—24no—
250C13×C4⋊C4—21no—
251C13×C4⋊C4C2412yes—
252C13×C4⋊C4C2412yes—
253C22⋊Dic13—24no—
254C22⋊Dic13—24no—
255C22⋊Dic13C2×D414yes—
256#6107—28no—
257#6107—44no—
258#6103—24no—
259#6103—24no—
260#6103—24no—
261#6103C2×D414yes—
262C4⋊Dic13—21no—
263C4⋊Dic13—21no—
264C4⋊Dic13—24no—
265C4⋊Dic13—24no—
266C4⋊Dic13—24no—
267C4⋊Dic13C2412yes—
268C4⋊Dic13C2412yes—
269#6101—24no—
270#6101—24no—
271#6101—24no—
272#6101—24no—
273#6101—24no—
274#6101—24no—
275#6101—24no—
276#6101C2×D414yes—
277C4×Dic13—24no—
278C4×Dic13—24no—
279C4×Dic13—24no—
280C4×Dic13C2×D412yes—
281C4×Dic13C2412yes—
282C2×#1055—22no—
283C2×#1055—22no—
284C2×#1055C2412yes—
285C2×#1055C2412yes—
286Dic52—44no—
287#6094—44no—
288C2×#552—131no—
289C2×D4×Q8—131no—
290#3312—1316no—
291C2×#491—131no—
292C2×#485—131no—
293C2×#483—131no—
294C2×#479—131no—
295C2×#470—131no—
296C2×#467—131no—
297C2×#462—131no—
298C2×#451—131no—
299C2×#451—131no—
300C2×#441—131no—
301C2×#435—131no—
302C2×#419—131no—
303C22×#103D1311yescharacteristic, complemented
304C23×C13—22no—
305C23×C13—22no—
306C23×C13#13714yes—
307C23×C13C22×D412yes—
308C23×C13C22×D411yescharacteristic
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13C22×D412yes—
313Q8×C13—24no—
314Q8×C13—22no—
315Q8×C13—22no—
316Q8×C13—22no—
317Q8×C13—48no—
318Q8×C13—42no—
319Q8×C13C2×#4114yes—
320C2×C4×C13—24no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—24no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—48no—
330C2×C4×C13—42no—
331C2×C4×C13—48no—
332C2×C4×C13—42no—
333C2×C4×C13—42no—
334C2×C4×C13C22×D412yes—
335C2×C4×C13C22×D411yescharacteristic
336C2×C4×C13C2×#4112yes—
337C2×C4×C13H(5,𝔽2)12yes—
338C2×C4×C13C2511yescharacteristic
339C22⋊D13—28no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—42no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13—42no—
351C2×Dic13C22×D412yes—
352C2×Dic13C22×D412yes—
353C2×Dic13C22×D412yes—
354C4×D13—24no—
355C4×D13—22no—
356C4×D13—22no—
357C4×D13—48no—
358Dic26—22no—
359Dic26—22no—
360Dic26—22no—
361Dic26—22no—
362Dic26—48no—
363Dic26—42no—
364Dic26—42no—
365C8×C13—22no—
366C8×C13—22no—
367#1055—22no—
368#1055—22no—
369C23×Q8—131no—
370C23×Q8C2×D1311yescharacteristic
371C22×Q16—131no—
372C22×Q16—131no—
373C22×Q16—131no—
374C22×M16—131no—
375C23×C8C2×D1311yescharacteristic
376#552—138no—
377#552—264no—
378D4×Q8—138no—
379D4×Q8—264no—
380C2×C4⋊Q8—131no—
381C2×C4⋊Q8—261no—
382C2×#126—261no—
383C2×#125—131no—
384C2×#125—261no—
385C2×#123—261no—
386C2×C22⋊Q8—131no—
387C2×C22⋊Q8—131no—
388C2×C22⋊Q8—131no—
389C2×C22⋊Q8—131no—
390C2×C22⋊Q8—261no—
391C2×C22⋊Q8—261no—
392C2×C4×Q8—131no—
393C2×C4×Q8—131no—
394C2×C4×D4—131no—
395C2×C4×D4—261no—
396C2×#117—131no—
397C2×#117—261no—
398C22×C4⋊C4C2×D1311yescharacteristic
399#491—138no—
400#485—138no—
401#483—138no—
402#479—138no—
403#470—138no—
404#467—138no—
405#462—138no—
406#451—138no—
407#451—138no—
408#441—138no—
409#435—138no—
410C2×#107—131no—
411C2×#106—131no—
412C2×#106—131no—
413C2×C4⋊C8—131no—
414#419—138no—
415C2×#103—131no—
416C2×#103—131no—
417C2×#103—131no—
418C2×#103—131no—
419C2×#103—131no—
420C2×#103—131no—
421C2×#103C2×D1311yescharacteristic
422C2×#103C2×D1311yescharacteristic
423C2×#103C2×D1311yescharacteristic
424C2×#103C2×D1311yescharacteristic
425C2×#103C2×D1318yescomplemented
426C2×C22⋊C8—131no—
427C2×C22⋊C8—131no—
428C2×#97—131no—
429C22×C13—22no—
430C22×C13—28no—
431C22×C13—22no—
432C22×C13#54612yes—
433C22×C13C2×#13714yes—
434C22×C13C2×#13712yes—
435C22×C13#57812yes—
436C22×C13C23×D411yescharacteristic
437C2×D13—22no—
438C2×D13—22no—
439C2×D13—22no—
440C2×D13—44no—
441C4×C13—24no—
442C4×C13—22no—
443C4×C13—42no—
444C4×C13—42no—
445C4×C13—42no—
446C4×C13#54612yes—
447C4×C13C22×#4111yescharacteristic
448C4×C13C2×H(5,𝔽2)11yescharacteristic
449Dic13—22no—
450Dic13—22no—
451Dic13—22no—
452Dic13—42no—
453Dic13—42no—
454Dic13—42no—
455Dic13—42no—
456C22×Q8—21no—
457C22×Q8—22no—
458C22×Q8—24no—
459C22×Q8—42no—
460C22×Q8—134no—
461C22×Q8—131no—
462C22×Q8—131no—
463C22×Q8—261no—
464C22×Q8—262no—
465C22×Q8—264no—
466C22×Q8—522no—
467C22×Q8C22×D1311yescharacteristic
468C22×Q8C22×D1314yes—
469C22×Q8C22×D1311yescharacteristic
470C22×D4—131no—
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—131no—
474C23×C4—261no—
475C23×C4C22×D1311yescharacteristic
476C2×Q16—134no—
477C2×Q16—134no—
478C2×Q16—134no—
479C2×Q16—264no—
480C2×Q16—522no—
481C2×Q16—522no—
482C2×M16—134no—
483C2×M16—522no—
484C22×C8—42no—
485C22×C8—131no—
486C22×C8—131no—
487C22×C8C22×D1311yescharacteristic
488C22×C8C22×D1311yescharacteristic
489C22×C8C22×D1314yes—
490C4⋊Q8—134no—
491C4⋊Q8—262no—
492C4⋊Q8—268no—
493#126—268no—
494#125—134no—
495#125—262no—
496#125—268no—
497#123—268no—
498C22⋊Q8—134no—
499C22⋊Q8—134no—
500C22⋊Q8—134no—
501C22⋊Q8—134no—
502C22⋊Q8—268no—
503C22⋊Q8—268no—
504C22⋊Q8—262no—
505C22⋊Q8—262no—
506C22⋊Q8—262no—
507C22⋊Q8—262no—
508C4×Q8—134no—
509C4×Q8—134no—
510C4×Q8—262no—
511C4×Q8—262no—
512C4×D4—134no—
513C4×D4—134no—
514C4×D4—268no—
515#117—134no—
516#117—268no—
517#117—262no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—131no—
521C2×C4⋊C4—131no—
522C2×C4⋊C4—131no—
523C2×C4⋊C4—261no—
524C2×C4⋊C4—261no—
525C2×C4⋊C4—261no—
526C2×C4⋊C4—261no—
527C2×C4⋊C4—261no—
528C2×C4⋊C4—261no—
529C2×C4⋊C4—261no—
530C2×C4⋊C4—261no—
531C2×C4⋊C4—261no—
532C2×C4⋊C4—261no—
533C2×C4⋊C4C22×D1311yescharacteristic
534C2×C4⋊C4C22×D1311yescharacteristic
535C2×C4⋊C4C22×D1314yes—
536C2×C22⋊C4—131no—
537C2×C22⋊C4—131no—
538C2×C22⋊C4—261no—
539C2×C22⋊C4—261no—
540C2×C22⋊C4—261no—
541C2×C22⋊C4—261no—
542C2×C22⋊C4—261no—
543C2×C42—131no—
544C2×C42—261no—
545C2×C42—261no—
546C2×C42—261no—
547#107—134no—
548#106—134no—
549#106—134no—
550C4⋊C8—134no—
551#103—134no—
552#103—134no—
553#103—134no—
554#103—134no—
555#103—134no—
556#103—134no—
557#103C22×D1314yes—
558#103C22×D1314yes—
559#103C22×D1314yes—
560#103C22×D1314yes—
561C22⋊C8—134no—
562C22⋊C8—134no—
563#97—134no—
564C2×C13—24no—
565C2×C13#331214yescomplemented
566C2×C13C2×#54611yescharacteristic
567C2×C13C22×#13711yescharacteristic
568C2×C13C2×#57811yescharacteristic
569D13—42no—
570C24—131no—
571C24D4×D1311yescharacteristic
572C2×Q8—21no—
573C2×Q8—24no—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—28no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8—48no—
582C2×Q8—132no—
583C2×Q8—132no—
584C2×Q8—264no—
585C2×Q8—261no—
586C2×Q8—261no—
587C2×Q8—268no—
588C2×Q8—262no—
589C2×Q8—262no—
590C2×Q8—262no—
591C2×Q8—262no—
592C2×Q8—524no—
593C2×Q8—524no—
594C2×Q8—528no—
595C2×Q8#612714yes—
596C2×Q8C23×D1312yes—
597C2×Q8C23×D1312yes—
598C2×D4—134no—
599C2×D4—264no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—131no—
611C22×C4—131no—
612C22×C4—131no—
613C22×C4—132no—
614C22×C4—132no—
615C22×C4—264no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—524no—
623C22×C4D4×D1312yes—
624C22×C4D4×D1311yescharacteristic
625C22×C4C23×D1312yes—
626C22×C4C23×D1311yescharacteristic
627Q16—268no—
628Q16—524no—
629Q16—524no—
630M16—524no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—44no—
634C2×C8—132no—
635C2×C8—132no—
636C2×C8—262no—
637C2×C8—262no—
638C2×C8C23×D1312yes—
639C2×C8C23×D1312yes—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—24no—
643C4⋊C4—134no—
644C4⋊C4—132no—
645C4⋊C4—132no—
646C4⋊C4—264no—
647C4⋊C4—264no—
648C4⋊C4—264no—
649C4⋊C4—264no—
650C4⋊C4—264no—
651C4⋊C4—264no—
652C4⋊C4—264no—
653C4⋊C4—264no—
654C4⋊C4—261no—
655C4⋊C4—261no—
656C4⋊C4—264no—
657C4⋊C4—264no—
658C4⋊C4C23×D1312yes—
659C4⋊C4C23×D1312yes—
660C22⋊C4—134no—
661C22⋊C4—134no—
662C22⋊C4—264no—
663C22⋊C4—264no—
664C22⋊C4—264no—
665C22⋊C4—264no—
666C22⋊C4—264no—
667C42—132no—
668C42—132no—
669C42—264no—
670C42—264no—
671C42—264no—
672C13C2×#331211yescharacteristic, complemented, Sylow
673C23—22no—
674C23—22no—
675C23—132no—
676C23—262no—
677C23—262no—
678C23—262no—
679C23#8816914yes—
680C23C2×D4×D1312yes—
681C23C2×D4×D1311yescharacteristic
682Q8—24no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—48no—
687Q8—42no—
688Q8—262no—
689Q8—262no—
690Q8—262no—
691Q8—262no—
692Q8—528no—
693Q8—522no—
694Q8—522no—
695Q8C2×#612714yes—
696D4—268no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—48no—
707C2×C4—42no—
708C2×C4—48no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—132no—
712C2×C4—132no—
713C2×C4—132no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—264no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—528no—
725C2×C4—522no—
726C2×C4—522no—
727C2×C4—522no—
728C2×C4—522no—
729C2×C4C2×#612712yes—
730C2×C4C2×D4×D1312yes—
731C2×C4C2×D4×D1311yescharacteristic
732C2×C4#8825112yes—
733C2×C4C24×D1311yescharacteristic
734C8—22no—
735C8—22no—
736C8—262no—
737C8—262no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—262no—
742C22—262no—
743C22—262no—
744C22—524no—
745C22#1171919512yes—
746C22C2×#8816914yes—
747C22C2×#8816912yes—
748C22#1171947112yes—
749C22C22×D4×D1311yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—262no—
756C4—262no—
757C4—262no—
758C4—522no—
759C4—522no—
760C4—522no—
761C4—522no—
762C4#1171919512yes—
763C4C22×#612711yescharacteristic
764C4C2×#8825111yescharacteristic
765C2—24no—
766C2—522no—
767C2#1312688314yesdirect product factor
768C2C2×#1171919511yescharacteristic
769C2C22×#8816911yescharacteristic
770C2C2×#1171947111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#103C2
socleC23×C13C22×D4
prime radicalC22×C22⋊D13D4
hypercenterC22×#103D13
hypocenterC13C2×#3312
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. #13126883C2direct (N × H)
4. C2×#11718458C2semidirect
5. C2×#11718475C2semidirect
6. C2×#11718632C2semidirect
7. C2×#11718457C2semidirect
8. C2×#11718477C2semidirect
9. C2×#11718777C2semidirect
10. C2×#11718454C2semidirect
11. C2×#11718469C2semidirect
12. C2×#11718889C2semidirect
13. C2×#11718450C2semidirect
15. C2×#11718463C2semidirect
16. C22×C13×#103C2semidirect
51. C2×C13×#103C22semidirect
52. #11718889C22semidirect
56. #11718777C22semidirect
64. #11718632C22semidirect
69. #11718477C22semidirect
70. #11718475C22semidirect
71. #11718469C22semidirect
72. #11718463C22semidirect
73. #11718458C22semidirect
74. #11718457C22semidirect
75. #11718454C22semidirect
76. #11718450C22semidirect
303. C22×#103D13semidirect
425. C2×#103C2×D13semidirect
565. C2×C13#3312semidirect
672. C13C2×#3312semidirect
767. C2#13126883direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192182
C2×Q8×C22⋊D132
#131268832
C2×#117184582
C2×#117184752
C2×#117186322
C2×#117184572
C2×#117184772
C2×#117187772
C2×#117184542
C2×#117184692
C2×#117188892
C2×#117184502
C2×#117187722
C2×#117184632
C22×C13×#1032
C2×#331213