Finite Group Databasebeta

← C2×#13127278 #16741452

Subgroups — C2×#13127278 #16741452

Order 3328.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719246C211yesmaximal, characteristic, complemented
2C2×#11719260C211yesmaximal, characteristic
3#13127278C2116yesmaximal, direct product factor
4C2×#11718363C211yesmaximal, characteristic, complemented
5C2×#11718383C211yesmaximal, characteristic, complemented
6C2×#11718398C211yesmaximal, characteristic, complemented
7C2×#11718382C211yesmaximal, characteristic, complemented
8C2×#11718397C211yesmaximal, characteristic, complemented
9C2×#11718511C211yesmaximal, characteristic, complemented
10C2×#11718508C211yesmaximal, characteristic, complemented
11C2×#11718795C211yesmaximal, characteristic, complemented
12C2×#11718775C211yesmaximal, characteristic, complemented
13C2×#11718371C211yesmaximal, characteristic, complemented
14C2×#11718782C211yesmaximal, characteristic, complemented
15C22×#88058C211yesmaximal, characteristic, complemented
16C2×C13×#435C211yesmaximal, characteristic, complemented
17C22×#6129—21no—
18C22×C13×M16C2211yescharacteristic
19C23×C8×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C2×#88189—21no—
22C2×#88184C2211yescharacteristic
23C2×#88184C2211yescharacteristic
24C2×#88180C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C2×#88178C2211yescharacteristic
29C2×#88178C2211yescharacteristic
30C22×#6095C2211yescharacteristic
31#11719260—24no—
32#11719260C2218yes—
33#11719246—24no—
34#11719246C2218yescomplemented
35C2×#88151—21no—
36C2×#88143—21no—
37C2×#88140—21no—
38C2×#88140—21no—
39C2×#88133—21no—
40C2×#88131—21no—
41C2×C4×D52C2211yescharacteristic
42C2×#88124C2211yescharacteristic
43C2×#88123C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C13×#435C2218yescomplemented
46C2×C13×C4⋊C8C2211yescharacteristic
47C2×C13×C22⋊C8C2211yescharacteristic
48C2×C13×C22⋊C8C2211yescharacteristic
49C2×C13×#97C2211yescharacteristic
50#11718795C2218yescomplemented
51#11718782C2218yescomplemented
52#11718775C2218yescomplemented
53C2×#88061C2211yescharacteristic
54C2×#88061C2211yescharacteristic
55C2×#88061C2211yescharacteristic
56C2×#88058C2211yescharacteristic
57C2×#88058C2211yescharacteristic
58C2×#88058C2211yescharacteristic
59C2×#88058C2211yescharacteristic
60C2×#88058C2211yescharacteristic
61C2×#88058C2211yescharacteristic
62C2×#88058C2218yescomplemented
63C2×#88057C2211yescharacteristic
64C2×#88057C2211yescharacteristic
65C2×#88057C2211yescharacteristic
66C2×#88056C2211yescharacteristic
67C2×#88056C2211yescharacteristic
68C2×#88056C2211yescharacteristic
69#11718511C2218yescomplemented
70#11718508C2218yescomplemented
71#11718398C2218yescomplemented
72#11718397C2218yescomplemented
73#11718383C2218yescomplemented
74#11718382C2218yescomplemented
75#11718371C2218yescomplemented
76#11718363C2218yescomplemented
77C22×D4×C13D411yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13—21no—
81C22×C22⋊D13—21no—
82C23×Dic13—21no—
83C23×Dic13—21no—
84C23×Dic13—21no—
85C2×#6129—28no—
86C2×#6129—48no—
87C22×D52C2311yescharacteristic
88C22×C4×D13—21no—
89C22×Dic26—21no—
90C22×Dic26C2311yescharacteristic
91C2×C13×M16—24no—
92C2×C13×M16C2314yes—
93C22×C8×C13—24no—
94C22×C8×C13C2311yescharacteristic
95C22×C8×C13C2311yescharacteristic
96C22×C8×C13C2311yescharacteristic
97C22×C8×C13C2314yes—
98C22×C8×C13C2311yescharacteristic
99C4×D4×C13D414yes—
100C4×D4×C13C2314yes—
101C2×C13×C4⋊C4D411yescharacteristic
102C2×C13×C22⋊C4D411yescharacteristic
103C2×C13×C22⋊C4D411yescharacteristic
104C2×C42×C13C2311yescharacteristic
105C2×C22⋊Dic13—21no—
106C2×C22⋊Dic13—21no—
107C2×C22⋊Dic13—21no—
108#88189—28no—
109#88184—22no—
110#88184—22no—
111#88184C2314yes—
112#88184C2314yes—
113C2×#6103—21no—
114C2×#6103—21no—
115C2×#6103—21no—
116#88180—22no—
117#88180C2314yes—
118C2×C4⋊Dic13—21no—
119C2×C4⋊Dic13—21no—
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13—21no—
122C2×C4⋊Dic13—22no—
123C2×C4⋊Dic13—22no—
124C2×C4⋊Dic13—22no—
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4⋊Dic13C2311yescharacteristic
127C2×C4⋊Dic13C2311yescharacteristic
128C2×C4⋊Dic13C2311yescharacteristic
129C2×C4⋊Dic13C2311yescharacteristic
130C2×C4⋊Dic13C2311yescharacteristic
131C2×C4⋊Dic13C2314yes—
132C2×C4⋊Dic13C2314yes—
133C2×C4⋊Dic13C2314yes—
134#88178—22no—
135#88178—22no—
136#88178C2314yes—
137#88178C2314yes—
138C2×#6101—21no—
139C2×#6101—21no—
140C2×#6101—21no—
141C2×#6101—21no—
142C2×#6101—21no—
143C2×C4×Dic13—21no—
144C2×C4×Dic13—21no—
145C2×#6095—24no—
146C2×#6095C2314yes—
147#88151—28no—
148#88143—28no—
149#88140—28no—
150#88140—28no—
151#88133—28no—
152#88131—28no—
153C4×D52—22no—
154C4×D52C2314yes—
155#88124—22no—
156#88124C2314yes—
157#88123—22no—
158#88123C2314yes—
159C4×Dic26—22no—
160C4×Dic26C2314yes—
161C13×C4⋊C8C2314yes—
162C13×C22⋊C8C2314yes—
163C13×C22⋊C8C2314yes—
164C13×#97C2314yes—
165#88061C2314yes—
166#88061C2314yes—
167#88061C2314yes—
168#88058C2314yes—
169#88058C2314yes—
170#88058C2314yes—
171#88058C2314yes—
172#88058C2314yes—
173#88058C2314yes—
174#88057C2314yes—
175#88057C2314yes—
176#88057C2314yes—
177#88056C2314yes—
178#88056C2314yes—
179#88056C2314yes—
180C2×#3343—131nomaximal, Sylow
181C24×C13C2×D411yescharacteristic
182C24×C13C2×D411yescharacteristic
183C23×D13—21no—
184C2×D4×C13—24no—
185C2×D4×C13C2×D414yes—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13C2×D411yescharacteristic
194C22×C4×C13C2×D412yes—
195C22×C4×C13C2×D412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2411yescharacteristic
199C2×C22⋊D13—24no—
200C2×C22⋊D13—24no—
201C2×C22⋊D13—44no—
202C2×C22⋊D13—44no—
203C22×Dic13—24no—
204C22×Dic13—24no—
205C22×Dic13—24no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—44no—
214C22×Dic13—44no—
215C22×Dic13—44no—
216#6129—432no—
217C2×D52—22no—
218C2×D52—22no—
219C2×D52—21no—
220C2×D52C2412yes—
221C2×C4×D13—24no—
222C2×C4×D13—44no—
223C2×Dic26—22no—
224C2×Dic26—22no—
225C2×Dic26—21no—
226C2×Dic26—24no—
227C2×Dic26—44no—
228C2×Dic26C2412yes—
229C13×M16—28no—
230C2×C8×C13—22no—
231C2×C8×C13—22no—
232C2×C8×C13—22no—
233C2×C8×C13—28no—
234C2×C8×C13#4114yescomplemented
235C2×C8×C13C2412yes—
236C2×C8×C13C2412yes—
237C2×C8×C13C2412yes—
238C2×C8×C13C2412yes—
239C13×C4⋊C4C2×D414yes—
240C13×C22⋊C4C2×D414yes—
241C13×C22⋊C4C2×D414yes—
242C42×C13C2×D412yes—
243C42×C13C2412yes—
244C22⋊Dic13—24no—
245C22⋊Dic13—24no—
246C22⋊Dic13—24no—
247#6103—24no—
248#6103—24no—
249#6103—24no—
250C4⋊Dic13—21no—
251C4⋊Dic13—21no—
252C4⋊Dic13—21no—
253C4⋊Dic13—24no—
254C4⋊Dic13—21no—
255C4⋊Dic13—21no—
256C4⋊Dic13—21no—
257C4⋊Dic13—24no—
258C4⋊Dic13—24no—
259C4⋊Dic13—24no—
260C4⋊Dic13C2412yes—
261C4⋊Dic13C2412yes—
262C4⋊Dic13C2412yes—
263C4⋊Dic13C2412yes—
264C4⋊Dic13C2412yes—
265C4⋊Dic13C2412yes—
266#6101—24no—
267#6101—24no—
268#6101—24no—
269#6101—24no—
270#6101—24no—
271C4×Dic13—24no—
272C4×Dic13—24no—
273#6095—28no—
274C2×#552—131no—
275C2×#547—131no—
276#3343—1316no—
277C2×#501—131no—
278C2×#484—131no—
279C2×#482—131no—
280C2×#483—131no—
281C2×#480—131no—
282C2×#477—131no—
283C2×#478—131no—
284C2×#468—131no—
285C2×#465—131no—
286C2×#440—131no—
287C2×#435D1311yescharacteristic, complemented
288C2×#428—131no—
289C22×#107—131no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13AGL(1,ℤ/8)14yes—
296C23×C13C22×D412yes—
297C23×C13C22×D412yes—
298C23×C13C22×D411yescharacteristic
299C22×D13—22no—
300C22×D13—42no—
301C22×D13—42no—
302C22×D13—42no—
303D4×C13—28no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—24no—
309C2×C4×C13—24no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13C22×D412yes—
315C2×C4×C13C22×D412yes—
316C2×C4×C13C22×D412yes—
317C2×C4×C13C22×D412yes—
318C2×C4×C13C22×D411yescharacteristic
319C2×C4×C13C2×#4112yes—
320C2×C4×C132−1+412yes—
321C2×C4×C13C2511yescharacteristic
322C22⋊D13—48no—
323C22⋊D13—48no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—48no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—48no—
337C2×Dic13—48no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341D52—22no—
342D52—22no—
343D52—42no—
344C4×D13—48no—
345Dic26—22no—
346Dic26—22no—
347Dic26—48no—
348Dic26—42no—
349C8×C13—22no—
350C8×C13—22no—
351C8×C13—22no—
352C8×C13C2×#4114yescomplemented
353C22×#41—261no—
354C22×SD16—131no—
355C22×M16C2×D1311yescharacteristic
356C23×C8C2×D1311yescharacteristic
357#552—138no—
358#552—264no—
359#547—138no—
360#547—264no—
361C2×C4⋊Q8—131no—
362C2×#126—261no—
363C2×#125—131no—
364C2×#125—261no—
365C2×#123—261no—
366C2×#123—261no—
367C2×#123—261no—
368C2×C22⋊Q8—131no—
369C2×C22⋊Q8—131no—
370C2×C22⋊Q8—261no—
371C2×#121—131no—
372C2×#121—131no—
373C2×C4×Q8—131no—
374C2×C4×D4—131no—
375C2×C4×D4C2×D1311yescharacteristic
376C2×#117—131no—
377C2×#117—261no—
378C22×C4⋊C4—131no—
379C22×C4⋊C4—131no—
380C22×C4⋊C4—131no—
381#501—138no—
382#484—138no—
383#483—138no—
384#482—138no—
385#480—138no—
386#478—138no—
387#477—138no—
388#468—138no—
389#465—138no—
390#440—138no—
391#435C2×D1318yescomplemented
392#428—138no—
393C2×#107—131no—
394C2×#107—131no—
395C2×#107—131no—
396C2×#107—131no—
397C2×#107—138no—
398C2×#107—131no—
399C2×#107—131no—
400C2×#106—131no—
401C2×#106—131no—
402C2×#106—131no—
403C2×C4⋊C8C2×D1311yescharacteristic
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#102—131no—
408C2×#102—131no—
409C2×#102—131no—
410C2×C22⋊C8C2×D1311yescharacteristic
411C2×C22⋊C8C2×D1311yescharacteristic
412C2×#97C2×D1311yescharacteristic
413C22×C13—28no—
414C22×C13—22no—
415C22×C13—22no—
416C22×C13—22no—
417C22×C13—22no—
418C22×C13—22no—
419C22×C13—44no—
420C22×C13#54712yes—
421C22×C13C2×AGL(1,ℤ/8)14yes—
422C22×C13C2×AGL(1,ℤ/8)12yes—
423C22×C13#57812yes—
424C22×C13C23×D411yescharacteristic
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—42no—
428C2×D13—84no—
429C4×C13—22no—
430C4×C13—22no—
431C4×C13—22no—
432C4×C13—22no—
433C4×C13#54712yes—
434C4×C13C22×#4111yescharacteristic
435C4×C13C2×2−1+411yescharacteristic
436Dic13—42no—
437Dic13—42no—
438Dic13—42no—
439Dic13—42no—
440Dic13—42no—
441Dic13—42no—
442Dic13—42no—
443C2×#41—268no—
444C2×#41—528no—
445C22×Q8—131no—
446C22×Q8—261no—
447C22×D4—131no—
448C22×D4—261no—
449C22×D4—261no—
450C22×D4D5211yescharacteristic
451C23×C4—261no—
452C23×C4—261no—
453C23×C4—261no—
454C23×C4—261no—
455C23×C4C22×D1311yescharacteristic
456C23×C4C22×D1311yescharacteristic
457C2×SD16—134no—
458C2×SD16—264no—
459C2×M16—24no—
460C2×M16C22×D1314yes—
461C22×C8—24no—
462C22×C8C22×D1311yescharacteristic
463C22×C8C22×D1314yes—
464C22×C8C22×D1311yescharacteristic
465C22×C8C22×D1311yescharacteristic
466C22×C8C22×D1311yescharacteristic
467C4⋊Q8—134no—
468C4⋊Q8—262no—
469#126—268no—
470#125—134no—
471#125—268no—
472#125—262no—
473#123—268no—
474#123—268no—
475#123—268no—
476C22⋊Q8—134no—
477C22⋊Q8—134no—
478C22⋊Q8—262no—
479C22⋊Q8—262no—
480C22⋊Q8—268no—
481#121—134no—
482#121—134no—
483#121—262no—
484#121—262no—
485C4×Q8—134no—
486C4×Q8—262no—
487C4×D4—134no—
488C4×D4—262no—
489C4×D4D5214yes—
490C4×D4C22×D1314yes—
491#117—134no—
492#117—262no—
493#117—268no—
494C2×C4⋊C4—131no—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—131no—
497C2×C4⋊C4—131no—
498C2×C4⋊C4—131no—
499C2×C4⋊C4—134no—
500C2×C4⋊C4—134no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—262no—
507C2×C4⋊C4—262no—
508C2×C4⋊C4—262no—
509C2×C4⋊C4—261no—
510C2×C4⋊C4—261no—
511C2×C4⋊C4—261no—
512C2×C4⋊C4—261no—
513C2×C4⋊C4—261no—
514C2×C4⋊C4—261no—
515C2×C4⋊C4D5211yescharacteristic
516C2×C22⋊C4—261no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C22⋊C4D5211yescharacteristic
523C2×C22⋊C4D5211yescharacteristic
524C2×C42—261no—
525C2×C42—261no—
526C2×C42C22×D1311yescharacteristic
527#107—134no—
528#107—134no—
529#107—134no—
530#107—134no—
531#107—134no—
532#107—134no—
533#106—134no—
534#106—134no—
535#106—134no—
536C4⋊C8C22×D1314yes—
537#103—134no—
538#103—134no—
539#103—134no—
540#102—134no—
541#102—134no—
542#102—134no—
543C22⋊C8C22×D1314yes—
544C22⋊C8C22×D1314yes—
545#97C22×D1314yes—
546C2×C13—24no—
547C2×C13—42no—
548C2×C13#334314yescomplemented
549C2×C13C2×#54711yescharacteristic
550C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
551C2×C13C2×#57811yescharacteristic
552D13—82no—
553C24—261no—
554C24C2×D5211yescharacteristic
555C24C2×D5211yescharacteristic
556#41—5232no—
557C2×Q8—132no—
558C2×Q8—261no—
559C2×Q8—264no—
560C2×Q8—262no—
561C2×Q8—262no—
562C2×Q8—524no—
563C2×D4—24no—
564C2×D4—132no—
565C2×D4—264no—
566C2×D4—264no—
567C2×D4—261no—
568C2×D4—262no—
569C2×D4—262no—
570C2×D4—524no—
571C2×D4—524no—
572C2×D4C2×D5214yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—264no—
578C22×C4—264no—
579C22×C4—264no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—264no—
588C22×C4—524no—
589C22×C4—524no—
590C22×C4—524no—
591C22×C4—524no—
592C22×C4C2×D5212yes—
593C22×C4C2×D5212yes—
594C22×C4C2×D5211yescharacteristic
595C22×C4C2×D5211yescharacteristic
596C22×C4C2×D5211yescharacteristic
597C22×C4C2×D5211yescharacteristic
598C22×C4C23×D1312yes—
599C22×C4C23×D1312yes—
600C22×C4C23×D1311yescharacteristic
601SD16—268no—
602M16—28no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—28no—
607C2×C8#612914yescomplemented
608C2×C8C23×D1312yes—
609C2×C8C23×D1312yes—
610C2×C8C23×D1312yes—
611C2×C8C23×D1312yes—
612C4⋊C4—132no—
613C4⋊C4—132no—
614C4⋊C4—132no—
615C4⋊C4—132no—
616C4⋊C4—132no—
617C4⋊C4—132no—
618C4⋊C4—261no—
619C4⋊C4—261no—
620C4⋊C4—261no—
621C4⋊C4—261no—
622C4⋊C4—264no—
623C4⋊C4—264no—
624C4⋊C4—261no—
625C4⋊C4—264no—
626C4⋊C4—261no—
627C4⋊C4—264no—
628C4⋊C4—264no—
629C4⋊C4—264no—
630C4⋊C4—264no—
631C4⋊C4—264no—
632C4⋊C4—264no—
633C4⋊C4C2×D5214yes—
634C22⋊C4—264no—
635C22⋊C4—264no—
636C22⋊C4—264no—
637C22⋊C4—264no—
638C22⋊C4—264no—
639C22⋊C4—264no—
640C22⋊C4C2×D5214yes—
641C22⋊C4C2×D5214yes—
642C42—264no—
643C42—264no—
644C42C2×D5212yes—
645C42C23×D1312yes—
646C13C2×#334311yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—262no—
653C23—522no—
654C23—522no—
655C23—522no—
656C23#8816214yes—
657C23C22×D5212yes—
658C23C22×D5212yes—
659C23C22×D5211yescharacteristic
660Q8—262no—
661Q8—262no—
662Q8—528no—
663Q8—522no—
664D4—28no—
665D4—262no—
666D4—262no—
667D4—528no—
668D4—528no—
669D4—522no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—528no—
688C2×C4—528no—
689C2×C4—528no—
690C2×C4—522no—
691C2×C4—522no—
692C2×C4—522no—
693C2×C4—522no—
694C2×C4—522no—
695C2×C4—528no—
696C2×C4—522no—
697C2×C4—522no—
698C2×C4C22×D5212yes—
699C2×C4C22×D5212yes—
700C2×C4C22×D5212yes—
701C2×C4C22×D5212yes—
702C2×C4C22×D5211yescharacteristic
703C2×C4C2×#612912yes—
704C2×C4#8825712yes—
705C2×C4C24×D1311yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8C2×#612914yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—522no—
718C22—522no—
719C22—522no—
720C22—1044no—
721C22#1171926012yes—
722C22C2×#8816214yes—
723C22C2×#8816212yes—
724C22#1171945812yes—
725C22C23×D5211yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—522no—
731C4—522no—
732C4—522no—
733C4—522no—
734C4—522no—
735C4—522no—
736C4—522no—
737C4#1171926012yes—
738C4C22×#612911yescharacteristic
739C4C2×#8825711yescharacteristic
740C2—24no—
741C2—42no—
742C2—1042no—
743C2#1312727814yesdirect product factor
744C2C2×#1171926011yescharacteristic
745C2C22×#8816211yescharacteristic
746C2C2×#1171945811yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#435C2
socleC23×C13C22×D4
prime radicalC2×#11719260C2
hypercenterC2×#435D13
hypocenterC13C2×#3343
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#11719246C2semidirect
3. #13127278C2direct (N × H)
4. C2×#11718363C2semidirect
5. C2×#11718383C2semidirect
6. C2×#11718398C2semidirect
7. C2×#11718382C2semidirect
8. C2×#11718397C2semidirect
9. C2×#11718511C2semidirect
10. C2×#11718508C2semidirect
11. C2×#11718795C2semidirect
12. C2×#11718775C2semidirect
13. C2×#11718371C2semidirect
14. C2×#11718782C2semidirect
15. C22×#88058C2semidirect
16. C2×C13×#435C2semidirect
34. #11719246C22semidirect
45. C13×#435C22semidirect
50. #11718795C22semidirect
51. #11718782C22semidirect
52. #11718775C22semidirect
62. C2×#88058C22semidirect
69. #11718511C22semidirect
70. #11718508C22semidirect
71. #11718398C22semidirect
72. #11718397C22semidirect
73. #11718383C22semidirect
74. #11718382C22semidirect
75. #11718371C22semidirect
76. #11718363C22semidirect
234. C2×C8×C13#41semidirect
287. C2×#435D13semidirect
352. C8×C13C2×#41semidirect
391. #435C2×D13semidirect
548. C2×C13#3343semidirect
607. C2×C8#6129semidirect
646. C13C2×#3343semidirect
709. C8C2×#6129semidirect
743. C2#13127278direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192462
C2×#117192602
#131272782
C2×#117183632
C2×#117183832
C2×#117183982
C2×#117183822
C2×#117183972
C2×#117185112
C2×#117185082
C2×#117187952
C2×#117187752
C2×#117183712
C2×#117187822
C22×#880582
C2×C13×#4352
C2×#334313