Finite Group Databasebeta

← C2×#21455947 #30548214

Subgroups — C2×#21455947 #30548214

Order 15616.

2118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic
2C2×C4×Q8×D61C211yesmaximal, characteristic
3#21455947C2116yesmaximal, direct product factor
4C2×#16840094C211yesmaximal, characteristic
5C2×#16840091C211yesmaximal, characteristic
6C2×#16840046C211yesmaximal, characteristic, complemented
7C2×#16840045C211yesmaximal, characteristic, complemented
8C2×#16839971C211yesmaximal, characteristic, complemented
9C2×#16839970C211yesmaximal, characteristic, complemented
10C2×#16839919C211yesmaximal, characteristic
11C2×#16839916C211yesmaximal, characteristic
12C2×#16839870C211yesmaximal, characteristic, complemented
13C2×#16839867C211yesmaximal, characteristic, complemented
14C2×#16839867C211yesmaximal, characteristic, complemented
15C2×#16839817C211yesmaximal, characteristic
16C2×C61×#441C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21#16840316—24no—
22#16840316C2218yes—
23C2×#14519776C2211yescharacteristic
24C2×#14519775C2211yescharacteristic
25C2×#14519767—21no—
26C2×#14519757C2211yescharacteristic
27C2×#14519755—21no—
28C2×#14519753C2211yescharacteristic
29C2×Q8×Dic61C2211yescharacteristic
30C2×C4×Dic122—21no—
31C2×C4×Dic122—21no—
32C2×C4×Dic122C2211yescharacteristic
33C2×C4×Dic122C2211yescharacteristic
34C2×#14519742—21no—
35C2×#14519742C2211yescharacteristic
36C4×Q8×D61—24no—
37C4×Q8×D61C2218yes—
38C2×#14519734—21no—
39C2×C4⋊C4×D61—21no—
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C42×D61—21no—
42C2×C42×D61C2211yescharacteristic
43#16840094C2218yes—
44#16840091C2218yes—
45#16840046C2218yescomplemented
46#16840045C2218yescomplemented
47#16839971C2218yescomplemented
48#16839970C2218yescomplemented
49#16839919C2218yes—
50#16839916C2218yes—
51#16839870C2218yescomplemented
52#16839867C2218yescomplemented
53#16839867C2218yescomplemented
54#16839817C2218yes—
55C2×#14519709C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519688C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×Q8×C61C2211yescharacteristic
72C61×#441C2218yescomplemented
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C2×Q8×D61—24no—
82C2×Q8×D61—22no—
83C2×Q8×D61—24no—
84C2×Q8×D61C2314yes—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C2×Dic244—24no—
91C2×Dic244C2314yes—
92C2×#11758202—24no—
93C2×#11758202—24no—
94C2×#11758202C2314yes—
95C2×#11758202C2314yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98#14519776—22no—
99#14519776C2314yes—
100#14519775—22no—
101#14519775C2314yes—
102#14519767—28no—
103#14519757—22no—
104#14519757C2314yes—
105#14519755—28no—
106#14519753—22no—
107#14519753C2314yes—
108Q8×Dic61—22no—
109Q8×Dic61C2314yes—
110C4×Dic122—22no—
111C4×Dic122—22no—
112C4×Dic122—28no—
113C4×Dic122—28no—
114C4×Dic122C2314yes—
115C4×Dic122C2314yes—
116#14519742—22no—
117#14519742—28no—
118#14519742C2314yes—
119#14519734—28no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C4⋊C4×D61—28no—
133C4⋊C4×D61—22no—
134C4⋊C4×D61C2314yes—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144C42×D61—28no—
145C42×D61D414yes—
146C42×D61C2314yes—
147#14519709C2314yes—
148#14519708C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519706C2314yes—
152#14519702C2314yes—
153#14519702C2314yes—
154#14519701C2314yes—
155#14519701C2314yes—
156#14519700C2314yes—
157#14519700C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160#14519688C2314yes—
161C22×Q8×C61C2311yescharacteristic
162C22×Q8×C61C2311yescharacteristic
163C2×Q16×C61—24no—
164C2×Q16×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C4×Q8×C61—22no—
168C4×Q8×C61—22no—
169C4×Q8×C61C2314yes—
170C4×Q8×C61C2314yes—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C42×C61—21no—
176C2×C42×C61—21no—
177C2×C42×C61C2311yescharacteristic
178#106×C61C2314yes—
179#103×C61C2314yes—
180#103×C61C2314yes—
181#97×C61C2314yes—
182C23×D61C2×D411yescharacteristic
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—22no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61#4114yes—
189C2×Q8×C61C2412yes—
190C2×Q8×C61C2412yes—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2411yescharacteristic
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205Q8×D61—216no—
206Q8×D61—28no—
207Q8×D61—28no—
208C2×C4×D61—28no—
209C2×C4×D61—24no—
210C2×C4×D61—24no—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—44no—
216C2×C4×D61C2×D414yes—
217C2×C4×D61C2×D414yes—
218C2×C4×D61C2×D412yes—
219C2×C4×D61C2412yes—
220C2×Dic122—28no—
221C2×Dic122—21no—
222C2×Dic122—22no—
223C2×Dic122—24no—
224C2×Dic122—22no—
225C2×Dic122—22no—
226C2×Dic122—21no—
227C2×Dic122—24no—
228C2×Dic122—44no—
229C2×Dic122#4114yes—
230C2×Dic122C2412yes—
231C2×Dic122C2412yes—
232Q16×C61—28no—
233C2×C8×C61—22no—
234C2×C8×C61—22no—
235C2×C8×C61C2412yes—
236C2×C8×C61C2412yes—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61C2412yes—
242C4⋊C4×C61C2412yes—
243C42×C61—24no—
244C42×C61—24no—
245C42×C61C2×D412yes—
246C42×C61C2412yes—
247#11758202—28no—
248#11758202—28no—
249#11758198—24no—
250#11758198—24no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—24no—
254C4⋊Dic61—24no—
255C4⋊Dic61C2412yes—
256C4⋊Dic61C2412yes—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265C4×Dic61—24no—
266C4×Dic61—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61C2×D412yes—
270C4×Dic61C2×D414yes—
271C4×Dic61C2×D414yes—
272C4×Dic61C2412yes—
273C2×#92418—22no—
274C2×#92418—22no—
275C2×#92418C2412yes—
276C2×#92418C2412yes—
277Dic244—28no—
278C23×C61C22×D411yescharacteristic
279C22×D61—22no—
280C22×D61—22no—
281C22×D61#13714yes—
282C22×D61C22×D412yes—
283Q8×C61—24no—
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—42no—
288Q8×C61C2×#4114yes—
289C2×C4×C61—24no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61C22×D412yes—
300C2×C4×C61C22×D412yes—
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C2×#4112yes—
303C2×C4×C61C2×#4112yes—
304C2×C4×C61C2511yescharacteristic
305C2×Dic61—22no—
306C2×Dic61—24no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61#13714yes—
316C2×Dic61C22×D412yes—
317C2×Dic61C22×D412yes—
318C2×Dic61C22×D412yes—
319C4×D61—216no—
320C4×D61—28no—
321C4×D61—24no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—28no—
325C4×D61—48no—
326Dic122—216no—
327Dic122—24no—
328Dic122—22no—
329Dic122—22no—
330Dic122—22no—
331Dic122—42no—
332Dic122—48no—
333Dic122C2×#4114yes—
334C8×C61—22no—
335C8×C61—22no—
336#92418—22no—
337#92418—22no—
338C2×#3113—611nomaximal, Sylow
339C22×C61#52512yes—
340C22×C61C2×#13712yes—
341C22×C61C2×#13712yes—
342C22×C61C23×D411yescharacteristic
343C2×D61—28no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61C2×#13714yes—
347C4×C61—24no—
348C4×C61—22no—
349C4×C61—22no—
350C4×C61—42no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61#52512yes—
354C4×C61C22×#4111yescharacteristic
355C4×C61C22×#4111yescharacteristic
356Dic61—22no—
357Dic61—24no—
358Dic61—22no—
359Dic61—42no—
360Dic61—42no—
361Dic61—42no—
362Dic61C2×#13714yes—
363C2×#533—611no—
364C22×C4×Q8—611no—
365#3113—6116no—
366C2×#483—611no—
367C2×#483—611no—
368C2×#475—611no—
369C2×#475—611no—
370C2×#462—611no—
371C2×#462—611no—
372C2×#451—611no—
373C2×#451—611no—
374C2×#441—611no—
375C2×#441—611no—
376C2×#441—611no—
377C2×#441D6111yescharacteristic, complemented
378C2×#432—611no—
379C2×C61#311314yescomplemented
380C2×C61C2×#52511yescharacteristic
381C2×C61C22×#13711yescharacteristic
382C2×C61C22×#13711yescharacteristic
383D61—24no—
384C23×Q8—611no—
385C22×Q16—611no—
386C22×Q16—611no—
387C22×Q16—611no—
388C22×Q16C2×D6111yescharacteristic
389#533—618no—
390#533—1224no—
391C2×C4⋊Q8—611no—
392C2×C4⋊Q8—611no—
393C2×#125—1221no—
394C2×C22⋊Q8—611no—
395C2×C22⋊Q8—611no—
396C2×C22⋊Q8—1221no—
397C2×C4×Q8—611no—
398C2×C4×Q8—618no—
399C2×C4×Q8—611no—
400C2×C4×Q8—611no—
401C2×C4×Q8—611no—
402C2×C4×Q8—1221no—
403C2×C4×Q8—1221no—
404C2×C4×Q8—1221no—
405C2×C4×Q8—1224no—
406C2×C4×Q8C2×D6111yescharacteristic
407C2×C4×Q8C2×D6111yescharacteristic
408C2×#117—1221no—
409C22×C4⋊C4—611no—
410C22×C4⋊C4—1221no—
411C22×C42—611no—
412C22×C42—1221no—
413#483—618no—
414#483—618no—
415#475—618no—
416#475—618no—
417#462—618no—
418#462—618no—
419#451—618no—
420#451—618no—
421#441—618no—
422#441—618no—
423#441—618no—
424#441C2×D6118yescomplemented
425#432—618no—
426C2×#106—611no—
427C2×#106—611no—
428C2×#106—611no—
429C2×#106C2×D6111yescharacteristic
430C2×C4⋊C8—611no—
431C2×C4⋊C8—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103C2×D6111yescharacteristic
439C2×#103C2×D6111yescharacteristic
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×#97—611no—
443C2×#97C2×D6111yescharacteristic
444C61C2×#311311yescharacteristic, complemented, Sylow
445C22×Q8—614no—
446C22×Q8—611no—
447C22×Q8—611no—
448C22×Q8—1221no—
449C22×Q8—1221no—
450C22×Q8—1222no—
451C22×Q8—1224no—
452C22×Q8—1224no—
453C22×Q8C22×D6111yescharacteristic
454C22×Q8C22×D6111yescharacteristic
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—1221no—
459C23×C4—1221no—
460C2×Q16—24no—
461C2×Q16—614no—
462C2×Q16—614no—
463C2×Q16—614no—
464C2×Q16—1224no—
465C2×Q16—1224no—
466C2×Q16—1224no—
467C2×Q16C22×D6114yes—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8C22×D6111yescharacteristic
471C22×C8C22×D6111yescharacteristic
472C4⋊Q8—614no—
473C4⋊Q8—614no—
474C4⋊Q8—1222no—
475C4⋊Q8—1222no—
476#125—1228no—
477C22⋊Q8—614no—
478C22⋊Q8—614no—
479C22⋊Q8—1222no—
480C22⋊Q8—1228no—
481C22⋊Q8—1222no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—614no—
485C4×Q8—614no—
486C4×Q8—614no—
487C4×Q8—614no—
488C4×Q8—1228no—
489C4×Q8—1228no—
490C4×Q8—1228no—
491C4×Q8—1222no—
492C4×Q8—1222no—
493C4×Q8—1222no—
494C4×Q8—1222no—
495C4×Q8C22×D6114yes—
496C4×Q8C22×D6114yes—
497#117—1228no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—614no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—1228no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4C22×D6111yescharacteristic
516C2×C4⋊C4C22×D6111yescharacteristic
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—611no—
522C2×C42—611no—
523C2×C42—611no—
524C2×C42—614no—
525C2×C42—614no—
526C2×C42—1228no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42C22×D6111yescharacteristic
532#106—614no—
533#106—614no—
534#106—614no—
535#106C22×D6114yes—
536C4⋊C8—614no—
537C4⋊C8—614no—
538#103—614no—
539#103—614no—
540#103—614no—
541#103—614no—
542#103—614no—
543#103—614no—
544#103C22×D6114yes—
545#103C22×D6114yes—
546C22⋊C8—614no—
547C22⋊C8—614no—
548#97—614no—
549#97C22×D6114yes—
550C24—611no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—614no—
557C2×Q8—612no—
558C2×Q8—612no—
559C2×Q8—1224no—
560C2×Q8—1224no—
561C2×Q8—1228no—
562C2×Q8—1228no—
563C2×Q8—12216no—
564C2×Q8—1228no—
565C2×Q8—1221no—
566C2×Q8—1221no—
567C2×Q8—1222no—
568C2×Q8—1222no—
569C2×Q8—1222no—
570C2×Q8—2444no—
571C2×Q8#1175822214yes—
572C2×Q8C23×D6112yes—
573C2×Q8C23×D6112yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—614no—
582C22×C4—614no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—1224no—
586C22×C4—1224no—
587C22×C4—1224no—
588C22×C4—1228no—
589C22×C4—1224no—
590C22×C4—1221no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—2444no—
597C22×C4D4×D6111yescharacteristic
598C22×C4D4×D6111yescharacteristic
599C22×C4C23×D6111yescharacteristic
600Q16—28no—
601Q16—1228no—
602Q16—1228no—
603Q16—1228no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—1222no—
609C2×C8—1222no—
610C2×C8C23×D6112yes—
611C2×C8C23×D6112yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—612no—
617C4⋊C4—612no—
618C4⋊C4—1224no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4C23×D6112yes—
631C4⋊C4C23×D6112yes—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C42—24no—
635C42—24no—
636C42—614no—
637C42—614no—
638C42—612no—
639C42—612no—
640C42—1224no—
641C42—1224no—
642C42—1224no—
643C42—1224no—
644C42D4×D6112yes—
645C42C23×D6112yes—
646C23—614no—
647C23—612no—
648C23—1222no—
649C23—1222no—
650C23C2×D4×D6111yescharacteristic
651Q8—24no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—614no—
657Q8—12216no—
658Q8—1224no—
659Q8—1222no—
660Q8—1222no—
661Q8—1222no—
662Q8—2448no—
663Q8—2442no—
664Q8C2×#1175822214yes—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—614no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—612no—
679C2×C4—1228no—
680C2×C4—1228no—
681C2×C4—12216no—
682C2×C4—1222no—
683C2×C4—1224no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1224no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—2448no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4C2×D4×D6112yes—
697C2×C4C2×D4×D6112yes—
698C2×C4C2×D4×D6111yescharacteristic
699C2×C4#41×D6112yes—
700C2×C4C2×#1175822212yes—
701C2×C4C24×D6111yescharacteristic
702C8—22no—
703C8—22no—
704C8—1222no—
705C8—1222no—
706C22—614no—
707C22—1228no—
708C22—1222no—
709C22—1222no—
710C22#1684027112yes—
711C22#137×D6112yes—
712C22#137×D6112yes—
713C22C22×D4×D6111yescharacteristic
714C4—22no—
715C4—22no—
716C4—24no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—614no—
721C4—1222no—
722C4—1222no—
723C4—1224no—
724C4—2442no—
725C4—2442no—
726C4—2442no—
727C4#1684027112yes—
728C4C2×#41×D6111yescharacteristic
729C4C22×#1175822211yescharacteristic
730C2—1224no—
731C2#2145594714yesdirect product factor
732C2C2×#1684027111yescharacteristic
733C2C2×#137×D6111yescharacteristic
734C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#441C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenterC2×#441D61
hypocenterC61C2×#3113
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #21455947C2direct (N × H)
6. C2×#16840046C2semidirect
7. C2×#16840045C2semidirect
8. C2×#16839971C2semidirect
9. C2×#16839970C2semidirect
12. C2×#16839870C2semidirect
13. C2×#16839867C2semidirect
14. C2×#16839867C2semidirect
16. C2×C61×#441C2semidirect
45. #16840046C22semidirect
46. #16840045C22semidirect
47. #16839971C22semidirect
48. #16839970C22semidirect
51. #16839870C22semidirect
52. #16839867C22semidirect
53. #16839867C22semidirect
72. C61×#441C22semidirect
377. C2×#441D61semidirect
379. C2×C61#3113semidirect
424. #441C2×D61semidirect
444. C61C2×#3113semidirect
731. C2#21455947direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403162
C2×C4×Q8×D612
#214559472
C2×#168400942
C2×#168400912
C2×#168400462
C2×#168400452
C2×#168399712
C2×#168399702
C2×#168399192
C2×#168399162
C2×#168398702
C2×#168398672
C2×#168398172
C2×C61×#4412
C2×#311361