Finite Group Databasebeta

← C2×#21457151 #30552813

Subgroups — C2×#21457151 #30552813

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840314C211yesmaximal, characteristic, complemented
2C2×#16840298C211yesmaximal, characteristic
3#21457151C2116yesmaximal, direct product factor
4C2×#16840068C211yesmaximal, characteristic, complemented
5C2×#16840067C211yesmaximal, characteristic, complemented
6C2×#16840045C211yesmaximal, characteristic, complemented
7C2×#16840041C211yesmaximal, characteristic, complemented
8C2×#16840001C211yesmaximal, characteristic, complemented
9C2×#16839993C211yesmaximal, characteristic
10C2×#16839991C211yesmaximal, characteristic
11C2×#16839987C211yesmaximal, characteristic, complemented
12C2×#16839986C211yesmaximal, characteristic, complemented
13C2×#16839970C211yesmaximal, characteristic, complemented
14C2×#16839966C211yesmaximal, characteristic, complemented
15C22×#14519706C211yesmaximal, characteristic, complemented
16C2×C61×#467C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C23×#92418C2211yescharacteristic
21#16840314—24no—
22#16840314C2218yescomplemented
23C2×#14519776C2211yescharacteristic
24C2×#14519775C2211yescharacteristic
25#16840298—24no—
26#16840298C2218yes—
27C2×#14519772—21no—
28C2×#14519768C2211yescharacteristic
29C2×#14519767—21no—
30C2×#14519766C2211yescharacteristic
31C2×#14519761—21no—
32C2×#14519756C2211yescharacteristic
33C2×#14519754—21no—
34C2×#14519751C2211yescharacteristic
35C2×Q8×Dic61C2211yescharacteristic
36C2×Q8×Dic61C2211yescharacteristic
37C2×#14519742—21no—
38C2×#14519742C2211yescharacteristic
39C2×#14519739C2211yescharacteristic
40C2×#14519737—21no—
41C2×#14519735—21no—
42C2×#14519733—21no—
43C22×C4×Dic61C2211yescharacteristic
44#16840068C2218yescomplemented
45#16840067C2218yescomplemented
46#16840045C2218yescomplemented
47#16840041C2218yescomplemented
48#16840001C2218yescomplemented
49#16839993C2218yes—
50#16839991C2218yes—
51#16839987C2218yescomplemented
52#16839986C2218yescomplemented
53#16839970C2218yescomplemented
54#16839966C2218yescomplemented
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2218yescomplemented
63C2×#14519702C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519701C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#467C2218yescomplemented
74C2×#107×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C23×Dic61D411yescharacteristic
82C23×Dic61D411yescharacteristic
83C22×C4×D61—21no—
84C2×#11758202—42no—
85C2×#11758202C2314yes—
86C2×#11758190—42no—
87C2×#11758190C2314yes—
88C2×#11758201—42no—
89C2×#11758201C2314yes—
90C22×#92418—42no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C22×#92418C2314yes—
94#14519776—22no—
95#14519776C2314yes—
96#14519775—22no—
97#14519775C2314yes—
98#14519772—28no—
99#14519768—22no—
100#14519768C2314yes—
101#14519767—28no—
102#14519766—22no—
103#14519766C2314yes—
104#14519761—28no—
105#14519756—22no—
106#14519756C2314yes—
107#14519754—28no—
108#14519751—22no—
109#14519751C2314yes—
110Q8×Dic61—22no—
111Q8×Dic61—22no—
112Q8×Dic61C2314yes—
113Q8×Dic61C2314yes—
114#14519742—28no—
115#14519742—22no—
116#14519742C2314yes—
117#14519739—22no—
118#14519739C2314yes—
119#14519737—28no—
120#14519735—28no—
121#14519733—28no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×C22⋊Dic61—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D414yes—
144C2×C4×Dic61C2311yescharacteristic
145C2×C4×Dic61C2311yescharacteristic
146C2×C4×Dic61C2314yes—
147#14519710C2314yes—
148#14519709C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519706C2314yes—
152#14519706C2314yes—
153#14519706C2314yes—
154#14519702C2314yes—
155#14519701C2314yes—
156#14519701C2314yes—
157#14519700C2314yes—
158#14519699C2314yes—
159#14519697C2314yes—
160C22×Q8×C61C2311yescharacteristic
161C22×Q8×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C2×Q16×C61—42no—
164C2×Q16×C61C2314yes—
165C22×C8×C61—42no—
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2314yes—
169C22⋊Q8×C61—22no—
170C22⋊Q8×C61—22no—
171C22⋊Q8×C61C2314yes—
172C22⋊Q8×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179#107×C61C2314yes—
180#103×C61C2314yes—
181#103×C61C2314yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61C2412yes—
191C2×Q8×C61C2412yes—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2411yescharacteristic
202C2×C22⋊D61—24no—
203C2×C22⋊D61—44no—
204C22×Dic61—24no—
205C22×Dic61—24no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D414yes—
213C22×Dic61C2×D414yes—
214C22×Dic61C2×D411yescharacteristic
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—21no—
218C2×D244C2412yes—
219C2×C4×D61—24no—
220C2×C4×D61—44no—
221C2×Dic122—22no—
222C2×Dic122—22no—
223C2×Dic122—21no—
224C2×Dic122—24no—
225C2×Dic122—44no—
226C2×Dic122C2412yes—
227Q16×C61—44no—
228C2×C8×C61—22no—
229C2×C8×C61—22no—
230C2×C8×C61—44no—
231C2×C8×C61C2412yes—
232C2×C8×C61C2412yes—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61C2412yes—
238C4⋊C4×C61C2412yes—
239C22⋊C4×C61—24no—
240C22⋊C4×C61—24no—
241C22⋊Dic61—24no—
242#11758202—44no—
243#11758201—44no—
244#11758198—24no—
245#11758198—24no—
246#11758198—24no—
247#11758198—24no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—24no—
251C4⋊Dic61—24no—
252C4⋊Dic61—24no—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255#11758196—24no—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261C4×Dic61—24no—
262C4×Dic61—24no—
263C4×Dic61—24no—
264C4×Dic61C2×D414yes—
265C4×Dic61C2×D412yes—
266C4×Dic61C2×D412yes—
267C4×Dic61C2×D414yes—
268C4×Dic61C2412yes—
269C4×Dic61C2412yes—
270C2×#92418—22no—
271C2×#92418—22no—
272C2×#92418—44no—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275#11758190—44no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61#13714yes—
279C23×C61C22×D412yes—
280C23×C61C22×D411yescharacteristic
281C22×D61—22no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—22no—
288Q8×C61—22no—
289Q8×C61—42no—
290Q8×C61—42no—
291C2×C4×C61—22no—
292C2×C4×C61—24no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61H(5,𝔽2)12yes—
306C2×C4×C612−1+412yes—
307C2×C4×C61C2511yescharacteristic
308C22⋊D61—48no—
309C2×Dic61—22no—
310C2×Dic61—28no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—28no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61#13514yes—
321C2×Dic61C22×D412yes—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324C2×Dic61C22×D412yes—
325D244—22no—
326D244—22no—
327D244—42no—
328C4×D61—48no—
329Dic122—22no—
330Dic122—22no—
331Dic122—42no—
332Dic122—48no—
333C8×C61—22no—
334C8×C61—22no—
335#92418—22no—
336#92418—22no—
337C2×#3248—611nomaximal, Sylow
338C22×C61—22no—
339C22×C61—28no—
340C22×C61—22no—
341C22×C61#53712yes—
342C22×C61C2×#13512yes—
343C22×C61C2×#13714yes—
344C22×C61C2×#13712yes—
345C22×C61C23×D411yescharacteristic
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—84no—
350C4×C61—22no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61#53712yes—
356C4×C61C2×H(5,𝔽2)11yescharacteristic
357C4×C61C2×2−1+411yescharacteristic
358Dic61—22no—
359Dic61—22no—
360Dic61—22no—
361Dic61—42no—
362Dic61—42no—
363Dic61—42no—
364Dic61C2×#13514yes—
365C2×#533—611no—
366C2×#529—611no—
367#3248—6116no—
368C2×#479—611no—
369C2×#479—611no—
370C2×#475—611no—
371C2×#474—611no—
372C2×#467—611no—
373C2×#467D6111yescharacteristic, complemented
374C2×#465—611no—
375C2×#465—611no—
376C2×#464—611no—
377C2×#464—611no—
378C2×#462—611no—
379C2×#461—611no—
380C22×C4⋊C8—611no—
381C2×C61—24no—
382C2×C61#324814yescomplemented
383C2×C61C2×#53711yescharacteristic
384C2×C61C22×#13511yescharacteristic
385C2×C61C22×#13711yescharacteristic
386D61—82no—
387C22×Q16—611no—
388C22×Q16C2×D6111yescharacteristic
389C22×SD16—611no—
390C22×SD16—611no—
391C23×C8—611no—
392C23×C8C2×D6111yescharacteristic
393#533—618no—
394#533—1224no—
395C2×C4⋊Q8—611no—
396C2×C4⋊Q8—611no—
397#529—618no—
398#529—1224no—
399C2×#126—1221no—
400C2×#125—611no—
401C2×#125—1221no—
402C2×#124—611no—
403C2×#123—1221no—
404C2×C22⋊Q8—611no—
405C2×C22⋊Q8—1221no—
406C2×C22⋊Q8C2×D6111yescharacteristic
407C2×C22⋊Q8C2×D6111yescharacteristic
408C2×#121—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×Q8—611no—
412C2×C4×Q8—1221no—
413C2×C4×D4—611no—
414C2×C4×D4—1221no—
415C2×#117—1221no—
416C2×#117—1221no—
417C22×C42—611no—
418#479—618no—
419#479—618no—
420#475—618no—
421#474—618no—
422#467—618no—
423#467C2×D6118yescomplemented
424#465—618no—
425#465—618no—
426#464—618no—
427#464—618no—
428#462—618no—
429#461—618no—
430C2×#107—611no—
431C2×#107C2×D6111yescharacteristic
432C2×#106—611no—
433C2×#106—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8—611no—
437C2×C4⋊C8—611no—
438C2×C4⋊C8—618no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103C2×D6111yescharacteristic
444C2×#103C2×D6111yescharacteristic
445C2×#102—611no—
446C2×#102—611no—
447C61C2×#324811yescharacteristic, complemented, Sylow
448C22×Q8—611no—
449C22×Q8—1221no—
450C22×Q8C22×D6111yescharacteristic
451C22×Q8C22×D6111yescharacteristic
452C22×D4—611no—
453C22×D4—1221no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—1221no—
457C23×C4C22×D6111yescharacteristic
458C2×Q16—42no—
459C2×Q16—614no—
460C2×Q16—2442no—
461C2×Q16C22×D6114yes—
462C2×SD16—614no—
463C2×SD16—614no—
464C2×SD16—2442no—
465C2×SD16—2442no—
466C22×C8—42no—
467C22×C8—611no—
468C22×C8—611no—
469C22×C8—614no—
470C22×C8—2442no—
471C22×C8C22×D6111yescharacteristic
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6114yes—
474C4⋊Q8—614no—
475C4⋊Q8—614no—
476C4⋊Q8—1222no—
477C4⋊Q8—1222no—
478#126—1228no—
479#125—614no—
480#125—1222no—
481#125—1228no—
482#124—614no—
483#124—1222no—
484#123—1228no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—614no—
488C22⋊Q8—1228no—
489C22⋊Q8—1222no—
490C22⋊Q8C22×D6114yes—
491C22⋊Q8C22×D6114yes—
492#121—614no—
493#121—1222no—
494C4×Q8—614no—
495C4×Q8—614no—
496C4×Q8—614no—
497C4×Q8—1222no—
498C4×Q8—1228no—
499C4×Q8—1222no—
500C4×Q8—1222no—
501C4×D4—614no—
502C4×D4—1222no—
503C4×D4—1228no—
504#117—1228no—
505#117—1228no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—611no—
529C2×C42—611no—
530C2×C42—614no—
531C2×C42—611no—
532C2×C42—611no—
533C2×C42—614no—
534C2×C42—1221no—
535C2×C42—1221no—
536C2×C42—1221no—
537#107—614no—
538#107C22×D6114yes—
539#106—614no—
540#106—614no—
541C4⋊C8—614no—
542C4⋊C8—614no—
543C4⋊C8—614no—
544C4⋊C8—614no—
545#103—614no—
546#103—614no—
547#103—614no—
548#103—614no—
549#103C22×D6114yes—
550#103C22×D6114yes—
551#102—614no—
552#102—614no—
553C24—1221no—
554C24D4×D6111yescharacteristic
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—612no—
562C2×Q8—1224no—
563C2×Q8—1221no—
564C2×Q8—1222no—
565C2×Q8—1222no—
566C2×Q8—2444no—
567C2×Q8C23×D6112yes—
568C2×Q8C23×D6112yes—
569C2×D4—612no—
570C2×D4—1224no—
571C2×D4—1221no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—2444no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—611no—
582C22×C4—614no—
583C22×C4—614no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—1224no—
588C22×C4—1224no—
589C22×C4—1224no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—2444no—
594C22×C4D4×D6112yes—
595C22×C4D4×D6111yescharacteristic
596C22×C4C23×D6112yes—
597C22×C4C23×D6111yescharacteristic
598Q16—44no—
599Q16—2444no—
600SD16—2444no—
601SD16—2444no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—44no—
605C2×C8—612no—
606C2×C8—612no—
607C2×C8—1222no—
608C2×C8—1222no—
609C2×C8—2444no—
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⋊C4C23×D6112yes—
630C4⋊C4C23×D6112yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C42—614no—
639C42—612no—
640C42—612no—
641C42—614no—
642C42—612no—
643C42—612no—
644C42—1224no—
645C42—1224no—
646C42—1224no—
647C23—22no—
648C23—22no—
649C23—1222no—
650C23—2442no—
651C23—2442no—
652C23—2442no—
653C23#1451980914yes—
654C23C2×D4×D6112yes—
655C23C2×D4×D6111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—1222no—
663Q8—1222no—
664Q8—2448no—
665Q8—2442no—
666D4—1222no—
667D4—1222no—
668D4—2448no—
669D4—2442no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—614no—
683C2×C4—612no—
684C2×C4—612no—
685C2×C4—612no—
686C2×C4—612no—
687C2×C4—1228no—
688C2×C4—1222no—
689C2×C4—1228no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—2448no—
696C2×C4—2442no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4C2×D4×D6112yes—
700C2×C4C2×D4×D6111yescharacteristic
701C2×C4#1451982212yes—
702C2×C4#1451982412yes—
703C2×C4C24×D6111yescharacteristic
704C8—22no—
705C8—22no—
706C8—1222no—
707C8—1222no—
708C22—22no—
709C22—22no—
710C22—28no—
711C22—4884no—
712C22—2442no—
713C22—2442no—
714C22—2442no—
715C22#1684033912yes—
716C22#135×D6112yes—
717C22C2×#1451980914yes—
718C22C2×#1451980912yes—
719C22C22×D4×D6111yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—614no—
726C4—1222no—
727C4—1222no—
728C4—1222no—
729C4—2442no—
730C4—2442no—
731C4—2442no—
732C4#1684033912yes—
733C4C2×#1451982211yescharacteristic
734C4C2×#1451982411yescharacteristic
735C2—24no—
736C2—4882no—
737C2#2145715114yesdirect product factor
738C2C2×#1684033911yescharacteristic
739C2C2×#135×D6111yescharacteristic
740C2C22×#1451980911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#467C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenterC2×#467D61
hypocenterC61C2×#3248
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#16840314C2semidirect
3. #21457151C2direct (N × H)
4. C2×#16840068C2semidirect
5. C2×#16840067C2semidirect
6. C2×#16840045C2semidirect
7. C2×#16840041C2semidirect
8. C2×#16840001C2semidirect
11. C2×#16839987C2semidirect
12. C2×#16839986C2semidirect
13. C2×#16839970C2semidirect
14. C2×#16839966C2semidirect
15. C22×#14519706C2semidirect
16. C2×C61×#467C2semidirect
22. #16840314C22semidirect
44. #16840068C22semidirect
45. #16840067C22semidirect
46. #16840045C22semidirect
47. #16840041C22semidirect
48. #16840001C22semidirect
51. #16839987C22semidirect
52. #16839986C22semidirect
53. #16839970C22semidirect
54. #16839966C22semidirect
62. C2×#14519706C22semidirect
73. C61×#467C22semidirect
373. C2×#467D61semidirect
382. C2×C61#3248semidirect
423. #467C2×D61semidirect
447. C61C2×#3248semidirect
737. C2#21457151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403142
C2×#168402982
#214571512
C2×#168400682
C2×#168400672
C2×#168400452
C2×#168400412
C2×#168400012
C2×#168399932
C2×#168399912
C2×#168399872
C2×#168399862
C2×#168399702
C2×#168399662
C22×#145197062
C2×C61×#4672
C2×#324861