Finite Group Databasebeta

← C2×#21458875 #30561008

Subgroups — C2×#21458875 #30561008

Order 15616.

1970 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840494C211yesmaximal, characteristic
2C2×#16840490C211yesmaximal, characteristic, complemented
3#21458875C2116yesmaximal, direct product factor
4C2×#16840157C211yesmaximal, characteristic, complemented
5C2×#16840155C211yesmaximal, characteristic, complemented
6C2×#16840133C211yesmaximal, characteristic
7C2×#16839987C211yesmaximal, characteristic, complemented
8C2×#16839970C211yesmaximal, characteristic, complemented
9C2×#16839961C211yesmaximal, characteristic
10C2×#16839968C211yesmaximal, characteristic, complemented
11C2×#16839965C211yesmaximal, characteristic, complemented
12C2×#16839891C211yesmaximal, characteristic, complemented
13C2×#16839860C211yesmaximal, characteristic, complemented
14C2×#16839859C211yesmaximal, characteristic, complemented
15C2×#16839854C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24#16840494—24no—
25#16840494C2218yes—
26#16840490—24no—
27#16840490C2218yescomplemented
28C2×#14519777C2211yescharacteristic
29C2×#14519775C2211yescharacteristic
30C2×#14519775C2211yescharacteristic
31C2×#14519773C2211yescharacteristic
32C2×#14519769—21no—
33C2×#14519767—21no—
34C2×#14519767—21no—
35C2×#14519766C2211yescharacteristic
36C2×#14519763—21no—
37C2×#14519761—21no—
38C2×#14519759—21no—
39C2×Q8×Dic61C2211yescharacteristic
40C2×C4×Dic122—21no—
41C2×C4×Dic122C2211yescharacteristic
42C2×#14519742C2211yescharacteristic
43C2×#14519742C2211yescharacteristic
44C2×C4×D244C2211yescharacteristic
45C2×D4×Dic61C2211yescharacteristic
46C2×#14519737—21no—
47#16840157C2218yescomplemented
48#16840155C2218yescomplemented
49#16840133C2218yes—
50#16839987C2218yescomplemented
51#16839970C2218yescomplemented
52#16839968C2218yescomplemented
53#16839965C2218yescomplemented
54#16839961C2218yes—
55#16839891C2218yescomplemented
56#16839860C2218yescomplemented
57#16839859C2218yescomplemented
58#16839854C2218yescomplemented
59C2×#14519710C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519688C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#464C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C2×#11758202—24no—
86C2×#11758202—42no—
87C2×#11758202C2314yes—
88C2×#11758202C2314yes—
89C2×#11758190—42no—
90C2×#11758190—42no—
91C2×#11758190C2314yes—
92C2×#11758190C2314yes—
93C2×#11758200—24no—
94C2×#11758200—42no—
95C2×#11758200C2314yes—
96C2×#11758200C2314yes—
97C2×#11758201—24no—
98C2×#11758201C2314yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101#14519777—22no—
102#14519777C2314yes—
103#14519775—22no—
104#14519775—22no—
105#14519775C2314yes—
106#14519775C2314yes—
107#14519773—22no—
108#14519773C2314yes—
109#14519769—28no—
110#14519767—28no—
111#14519767—28no—
112#14519766—22no—
113#14519766C2314yes—
114#14519763—28no—
115#14519761—28no—
116#14519759—28no—
117Q8×Dic61—22no—
118Q8×Dic61C2314yes—
119C4×Dic122—28no—
120C4×Dic122D414yes—
121C4×Dic122C2314yes—
122#14519742—22no—
123#14519742—22no—
124#14519742C2314yes—
125#14519742C2314yes—
126C4×D244—22no—
127C4×D244C2314yes—
128D4×Dic61—22no—
129D4×Dic61C2314yes—
130#14519737—28no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61—21no—
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61D411yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196D411yescharacteristic
143C2×#11758196D411yescharacteristic
144C2×C22⋊Dic61—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×C4×Dic61—21no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153#14519710C2314yes—
154#14519706C2314yes—
155#14519706C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519701C2314yes—
159#14519697C2314yes—
160#14519688C2314yes—
161#14519687C2314yes—
162C8×Dic61C2314yes—
163C22×Q8×C61C2311yescharacteristic
164C22×Q8×C61C2311yescharacteristic
165C22×D4×C61C2311yescharacteristic
166C2×Q16×C61—42no—
167C2×Q16×C61C2314yes—
168C2×SD16×C61—42no—
169C2×SD16×C61C2314yes—
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172#124×C61—22no—
173#124×C61C2314yes—
174C4×Q8×C61—22no—
175C4×Q8×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C42×C61—21no—
181C2×C42×C61C2311yescharacteristic
182C4⋊C8×C61C2314yes—
183#103×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C23×D61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61C2412yes—
194C2×Q8×C61C2412yes—
195C2×D4×C61—21no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61C2412yes—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2411yescharacteristic
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—44no—
208C2×C22⋊D61—82no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—82no—
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—21no—
221C2×D244C2412yes—
222C2×C4×D61—24no—
223C2×C4×D61—82no—
224C2×Dic122—24no—
225C2×Dic122—22no—
226C2×Dic122—22no—
227C2×Dic122—22no—
228C2×Dic122—22no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122C2×D414yes—
232C2×Dic122C2412yes—
233C2×Dic122C2412yes—
234Q16×C61—44no—
235SD16×C61—44no—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61C2412yes—
239C2×C8×C61C2412yes—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C42×C61—24no—
246C42×C61C2×D412yes—
247C42×C61C2412yes—
248C22⋊Dic61—24no—
249#11758202—28no—
250#11758202—44no—
251#11758201—28no—
252#11758200—28no—
253#11758200—44no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257C4⋊Dic61—24no—
258C4⋊Dic61—24no—
259C4⋊Dic61—21no—
260C4⋊Dic61—24no—
261C4⋊Dic61C2×D414yes—
262C4⋊Dic61C2412yes—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269#11758196C2×D414yes—
270#11758196C2×D414yes—
271C4×Dic61—24no—
272C4×Dic61—24no—
273C4×Dic61—24no—
274C4×Dic61C2×D412yes—
275C4×Dic61C2×D412yes—
276C4×Dic61C2412yes—
277C4×Dic61C2412yes—
278C2×#92418—22no—
279C2×#92418#4114yes—
280C2×#92418C2412yes—
281C2×#92418C2412yes—
282#11758190—44no—
283#11758190—44no—
284C23×C61—22no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61—42no—
298Q8×C61—42no—
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—42no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61C22×D412yes—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4112yes—
314C2×C4×C61H(5,𝔽2)12yes—
315C2×C4×C61C2511yescharacteristic
316C22⋊D61—48no—
317C22⋊D61—84no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—84no—
328C2×Dic61#13714yes—
329C2×Dic61C22×D412yes—
330C2×Dic61C22×D412yes—
331C2×Dic61C22×D412yes—
332C2×Dic61C22×D412yes—
333D244—22no—
334D244—22no—
335D244—42no—
336C4×D61—84no—
337Dic122—28no—
338Dic122—22no—
339Dic122—22no—
340Dic122—22no—
341Dic122—22no—
342Dic122—42no—
343Dic122—42no—
344C8×C61—22no—
345C8×C61—22no—
346#92418—22no—
347#92418C2×#4114yes—
348C2×#3400—611nomaximal, Sylow
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—84no—
353C22×C61#55012yes—
354C22×C61C2×#13712yes—
355C22×C61#57712yes—
356C22×C61C23×D411yescharacteristic
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—84no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—42no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61#55012yes—
367C4×C61C22×#4111yescharacteristic
368C4×C61C2×H(5,𝔽2)11yescharacteristic
369Dic61—22no—
370Dic61—22no—
371Dic61—22no—
372Dic61—42no—
373Dic61—42no—
374Dic61—42no—
375Dic61C2×#13714yes—
376C2×#559—611no—
377C2×#557—611no—
378#3400—6116no—
379C2×#497—611no—
380C2×#497—611no—
381C2×#492—611no—
382C2×#464—611no—
383C2×#464D6111yescharacteristic, complemented
384C2×#462—611no—
385C2×#460—611no—
386C2×#461—611no—
387C2×#461—611no—
388C2×#446—611no—
389C2×#440—611no—
390C2×#440—611no—
391C2×C4×Q16—611no—
392C2×C61—82no—
393C2×C61#340014yescomplemented
394C2×C61C2×#55011yescharacteristic
395C2×C61C22×#13711yescharacteristic
396C2×C61C2×#57711yescharacteristic
397D61—82no—
398C22×Q16—611no—
399C22×Q16—611no—
400C22×Q16C2×D6111yescharacteristic
401C22×SD16—611no—
402C22×SD16—611no—
403C22×SD16—611no—
404C22×SD16—611no—
405C22×SD16—611no—
406C22×SD16C2×D6111yescharacteristic
407#559—618no—
408#559—1224no—
409#557—618no—
410#557—1224no—
411C2×C4⋊Q8—611no—
412C2×C4⋊Q8—611no—
413C2×C4⋊Q8—611no—
414C2×#127—611no—
415C2×#125—1221no—
416C2×#125—1221no—
417C2×#125—1221no—
418C2×#124—611no—
419C2×#124—1221no—
420C2×#124C2×D6111yescharacteristic
421C2×#123—1221no—
422C2×#123—1221no—
423C2×C4×Q8—611no—
424C2×C4×Q8—611no—
425C2×C4×Q8—611no—
426C2×C4×Q8—611no—
427C2×C4×Q8—1221no—
428C2×C4×Q8C2×D6111yescharacteristic
429C2×C4×D4—611no—
430C2×C4×D4—611no—
431C2×C4×D4—1221no—
432#497—618no—
433#497—618no—
434#492—618no—
435#464—618no—
436#464C2×D6118yescomplemented
437#462—618no—
438#461—618no—
439#461—618no—
440#460—618no—
441#446—618no—
442#440—618no—
443#440—618no—
444C4×Q16—618no—
445C2×#107—611no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×C4⋊C8C2×D6111yescharacteristic
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103C2×D6111yescharacteristic
453C2×#102—611no—
454C2×#102C2×D6111yescharacteristic
455C2×#97—611no—
456C2×#97—611no—
457C2×C4×C8—611no—
458C61C2×#340011yescharacteristic, complemented, Sylow
459C22×Q8—611no—
460C22×Q8—611no—
461C22×Q8—611no—
462C22×Q8C22×D6111yescharacteristic
463C22×Q8C22×D6111yescharacteristic
464C22×D4—611no—
465C22×D4—1221no—
466C22×D4—1221no—
467C22×D4C22×D6111yescharacteristic
468C23×C4—1221no—
469C23×C4—1221no—
470C2×Q16—42no—
471C2×Q16—614no—
472C2×Q16—614no—
473C2×Q16—1224no—
474C2×Q16—2442no—
475C2×Q16C22×D6114yes—
476C2×SD16—42no—
477C2×SD16—614no—
478C2×SD16—614no—
479C2×SD16—614no—
480C2×SD16—614no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16—1224no—
484C2×SD16—2442no—
485C2×SD16—2442no—
486C2×SD16—2442no—
487C2×SD16C22×D6114yes—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8C22×D6111yescharacteristic
491C22×C8C22×D6111yescharacteristic
492C4⋊Q8—614no—
493C4⋊Q8—614no—
494C4⋊Q8—614no—
495C4⋊Q8—1222no—
496C4⋊Q8—1222no—
497C4⋊Q8—1222no—
498#127—614no—
499#127—1222no—
500#125—1228no—
501#125—1228no—
502#125—1228no—
503#124—22no—
504#124—614no—
505#124—1222no—
506#124—1228no—
507#124C22×D6114yes—
508#123—1228no—
509#123—1228no—
510C4×Q8—22no—
511C4×Q8—614no—
512C4×Q8—614no—
513C4×Q8—614no—
514C4×Q8—614no—
515C4×Q8—614no—
516C4×Q8—1228no—
517C4×Q8—1222no—
518C4×Q8—1222no—
519C4×Q8—1222no—
520C4×Q8C22×D6114yes—
521C4×D4—614no—
522C4×D4—614no—
523C4×D4—1222no—
524C4×D4—1228no—
525C4×D4—1222no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4C22×D6111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C42—21no—
548C2×C42—611no—
549C2×C42—611no—
550C2×C42—1221no—
551C2×C42—1221no—
552C2×C42—1221no—
553C2×C42C22×D6111yescharacteristic
554#107—614no—
555C4⋊C8—614no—
556C4⋊C8—614no—
557C4⋊C8C22×D6114yes—
558#103—614no—
559#103—614no—
560#103—614no—
561#103C22×D6114yes—
562#102—614no—
563#102C22×D6114yes—
564#97—614no—
565#97—614no—
566C4×C8—614no—
567C24—21no—
568C24—1221no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—614no—
576C2×Q8—612no—
577C2×Q8—612no—
578C2×Q8—1224no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8—1222no—
582C2×Q8—1222no—
583C2×Q8—1222no—
584C2×Q8—1222no—
585C2×Q8C23×D6112yes—
586C2×Q8C23×D6112yes—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—612no—
591C2×D4—1224no—
592C2×D4—1224no—
593C2×D4—1221no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—4882no—
597C2×D4—2444no—
598C2×D4C23×D6112yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—1224no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1224no—
611C22×C4—4882no—
612C22×C4—4882no—
613C22×C4D4×D6111yescharacteristic
614C22×C4D4×D6111yescharacteristic
615C22×C4C23×D6111yescharacteristic
616Q16—44no—
617Q16—1228no—
618Q16—2444no—
619SD16—44no—
620SD16—1228no—
621SD16—1228no—
622SD16—2444no—
623SD16—2444no—
624SD16—2444no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—614no—
628C2×C8—612no—
629C2×C8—612no—
630C2×C8—1222no—
631C2×C8C23×D6112yes—
632C2×C8C23×D6112yes—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—614no—
636C4⋊C4—614no—
637C4⋊C4—614no—
638C4⋊C4—612no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1224no—
644C4⋊C4—1224no—
645C4⋊C4—1224no—
646C4⋊C4—1221no—
647C4⋊C4—1224no—
648C4⋊C4—1224no—
649C4⋊C4C23×D6112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C42—24no—
657C42—612no—
658C42—612no—
659C42—612no—
660C42—612no—
661C42—1224no—
662C42—1224no—
663C42—1224no—
664C42D4×D6112yes—
665C42C23×D6112yes—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—1222no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23C2×D4×D6111yescharacteristic
675Q8—22no—
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—42no—
681Q8—1228no—
682Q8—1222no—
683Q8—1222no—
684Q8—1222no—
685Q8—1222no—
686Q8—2442no—
687Q8—2442no—
688D4—22no—
689D4—22no—
690D4—42no—
691D4—1222no—
692D4—1222no—
693D4—4884no—
694D4—2448no—
695D4—2442no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—614no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—4884no—
716C2×C4—4884no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4C2×D4×D6112yes—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4#41×D6112yes—
724C2×C4#1451982212yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—22no—
728C8—614no—
729C8—1222no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—4884no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22#1684043012yes—
739C22#137×D6112yes—
740C22#1684056912yes—
741C22C22×D4×D6111yescharacteristic
742C4—22no—
743C4—22no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—614no—
748C4—1222no—
749C4—1222no—
750C4—1222no—
751C4—2442no—
752C4—2442no—
753C4—2442no—
754C4#1684043012yes—
755C4C2×#41×D6111yescharacteristic
756C4C2×#1451982211yescharacteristic
757C2—82no—
758C2—4882no—
759C2#2145887514yesdirect product factor
760C2C2×#1684043011yescharacteristic
761C2C2×#137×D6111yescharacteristic
762C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
prime radicalC2×#14519773C22
hypercenterC2×#464D61
hypocenterC61C2×#3400
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×#16840490C2semidirect
3. #21458875C2direct (N × H)
4. C2×#16840157C2semidirect
5. C2×#16840155C2semidirect
7. C2×#16839987C2semidirect
8. C2×#16839970C2semidirect
10. C2×#16839968C2semidirect
11. C2×#16839965C2semidirect
12. C2×#16839891C2semidirect
13. C2×#16839860C2semidirect
14. C2×#16839859C2semidirect
15. C2×#16839854C2semidirect
16. C2×C61×#464C2semidirect
27. #16840490C22semidirect
47. #16840157C22semidirect
48. #16840155C22semidirect
50. #16839987C22semidirect
51. #16839970C22semidirect
52. #16839968C22semidirect
53. #16839965C22semidirect
55. #16839891C22semidirect
56. #16839860C22semidirect
57. #16839859C22semidirect
58. #16839854C22semidirect
73. C61×#464C22semidirect
383. C2×#464D61semidirect
393. C2×C61#3400semidirect
436. #464C2×D61semidirect
458. C61C2×#3400semidirect
759. C2#21458875direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404942
C2×#168404902
#214588752
C2×#168401572
C2×#168401552
C2×#168401332
C2×#168399872
C2×#168399702
C2×#168399612
C2×#168399682
C2×#168399652
C2×#168398912
C2×#168398602
C2×#168398592
C2×#168398542
C2×C61×#4642
C2×#340061