Finite Group Databasebeta

← C2×#22622981 #33966973

Subgroups — C2×#22622981 #33966973

Order 18688.

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×#17989319C211yesmaximal, characteristic
2C2×#17989312C211yesmaximal, characteristic, complemented
3#22622981C2116yesmaximal, direct product factor
4C2×#17988980C211yesmaximal, characteristic, complemented
5C2×#17988958C211yesmaximal, characteristic
6C2×#17988811C211yesmaximal, characteristic, complemented
7C2×#17988806C211yesmaximal, characteristic, complemented
8C2×#17988795C211yesmaximal, characteristic, complemented
9C2×#17988785C211yesmaximal, characteristic
10C2×#17988790C211yesmaximal, characteristic, complemented
11C2×#17988789C211yesmaximal, characteristic, complemented
12C2×#17988715C211yesmaximal, characteristic, complemented
13C2×#17988689C211yesmaximal, characteristic, complemented
14C2×#17988688C211yesmaximal, characteristic, complemented
15C2×Q16×Dic73C211yesmaximal, characteristic, complemented
16C2×#497×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924017C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21C22×#11924015C2211yescharacteristic
22#17989319—24no—
23#17989319C2218yes—
24#17989312—24no—
25#17989312C2218yescomplemented
26C2×#14556589C2211yescharacteristic
27C2×#14556589C2211yescharacteristic
28C2×#14556587C2211yescharacteristic
29C2×#14556582—21no—
30C2×#14556581—21no—
31C2×#14556581—21no—
32C2×#14556580C2211yescharacteristic
33C2×#14556577—21no—
34C2×#14556575—21no—
35C2×#14556573—21no—
36C2×Q8×Dic73C2211yescharacteristic
37C2×Q8×Dic73C2211yescharacteristic
38C2×Q8×Dic73C2211yescharacteristic
39C2×C4×Dic146C2211yescharacteristic
40C2×C4×Dic146C2211yescharacteristic
41C2×#14556556—21no—
42C2×C4×D292C2211yescharacteristic
43C2×D4×Dic73C2211yescharacteristic
44C2×#14556551—21no—
45#17988980C2218yescomplemented
46#17988958C2218yes—
47#17988811C2218yescomplemented
48#17988806C2218yescomplemented
49#17988795C2218yescomplemented
50#17988790C2218yescomplemented
51#17988789C2218yescomplemented
52#17988785C2218yes—
53#17988715C2218yescomplemented
54#17988689C2218yescomplemented
55#17988688C2218yescomplemented
56Q16×Dic73C2218yescomplemented
57C2×#14556525C2211yescharacteristic
58C2×C4⋊#10596831C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556520C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556515C2211yescharacteristic
65C2×#14556513C2211yescharacteristic
66C2×#14556512C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C22×Q16×C73C2211yescharacteristic
71C22×SD16×C73C2211yescharacteristic
72C22×SD16×C73C2211yescharacteristic
73C2×C4⋊Q8×C73C2211yescharacteristic
74C2×#124×C73C2211yescharacteristic
75#497×C73C2218yescomplemented
76C2×#97×C73C2211yescharacteristic
77C22×Dic146D411yescharacteristic
78C22×Dic146C2311yescharacteristic
79C22×D292C2311yescharacteristic
80C22×C22⋊D73—21no—
81C22×C22⋊D73—21no—
82C23×Dic73—21no—
83C22×C4×D73—21no—
84C2×#11924018—42no—
85C2×#11924018C2314yes—
86C2×#11924017—24no—
87C2×#11924017C2314yes—
88C2×#11924016—42no—
89C2×#11924016C2314yes—
90C2×#11924015—42no—
91C2×#11924015—42no—
92C2×#11924015C2314yes—
93C2×#11924015C2314yes—
94C22×#10596831C2311yescharacteristic
95C22×#10596831C2311yescharacteristic
96#14556589—22no—
97#14556589—22no—
98#14556589C2314yes—
99#14556589C2314yes—
100#14556587—22no—
101#14556587C2314yes—
102#14556582—28no—
103#14556581—28no—
104#14556581—28no—
105#14556580—22no—
106#14556580C2314yes—
107#14556577—28no—
108#14556575—28no—
109#14556573—28no—
110Q8×Dic73—22no—
111Q8×Dic73—22no—
112Q8×Dic73—22no—
113Q8×Dic73C2314yes—
114Q8×Dic73C2314yes—
115Q8×Dic73C2314yes—
116C4×Dic146—22no—
117C4×Dic146D414yes—
118C4×Dic146C2314yes—
119C4×Dic146C2314yes—
120#14556556—28no—
121C4×D292—22no—
122C4×D292C2314yes—
123D4×Dic73—22no—
124D4×Dic73C2314yes—
125#14556551—28no—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73—21no—
129C2×C4⋊Dic73D411yescharacteristic
130C2×C4⋊Dic73C2311yescharacteristic
131C2×C4⋊Dic73C2311yescharacteristic
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007D411yescharacteristic
138C2×#11924007D411yescharacteristic
139C2×C22⋊Dic73—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73—21no—
147C2×C4×Dic73C2311yescharacteristic
148C2×C4×Dic73C2311yescharacteristic
149#14556525C2314yes—
150C4⋊#10596831C2314yes—
151#14556520C2314yes—
152#14556520C2314yes—
153#14556516C2314yes—
154#14556515C2314yes—
155#14556515C2314yes—
156#14556515C2314yes—
157#14556513C2314yes—
158#14556512C2314yes—
159#14556501C2314yes—
160C8×Dic73C2314yes—
161C22×Q8×C73C2311yescharacteristic
162C22×Q8×C73C2311yescharacteristic
163C22×Q8×C73C2311yescharacteristic
164C22×D4×C73C2311yescharacteristic
165C2×Q16×C73—24no—
166C2×Q16×C73—42no—
167C2×Q16×C73C2314yes—
168C2×Q16×C73C2314yes—
169C2×SD16×C73—24no—
170C2×SD16×C73—42no—
171C2×SD16×C73C2314yes—
172C2×SD16×C73C2314yes—
173C22×C8×C73C2311yescharacteristic
174C22×C8×C73C2311yescharacteristic
175C4⋊Q8×C73—22no—
176C4⋊Q8×C73C2314yes—
177#124×C73—22no—
178#124×C73C2314yes—
179C2×C4⋊C4×C73—21no—
180C2×C4⋊C4×C73—21no—
181C2×C22⋊C4×C73—21no—
182C2×C22⋊C4×C73—21no—
183C2×C42×C73C2311yescharacteristic
184#97×C73C2314yes—
185C23×D73—21no—
186C2×Dic146—24no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—21no—
190C2×Dic146C2×D414yes—
191C2×Dic146C2412yes—
192C2×D292—22no—
193C2×D292—22no—
194C2×D292—21no—
195C2×D292C2412yes—
196C2×C22⋊D73—24no—
197C2×C22⋊D73—24no—
198C2×C22⋊D73—44no—
199C2×C22⋊D73—82no—
200C22×Dic73—21no—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—24no—
204C22×Dic73—82no—
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C22×Dic73C2×D411yescharacteristic
208C22×Dic73C2×D411yescharacteristic
209C2×C4×D73—24no—
210C2×C4×D73—82no—
211#11924018—44no—
212#11924017—28no—
213#11924016—44no—
214#11924015—44no—
215#11924015—44no—
216C2×#10596831—22no—
217C2×#10596831—22no—
218C2×#10596831C2412yes—
219C2×#10596831C2412yes—
220C4⋊Dic73—21no—
221C4⋊Dic73—21no—
222C4⋊Dic73—24no—
223C4⋊Dic73—24no—
224C4⋊Dic73—24no—
225C4⋊Dic73C2×D414yes—
226C4⋊Dic73C2412yes—
227C4⋊Dic73C2412yes—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007C2×D414yes—
234#11924007C2×D414yes—
235C22⋊Dic73—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239C4×Dic73—24no—
240C4×Dic73—24no—
241C4×Dic73—24no—
242C4×Dic73—24no—
243C4×Dic73C2×D412yes—
244C4×Dic73C2×D412yes—
245C4×Dic73C2412yes—
246C4×Dic73C2412yes—
247C24×C73—21no—
248C2×Q8×C73—21no—
249C2×Q8×C73—21no—
250C2×Q8×C73—21no—
251C2×Q8×C73—22no—
252C2×Q8×C73—22no—
253C2×Q8×C73—22no—
254C2×Q8×C73—22no—
255C2×Q8×C73—22no—
256C2×Q8×C73—22no—
257C2×Q8×C73C2412yes—
258C2×Q8×C73C2412yes—
259C2×Q8×C73C2412yes—
260C2×D4×C73—21no—
261C2×D4×C73—22no—
262C2×D4×C73—22no—
263C2×D4×C73C2412yes—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73C2×D411yescharacteristic
268C22×C4×C73C2×D411yescharacteristic
269C22×C4×C73C2411yescharacteristic
270Q16×C73—28no—
271Q16×C73—44no—
272SD16×C73—28no—
273SD16×C73—44no—
274C2×C8×C73—22no—
275C2×C8×C73#4114yes—
276C2×C8×C73C2412yes—
277C2×C8×C73C2412yes—
278C4⋊C4×C73—24no—
279C4⋊C4×C73—24no—
280C22⋊C4×C73—24no—
281C22⋊C4×C73—24no—
282C42×C73C2×D412yes—
283C42×C73C2412yes—
284C23×C73—22no—
285C23×C73—42no—
286C23×C73—42no—
287C23×C73—42no—
288C23×C73C22×D411yescharacteristic
289C22×D73—22no—
290C22×D73—42no—
291C22×D73—42no—
292C22×D73—42no—
293Q8×C73—22no—
294Q8×C73—22no—
295Q8×C73—22no—
296Q8×C73—22no—
297Q8×C73—22no—
298Q8×C73—22no—
299Q8×C73—42no—
300Q8×C73—42no—
301Q8×C73—42no—
302D4×C73—22no—
303D4×C73—22no—
304D4×C73—42no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—42no—
311C2×C4×C73—42no—
312C2×C4×C73—42no—
313C2×C4×C73C22×D412yes—
314C2×C4×C73C22×D412yes—
315C2×C4×C73C22×D411yescharacteristic
316C2×C4×C73C2×#4112yes—
317C2×C4×C73H(5,𝔽2)12yes—
318C2×C4×C73C2511yescharacteristic
319C22⋊D73—48no—
320C22⋊D73—84no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—42no—
328C2×Dic73—42no—
329C2×Dic73—42no—
330C2×Dic73—84no—
331C2×Dic73#13714yes—
332C2×Dic73C22×D412yes—
333C2×Dic73C22×D412yes—
334C2×Dic73C22×D412yes—
335C2×Dic73C22×D412yes—
336D292—22no—
337D292—22no—
338D292—42no—
339C4×D73—84no—
340Dic146—28no—
341Dic146—22no—
342Dic146—22no—
343Dic146—42no—
344C8×C73—22no—
345C8×C73C2×#4114yes—
346#10596831—22no—
347#10596831—22no—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—84no—
352C22×C73#55012yes—
353C22×C73C2×#13712yes—
354C22×C73#57712yes—
355C22×C73C23×D411yescharacteristic
356C2×D73—42no—
357C2×D73—42no—
358C2×D73—42no—
359C2×D73—84no—
360C4×C73—22no—
361C4×C73—22no—
362C4×C73—42no—
363C4×C73—42no—
364C4×C73—42no—
365C4×C73#55012yes—
366C4×C73C22×#4111yescharacteristic
367C4×C73C2×H(5,𝔽2)11yescharacteristic
368Dic73—22no—
369Dic73—22no—
370Dic73—22no—
371Dic73—42no—
372Dic73—42no—
373Dic73—42no—
374Dic73C2×#13714yes—
375C2×#3400—731nomaximal, Sylow
376C2×C73—82no—
377C2×C73#340014yescomplemented
378C2×C73C2×#55011yescharacteristic
379C2×C73C22×#13711yescharacteristic
380C2×C73C2×#57711yescharacteristic
381D73—82no—
382C2×#559—731no—
383C2×#557—731no—
384#3400—7316no—
385C2×#497—731no—
386C2×#497D7311yescharacteristic, complemented
387C2×#492—731no—
388C2×#464—731no—
389C2×#464—731no—
390C2×#462—731no—
391C2×#460—731no—
392C2×#461—731no—
393C2×#461—731no—
394C2×#446—731no—
395C2×#440—731no—
396C2×#440—731no—
397C2×C4×Q16—731no—
398C73C2×#340011yescharacteristic, complemented, Sylow
399C22×Q16—731no—
400C22×Q16C2×D7311yescharacteristic
401C22×Q16C2×D7311yescharacteristic
402C22×SD16—731no—
403C22×SD16—731no—
404C22×SD16—731no—
405C22×SD16—731no—
406C22×SD16C2×D7311yescharacteristic
407C22×SD16C2×D7311yescharacteristic
408#559—738no—
409#559—1464no—
410#557—738no—
411#557—1464no—
412C2×C4⋊Q8—731no—
413C2×C4⋊Q8—731no—
414C2×C4⋊Q8C2×D7311yescharacteristic
415C2×#127—731no—
416C2×#125—1461no—
417C2×#125—1461no—
418C2×#125—1461no—
419C2×#124—731no—
420C2×#124—1461no—
421C2×#124C2×D7311yescharacteristic
422C2×#123—1461no—
423C2×#123—1461no—
424C2×C4×Q8—731no—
425C2×C4×Q8—731no—
426C2×C4×Q8—731no—
427C2×C4×Q8—731no—
428C2×C4×Q8—731no—
429C2×C4×Q8—1461no—
430C2×C4×D4—731no—
431C2×C4×D4—731no—
432C2×C4×D4—1461no—
433#497—738no—
434#497C2×D7318yescomplemented
435#492—738no—
436#464—738no—
437#464—738no—
438#462—738no—
439#461—738no—
440#461—738no—
441#460—738no—
442#446—738no—
443#440—738no—
444#440—738no—
445C4×Q16—738no—
446C2×#107—731no—
447C2×C4⋊C8—731no—
448C2×C4⋊C8—731no—
449C2×C4⋊C8—731no—
450C2×#103—731no—
451C2×#103—731no—
452C2×#103—731no—
453C2×#103—731no—
454C2×#102—731no—
455C2×#102—731no—
456C2×#97—731no—
457C2×#97C2×D7311yescharacteristic
458C2×C4×C8—731no—
459C22×Q8—731no—
460C22×Q8—731no—
461C22×Q8C22×D7311yescharacteristic
462C22×Q8C22×D7311yescharacteristic
463C22×Q8C22×D7311yescharacteristic
464C22×D4—731no—
465C22×D4—1461no—
466C22×D4—1461no—
467C22×D4C22×D7311yescharacteristic
468C23×C4—1461no—
469C23×C4—1461no—
470C2×Q16—24no—
471C2×Q16—42no—
472C2×Q16—2922no—
473C2×Q16—734no—
474C2×Q16C22×D7314yes—
475C2×Q16C22×D7314yes—
476C2×SD16—24no—
477C2×SD16—42no—
478C2×SD16—2922no—
479C2×SD16—2922no—
480C2×SD16—2922no—
481C2×SD16—734no—
482C2×SD16—734no—
483C2×SD16—734no—
484C2×SD16—734no—
485C2×SD16—1464no—
486C2×SD16C22×D7314yes—
487C2×SD16C22×D7314yes—
488C22×C8—731no—
489C22×C8—731no—
490C22×C8C22×D7311yescharacteristic
491C22×C8C22×D7311yescharacteristic
492C4⋊Q8—22no—
493C4⋊Q8—734no—
494C4⋊Q8—734no—
495C4⋊Q8—1462no—
496C4⋊Q8—1462no—
497C4⋊Q8C22×D7314yes—
498#127—734no—
499#127—1462no—
500#125—1468no—
501#125—1468no—
502#125—1468no—
503#124—22no—
504#124—734no—
505#124—1462no—
506#124—1468no—
507#124C22×D7314yes—
508#123—1468no—
509#123—1468no—
510C4×Q8—734no—
511C4×Q8—734no—
512C4×Q8—734no—
513C4×Q8—734no—
514C4×Q8—734no—
515C4×Q8—734no—
516C4×Q8—1462no—
517C4×Q8—1462no—
518C4×Q8—1462no—
519C4×Q8—1468no—
520C4×Q8—1462no—
521C4×D4—734no—
522C4×D4—734no—
523C4×D4—1462no—
524C4×D4—1468no—
525C4×D4—1462no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
530C2×C4⋊C4—731no—
531C2×C4⋊C4—731no—
532C2×C4⋊C4—731no—
533C2×C4⋊C4—1461no—
534C2×C4⋊C4—1461no—
535C2×C4⋊C4—1461no—
536C2×C4⋊C4—1461no—
537C2×C4⋊C4—1461no—
538C2×C4⋊C4—1461no—
539C2×C4⋊C4—1461no—
540C2×C4⋊C4—1461no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—1461no—
544C2×C22⋊C4—1461no—
545C2×C22⋊C4—1461no—
546C2×C22⋊C4—1461no—
547C2×C42—731no—
548C2×C42—731no—
549C2×C42—1461no—
550C2×C42—1461no—
551C2×C42—1461no—
552C2×C42—1461no—
553C2×C42C22×D7311yescharacteristic
554#107—734no—
555C4⋊C8—734no—
556C4⋊C8—734no—
557C4⋊C8—734no—
558#103—734no—
559#103—734no—
560#103—734no—
561#103—734no—
562#102—734no—
563#102—734no—
564#97—734no—
565#97C22×D7314yes—
566C4×C8—734no—
567C24—21no—
568C24—1461no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—734no—
579C2×Q8—732no—
580C2×Q8—1464no—
581C2×Q8—1462no—
582C2×Q8—1462no—
583C2×Q8—1461no—
584C2×Q8C23×D7312yes—
585C2×Q8C23×D7312yes—
586C2×Q8C23×D7312yes—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—2924no—
591C2×D4—5842no—
592C2×D4—732no—
593C2×D4—1464no—
594C2×D4—1464no—
595C2×D4—1461no—
596C2×D4—1462no—
597C2×D4—1462no—
598C2×D4C23×D7312yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—5842no—
603C22×C4—5842no—
604C22×C4—731no—
605C22×C4—731no—
606C22×C4—731no—
607C22×C4—731no—
608C22×C4—1461no—
609C22×C4—1461no—
610C22×C4—1461no—
611C22×C4—1464no—
612C22×C4—1464no—
613C22×C4D4×D7311yescharacteristic
614C22×C4D4×D7311yescharacteristic
615C22×C4C23×D7311yescharacteristic
616Q16—28no—
617Q16—44no—
618Q16—2924no—
619SD16—28no—
620SD16—44no—
621SD16—2924no—
622SD16—2924no—
623SD16—2924no—
624SD16—1468no—
625C2×C8—22no—
626C2×C8—732no—
627C2×C8—732no—
628C2×C8—1462no—
629C2×C8—1462no—
630C2×C8#1192402714yes—
631C2×C8C23×D7312yes—
632C2×C8C23×D7312yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—734no—
636C4⋊C4—734no—
637C4⋊C4—734no—
638C4⋊C4—732no—
639C4⋊C4—732no—
640C4⋊C4—1464no—
641C4⋊C4—1464no—
642C4⋊C4—1464no—
643C4⋊C4—1464no—
644C4⋊C4—1464no—
645C4⋊C4—1464no—
646C4⋊C4—1464no—
647C4⋊C4—1464no—
648C4⋊C4—1461no—
649C4⋊C4—1461no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—1464no—
653C22⋊C4—1464no—
654C22⋊C4—1464no—
655C22⋊C4—1464no—
656C42—732no—
657C42—732no—
658C42—732no—
659C42—732no—
660C42—1464no—
661C42—1464no—
662C42—1464no—
663C42—1464no—
664C42D4×D7312yes—
665C42C23×D7312yes—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—2922no—
671C23—2922no—
672C23—2922no—
673C23—1462no—
674C23C2×D4×D7311yescharacteristic
675Q8—22no—
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—42no—
682Q8—42no—
683Q8—42no—
684Q8—2922no—
685Q8—1468no—
686Q8—1462no—
687Q8—1462no—
688D4—22no—
689D4—22no—
690D4—42no—
691D4—2928no—
692D4—2922no—
693D4—5844no—
694D4—1462no—
695D4—1462no—
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—2922no—
705C2×C4—2922no—
706C2×C4—2922no—
707C2×C4—5844no—
708C2×C4—5844no—
709C2×C4—734no—
710C2×C4—732no—
711C2×C4—732no—
712C2×C4—732no—
713C2×C4—732no—
714C2×C4—1462no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4C2×D4×D7312yes—
721C2×C4C2×D4×D7312yes—
722C2×C4C2×D4×D7311yescharacteristic
723C2×C4C2×#1192402712yes—
724C2×C4#1455663612yes—
725C2×C4C24×D7311yescharacteristic
726C8—22no—
727C8—1462no—
728C8—1462no—
729C8C2×#1192402714yes—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—2922no—
735C22—2922no—
736C22—2922no—
737C22—5844no—
738C22#1798925712yes—
739C22#137×D7312yes—
740C22#1798939612yes—
741C22C22×D4×D7311yescharacteristic
742C4—22no—
743C4—22no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—2922no—
748C4—2922no—
749C4—2922no—
750C4—734no—
751C4—1462no—
752C4—1462no—
753C4—1462no—
754C4#1798925712yes—
755C4C22×#1192402711yescharacteristic
756C4C2×#1455663611yescharacteristic
757C2—82no—
758C2—5842no—
759C2#2262298114yesdirect product factor
760C2C2×#1798925711yescharacteristic
761C2C2×#137×D7311yescharacteristic
762C2C2×#1798939611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#497×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556587C22
hypercenterC2×#497D73
hypocenterC73C2×#3400
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
2. C2×#17989312C2semidirect
3. #22622981C2direct (N × H)
4. C2×#17988980C2semidirect
6. C2×#17988811C2semidirect
7. C2×#17988806C2semidirect
8. C2×#17988795C2semidirect
10. C2×#17988790C2semidirect
11. C2×#17988789C2semidirect
12. C2×#17988715C2semidirect
13. C2×#17988689C2semidirect
14. C2×#17988688C2semidirect
15. C2×Q16×Dic73C2semidirect
16. C2×#497×C73C2semidirect
25. #17989312C22semidirect
45. #17988980C22semidirect
47. #17988811C22semidirect
48. #17988806C22semidirect
49. #17988795C22semidirect
50. #17988790C22semidirect
51. #17988789C22semidirect
53. #17988715C22semidirect
54. #17988689C22semidirect
55. #17988688C22semidirect
56. Q16×Dic73C22semidirect
75. #497×C73C22semidirect
377. C2×C73#3400semidirect
386. C2×#497D73semidirect
398. C73C2×#3400semidirect
434. #497C2×D73semidirect
759. C2#22622981direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893192
C2×#179893122
#226229812
C2×#179889802
C2×#179889582
C2×#179888112
C2×#179888062
C2×#179887952
C2×#179887852
C2×#179887902
C2×#179887892
C2×#179887152
C2×#179886892
C2×#179886882
C2×Q16×Dic732
C2×#497×C732
C2×#340073