Finite Group Databasebeta

← C2×#22620497 #33955706

Subgroups — C2×#22620497 #33955706

Order 18688.

2070 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989124C211yesmaximal, characteristic, complemented
2C2×#17989119C211yesmaximal, characteristic, complemented
3#22620497C2116yesmaximal, direct product factor
4C2×#17988987C211yesmaximal, characteristic, complemented
5C2×#17988968C211yesmaximal, characteristic, complemented
6C2×#17988943C211yesmaximal, characteristic, complemented
7C2×#17988940C211yesmaximal, characteristic, complemented
8C2×#17988827C211yesmaximal, characteristic, complemented
9C2×#17988822C211yesmaximal, characteristic
10C2×#17988817C211yesmaximal, characteristic, complemented
11C2×#17988813C211yesmaximal, characteristic, complemented
12C2×C4×#11924018C211yesmaximal, characteristic, complemented
13C2×C4×#11924017C211yesmaximal, characteristic, complemented
14C2×C4×#11924013C211yesmaximal, characteristic, complemented
15C2×C4×C8×D73C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924017C2211yescharacteristic
19C22×#11924013C2211yescharacteristic
20C22×C8×D73C2211yescharacteristic
21C22×C8×D73C2211yescharacteristic
22#17989124—24no—
23#17989124C2218yescomplemented
24#17989119—24no—
25#17989119C2218yescomplemented
26C2×#14556586—21no—
27C2×#14556584—21no—
28C2×#14556582C2211yescharacteristic
29C2×#14556582C2211yescharacteristic
30C2×#14556580C2211yescharacteristic
31C2×#14556578C2211yescharacteristic
32C2×#14556576—21no—
33C2×#14556573—21no—
34C2×#14556571C2211yescharacteristic
35C2×#14556567C2211yescharacteristic
36C2×#14556566C2211yescharacteristic
37C2×#14556562C2211yescharacteristic
38C2×C4×Dic146C2211yescharacteristic
39C2×C4×D292—21no—
40C2×C4×D292C2211yescharacteristic
41C2×C4×C22⋊D73—21no—
42C2×#14556550—21no—
43C2×#14556548—21no—
44C2×C42×D73C2211yescharacteristic
45#17988987C2218yescomplemented
46#17988968C2218yescomplemented
47#17988943C2218yescomplemented
48#17988940C2218yescomplemented
49#17988827C2218yescomplemented
50#17988822C2218yes—
51#17988817C2218yescomplemented
52#17988813C2218yescomplemented
53C4×#11924018C2218yescomplemented
54C4×#11924017C2218yescomplemented
55C4×#11924013C2218yescomplemented
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556523C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×C4×#10596831C2211yescharacteristic
66C2×C8×Dic73C2211yescharacteristic
67C2×C8×Dic73C2211yescharacteristic
68C4×C8×D73C2218yescomplemented
69C22×SD16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72C4×SD16×C73C2218yescomplemented
73C2×#106×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C4×C8×C73C2211yescharacteristic
77C22×Dic146C2311yescharacteristic
78C22×D292—21no—
79C22×D292C2311yescharacteristic
80C22×C22⋊D73—21no—
81C22×C4×D73—21no—
82C22×C4×D73D411yescharacteristic
83C22×C4×D73D411yescharacteristic
84C22×C4×D73C2311yescharacteristic
85C2×#11924018—24no—
86C2×#11924018C2314yes—
87C2×#11924017—24no—
88C2×#11924017C2314yes—
89C2×#11924013—24no—
90C2×#11924013C2314yes—
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2311yescharacteristic
93C2×C8×D73—24no—
94C2×C8×D73—24no—
95C2×C8×D73C2314yes—
96C2×C8×D73C2314yes—
97#14556586—28no—
98#14556584—28no—
99#14556582—22no—
100#14556582—22no—
101#14556582C2314yes—
102#14556582C2314yes—
103#14556580—22no—
104#14556580C2314yes—
105#14556578—22no—
106#14556578C2314yes—
107#14556576—28no—
108#14556573—28no—
109#14556571—22no—
110#14556571C2314yes—
111#14556567—22no—
112#14556567C2314yes—
113#14556566—22no—
114#14556566C2314yes—
115#14556562—22no—
116#14556562C2314yes—
117C4×Dic146—22no—
118C4×Dic146C2314yes—
119C4×D292—28no—
120C4×D292—22no—
121C4×D292C2314yes—
122C4×C22⋊D73—28no—
123#14556550—28no—
124#14556548—28no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73D411yescharacteristic
145C2×C4×Dic73D411yescharacteristic
146C2×C4×Dic73C2311yescharacteristic
147C42×D73D414yes—
148C42×D73C2314yes—
149#14556524C2314yes—
150#14556524C2314yes—
151#14556523C2314yes—
152#14556516C2314yes—
153#14556515C2314yes—
154#14556514C2314yes—
155#14556513C2314yes—
156#14556512C2314yes—
157#14556511C2314yes—
158C4×#10596831C2314yes—
159C8×Dic73C2314yes—
160C8×Dic73C2314yes—
161C22×Q8×C73C2311yescharacteristic
162C22×D4×C73C2311yescharacteristic
163C23×C4×C73—21no—
164C2×SD16×C73—24no—
165C2×SD16×C73C2314yes—
166C22×C8×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168C4×Q8×C73—22no—
169C4×Q8×C73C2314yes—
170C4×D4×C73—22no—
171C4×D4×C73C2314yes—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C22⋊C4×C73—21no—
176C2×C42×C73—21no—
177C2×C42×C73C2311yescharacteristic
178#106×C73C2314yes—
179#103×C73C2314yes—
180#102×C73C2314yes—
181C4×C8×C73C2314yes—
182C23×D73—21no—
183C23×D73C2×D411yescharacteristic
184C2×Dic146—22no—
185C2×Dic146—22no—
186C2×Dic146—21no—
187C2×Dic146C2412yes—
188C2×D292—22no—
189C2×D292—22no—
190C2×D292—24no—
191C2×D292—21no—
192C2×D292—44no—
193C2×D292C2412yes—
194C2×C22⋊D73—24no—
195C2×C22⋊D73—44no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C22×Dic73C2×D411yescharacteristic
202C2×C4×D73—24no—
203C2×C4×D73—24no—
204C2×C4×D73—22no—
205C2×C4×D73—22no—
206C2×C4×D73—24no—
207C2×C4×D73—44no—
208C2×C4×D73C2×D412yes—
209C2×C4×D73C2×D414yes—
210C2×C4×D73C2×D414yes—
211C2×C4×D73C2412yes—
212#11924018—28no—
213#11924017—28no—
214#11924013—28no—
215C2×#10596831—22no—
216C2×#10596831#4114yes—
217C2×#10596831C2412yes—
218C2×#10596831C2412yes—
219C8×D73—28no—
220C8×D73—28no—
221C4⋊Dic73—21no—
222C4⋊Dic73—21no—
223C4⋊Dic73—24no—
224C4⋊Dic73—24no—
225C4⋊Dic73—24no—
226C4⋊Dic73C2412yes—
227C4⋊Dic73C2412yes—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232C22⋊Dic73—24no—
233C22⋊Dic73—24no—
234C22⋊Dic73—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241C4×Dic73—24no—
242C4×Dic73C2×D412yes—
243C4×Dic73C2×D414yes—
244C4×Dic73C2×D414yes—
245C4×Dic73C2412yes—
246C24×C73—21no—
247C2×Q8×C73—21no—
248C2×Q8×C73—22no—
249C2×Q8×C73—22no—
250C2×Q8×C73C2412yes—
251C2×D4×C73—21no—
252C2×D4×C73—22no—
253C2×D4×C73—22no—
254C2×D4×C73C2412yes—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—24no—
259C22×C4×C73—44no—
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2411yescharacteristic
263SD16×C73—28no—
264C2×C8×C73—22no—
265C2×C8×C73#4114yes—
266C2×C8×C73C2412yes—
267C2×C8×C73C2412yes—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73C2412yes—
272C4⋊C4×C73C2412yes—
273C22⋊C4×C73—24no—
274C42×C73—24no—
275C42×C73C2×D412yes—
276C42×C73C2412yes—
277C23×C73—22no—
278C23×C73—42no—
279C23×C73—42no—
280C23×C73—42no—
281C23×C73C22×D411yescharacteristic
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—22no—
285C22×D73—42no—
286C22×D73—42no—
287C22×D73—42no—
288C22×D73#13514yes—
289C22×D73C22×D412yes—
290Q8×C73—22no—
291Q8×C73—22no—
292Q8×C73—42no—
293D4×C73—22no—
294D4×C73—22no—
295D4×C73—42no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—42no—
301C2×C4×C73—42no—
302C2×C4×C73—42no—
303C2×C4×C73—48no—
304C2×C4×C73#13514yes—
305C2×C4×C73C22×D412yes—
306C2×C4×C73C22×D411yescharacteristic
307C2×C4×C73C22×D412yes—
308C2×C4×C73C2×#4112yes—
309C2×C4×C73C2×#4112yes—
310C2×C4×C73C2511yescharacteristic
311C22⋊D73—48no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—42no—
319C2×Dic73—42no—
320C2×Dic73—42no—
321C2×Dic73C22×D412yes—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324D292—22no—
325D292—22no—
326D292—48no—
327D292—42no—
328C4×D73—28no—
329C4×D73—24no—
330C4×D73—28no—
331C4×D73—22no—
332C4×D73—22no—
333C4×D73—48no—
334Dic146—22no—
335Dic146—22no—
336Dic146—42no—
337C8×C73—22no—
338C8×C73C2×#4114yes—
339#10596831—22no—
340#10596831C2×#4114yes—
341C22×C73—42no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—84no—
345C22×C73#53212yes—
346C22×C73C2×#13512yes—
347C22×C73C2×#13512yes—
348C22×C73C23×D411yescharacteristic
349C2×D73—28no—
350C2×D73—22no—
351C2×D73—22no—
352C2×D73—42no—
353C2×D73—42no—
354C2×D73—42no—
355C2×D73—84no—
356C2×D73C2×#13514yes—
357C4×C73—22no—
358C4×C73—42no—
359C4×C73—42no—
360C4×C73—42no—
361C4×C73#53212yes—
362C4×C73C2×#13514yes—
363C4×C73C22×#4111yescharacteristic
364C4×C73C22×#4111yescharacteristic
365Dic73—22no—
366Dic73—22no—
367Dic73—22no—
368Dic73—42no—
369Dic73—42no—
370Dic73—42no—
371C2×#3168—731nomaximal, Sylow
372C2×C73—82no—
373C2×C73#316814yescomplemented
374C2×C73C2×#53211yescharacteristic
375C2×C73C22×#13511yescharacteristic
376C2×C73C22×#13511yescharacteristic
377D73—24no—
378D73—82no—
379C2×#529—731no—
380C2×#529—731no—
381#3168—7316no—
382C2×#499—731no—
383C2×#495—731no—
384C2×#488—731no—
385C2×#488—731no—
386C2×#467—731no—
387C2×#466—731no—
388C2×#465—731no—
389C2×#465—731no—
390C2×C4×Q16—731no—
391C2×C4×SD16—731no—
392C2×C4×SD16D7311yescharacteristic, complemented
393C2×C4×D8—731no—
394C22×C4×C8—731no—
395C73C2×#316811yescharacteristic, complemented, Sylow
396C22×Q16—731no—
397C22×SD16—731no—
398C22×SD16C2×D7311yescharacteristic
399C22×D8—731no—
400C23×C8—731no—
401C23×C8—731no—
402#529—738no—
403#529—738no—
404#529—1464no—
405#529—1464no—
406C2×#126—1461no—
407C2×#126—1461no—
408C2×#125—731no—
409C2×#125—731no—
410C2×#124—731no—
411C2×#124—731no—
412C2×#123—1461no—
413C2×#123—1461no—
414C2×C22⋊Q8—731no—
415C2×C22⋊Q8—731no—
416C2×#121—731no—
417C2×#121—731no—
418C2×C4×Q8—731no—
419C2×C4×Q8C2×D7311yescharacteristic
420C2×C4×D4—731no—
421C2×C4×D4—1461no—
422C2×C4×D4—1461no—
423C2×C4×D4C2×D7311yescharacteristic
424C2×#117—1461no—
425C2×#117—1461no—
426C22×C42—731no—
427#499—738no—
428#495—738no—
429#488—738no—
430#488—738no—
431#467—738no—
432#466—738no—
433#465—738no—
434#465—738no—
435C4×Q16—738no—
436C4×SD16—738no—
437C4×SD16C2×D7318yescomplemented
438C4×D8—738no—
439C2×#107—731no—
440C2×#107—731no—
441C2×#106—731no—
442C2×#106C2×D7311yescharacteristic
443C2×#103—731no—
444C2×#103—731no—
445C2×#103—731no—
446C2×#103C2×D7311yescharacteristic
447C2×#102—731no—
448C2×#102—731no—
449C2×#102—731no—
450C2×#102C2×D7311yescharacteristic
451C2×C4×C8—731no—
452C2×C4×C8—731no—
453C2×C4×C8—731no—
454C2×C4×C8—738no—
455C2×C4×C8C2×D7311yescharacteristic
456C22×Q8—731no—
457C22×Q8C22×D7311yescharacteristic
458C22×D4—731no—
459C22×D4—1461no—
460C22×D4—1461no—
461C22×D4C22×D7311yescharacteristic
462C23×C4—21no—
463C23×C4—731no—
464C23×C4—731no—
465C23×C4—731no—
466C23×C4—1461no—
467C2×Q16—734no—
468C2×Q16—1464no—
469C2×SD16—24no—
470C2×SD16—734no—
471C2×SD16—1464no—
472C2×SD16C22×D7314yes—
473C2×D8—734no—
474C2×D8—1464no—
475C22×C8—731no—
476C22×C8—731no—
477C22×C8—734no—
478C22×C8—734no—
479C22×C8—1464no—
480C22×C8—1464no—
481C22×C8C22×D7311yescharacteristic
482C22×C8C22×D7311yescharacteristic
483#126—1468no—
484#126—1468no—
485#125—734no—
486#125—734no—
487#125—1462no—
488#125—1462no—
489#124—734no—
490#124—734no—
491#124—1462no—
492#124—1462no—
493#123—1468no—
494#123—1468no—
495C22⋊Q8—734no—
496C22⋊Q8—734no—
497C22⋊Q8—1462no—
498C22⋊Q8—1462no—
499#121—734no—
500#121—734no—
501#121—1462no—
502#121—1462no—
503C4×Q8—22no—
504C4×Q8—734no—
505C4×Q8—1462no—
506C4×Q8C22×D7314yes—
507C4×D4—22no—
508C4×D4—734no—
509C4×D4—1468no—
510C4×D4—1468no—
511C4×D4—1462no—
512C4×D4C22×D7314yes—
513#117—1468no—
514#117—1468no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—731no—
517C2×C4⋊C4—731no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4—1461no—
522C2×C4⋊C4—1461no—
523C2×C4⋊C4—1461no—
524C2×C4⋊C4—1461no—
525C2×C4⋊C4C22×D7311yescharacteristic
526C2×C4⋊C4C22×D7311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—1461no—
529C2×C22⋊C4—1461no—
530C2×C22⋊C4—1461no—
531C2×C22⋊C4—1461no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C22⋊C4—1461no—
536C2×C22⋊C4—1461no—
537C2×C42—21no—
538C2×C42—731no—
539C2×C42—731no—
540C2×C42—731no—
541C2×C42—734no—
542C2×C42—734no—
543C2×C42—1461no—
544C2×C42C22×D7311yescharacteristic
545#107—734no—
546#107—734no—
547#106—734no—
548#106C22×D7314yes—
549#103—734no—
550#103—734no—
551#103—734no—
552#103C22×D7314yes—
553#102—734no—
554#102—734no—
555#102—734no—
556#102C22×D7314yes—
557C4×C8—734no—
558C4×C8—734no—
559C4×C8—734no—
560C4×C8C22×D7314yes—
561C24—21no—
562C24—731no—
563C24—1461no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—732no—
568C2×Q8—1462no—
569C2×Q8—1462no—
570C2×Q8—1461no—
571C2×Q8C23×D7312yes—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—2924no—
576C2×D4—2924no—
577C2×D4—732no—
578C2×D4—1464no—
579C2×D4—1464no—
580C2×D4—1461no—
581C2×D4—1462no—
582C2×D4—1462no—
583C2×D4C23×D7312yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—2924no—
590C22×C4—731no—
591C22×C4—731no—
592C22×C4—731no—
593C22×C4—734no—
594C22×C4—732no—
595C22×C4—734no—
596C22×C4—732no—
597C22×C4—1464no—
598C22×C4—1461no—
599C22×C4—1461no—
600C22×C4—1461no—
601C22×C4—1464no—
602C22×C4—1464no—
603C22×C4—1462no—
604C22×C4—1462no—
605C22×C4D4×D7311yescharacteristic
606C22×C4D4×D7311yescharacteristic
607C22×C4C23×D7311yescharacteristic
608Q16—1468no—
609SD16—28no—
610SD16—1468no—
611D8—1468no—
612C2×C8—22no—
613C2×C8—734no—
614C2×C8—732no—
615C2×C8—732no—
616C2×C8—1468no—
617C2×C8—1462no—
618C2×C8—1468no—
619C2×C8#1192402814yes—
620C2×C8C23×D7312yes—
621C2×C8C23×D7312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—732no—
626C4⋊C4—732no—
627C4⋊C4—1464no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1464no—
632C4⋊C4—1464no—
633C4⋊C4—1464no—
634C4⋊C4—1461no—
635C4⋊C4—1461no—
636C4⋊C4C23×D7312yes—
637C4⋊C4C23×D7312yes—
638C22⋊C4—24no—
639C22⋊C4—1464no—
640C22⋊C4—1464no—
641C22⋊C4—1464no—
642C22⋊C4—1464no—
643C22⋊C4—1464no—
644C22⋊C4—1464no—
645C22⋊C4—1464no—
646C22⋊C4—1464no—
647C22⋊C4—1464no—
648C42—24no—
649C42—734no—
650C42—732no—
651C42—734no—
652C42—732no—
653C42—1464no—
654C42D4×D7312yes—
655C42C23×D7312yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—2922no—
661C23—2922no—
662C23—2922no—
663C23—732no—
664C23—734no—
665C23—1462no—
666C23—1462no—
667C23—1462no—
668C23C2×D4×D7311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—2922no—
673Q8—1462no—
674Q8—1462no—
675D4—22no—
676D4—22no—
677D4—42no—
678D4—2928no—
679D4—2928no—
680D4—2922no—
681D4—1462no—
682D4—1462no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—48no—
691C2×C4—2922no—
692C2×C4—2922no—
693C2×C4—2922no—
694C2×C4—2928no—
695C2×C4—732no—
696C2×C4—732no—
697C2×C4—732no—
698C2×C4—1468no—
699C2×C4—1462no—
700C2×C4—1462no—
701C2×C4—1462no—
702C2×C4—1462no—
703C2×C4—1462no—
704C2×C4—1462no—
705C2×C4—1464no—
706C2×C4—1462no—
707C2×C4—1462no—
708C2×C4—1468no—
709C2×C4#1455661214yes—
710C2×C4C2×D4×D7312yes—
711C2×C4C2×D4×D7311yescharacteristic
712C2×C4C2×D4×D7312yes—
713C2×C4#41×D7312yes—
714C2×C4C2×#1192402812yes—
715C2×C4C24×D7311yescharacteristic
716C8—22no—
717C8—734no—
718C8—1462no—
719C8C2×#1192402814yes—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—2922no—
725C22—2922no—
726C22—2922no—
727C22—5844no—
728C22—734no—
729C22—1468no—
730C22—1462no—
731C22—1462no—
732C22#1798913412yes—
733C22#135×D7312yes—
734C22C2×#1455661212yes—
735C22C22×D4×D7311yescharacteristic
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—2922no—
741C4—2922no—
742C4—2922no—
743C4—1462no—
744C4—1462no—
745C4—1462no—
746C4#1798913412yes—
747C4C2×#1455661214yes—
748C4C2×#41×D7311yescharacteristic
749C4C22×#1192402811yescharacteristic
750C2—82no—
751C2—5842no—
752C2—1464no—
753C2#2262049714yesdirect product factor
754C2C2×#1798913411yescharacteristic
755C2C2×#135×D7311yescharacteristic
756C2C22×#1455661211yescharacteristic
subgroupG/H
centerC22×C4D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×C4×SD16×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988822C2
hypercenterC2×C4×SD16D73
hypocenterC73C2×#3168
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#17989124C2semidirect
2. C2×#17989119C2semidirect
3. #22620497C2direct (N × H)
4. C2×#17988987C2semidirect
5. C2×#17988968C2semidirect
6. C2×#17988943C2semidirect
7. C2×#17988940C2semidirect
8. C2×#17988827C2semidirect
10. C2×#17988817C2semidirect
11. C2×#17988813C2semidirect
12. C2×C4×#11924018C2semidirect
13. C2×C4×#11924017C2semidirect
14. C2×C4×#11924013C2semidirect
15. C2×C4×C8×D73C2semidirect
16. C2×C4×SD16×C73C2semidirect
23. #17989124C22semidirect
25. #17989119C22semidirect
45. #17988987C22semidirect
46. #17988968C22semidirect
47. #17988943C22semidirect
48. #17988940C22semidirect
49. #17988827C22semidirect
51. #17988817C22semidirect
52. #17988813C22semidirect
53. C4×#11924018C22semidirect
54. C4×#11924017C22semidirect
55. C4×#11924013C22semidirect
68. C4×C8×D73C22semidirect
72. C4×SD16×C73C22semidirect
373. C2×C73#3168semidirect
392. C2×C4×SD16D73semidirect
395. C73C2×#3168semidirect
437. C4×SD16C2×D73semidirect
753. C2#22620497direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891242
C2×#179891192
#226204972
C2×#179889872
C2×#179889682
C2×#179889432
C2×#179889402
C2×#179888272
C2×#179888222
C2×#179888172
C2×#179888132
C2×C4×#119240182
C2×C4×#119240172
C2×C4×#119240132
C2×C4×C8×D732
C2×C4×SD16×C732
C2×#316873