Finite Group Databasebeta

← C2×#22620485 #33955693

Subgroups — C2×#22620485 #33955693

Order 18688.

2286 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989139C211yesmaximal, characteristic, complemented
2C2×#17989132C211yesmaximal, characteristic
3#22620485C2116yesmaximal, direct product factor
4C2×#17988984C211yesmaximal, characteristic, complemented
5C2×#17988958C211yesmaximal, characteristic, complemented
6C2×#17988936C211yesmaximal, characteristic, complemented
7C2×#17988932C211yesmaximal, characteristic, complemented
8C2×#17988818C211yesmaximal, characteristic, complemented
9C2×#17988816C211yesmaximal, characteristic, complemented
10C2×#17988814C211yesmaximal, characteristic, complemented
11C2×#17988678C211yesmaximal, characteristic, complemented
12C2×SD16×Dic73C211yesmaximal, characteristic, complemented
13C2×#17988674C211yesmaximal, characteristic, complemented
14C2×#17988672C211yesmaximal, characteristic, complemented
15C22×C8×Dic73C211yesmaximal, characteristic, complemented
16C2×#465×C73C211yesmaximal, characteristic, complemented
17C22×#11924027—21no—
18C22×#11924017C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21C23×#10596831C2211yescharacteristic
22#17989139—24no—
23#17989139C2218yescomplemented
24#17989132—24no—
25#17989132C2218yes—
26C2×#14556590C2211yescharacteristic
27C2×#14556590C2211yescharacteristic
28C2×#14556589C2211yescharacteristic
29C2×#14556587C2211yescharacteristic
30C2×#14556581—21no—
31C2×#14556577—21no—
32C2×#14556570C2211yescharacteristic
33C2×#14556568—21no—
34C2×#14556565C2211yescharacteristic
35C2×#14556563—21no—
36C2×Q8×Dic73C2211yescharacteristic
37C2×#14556556—21no—
38C2×#14556556C2211yescharacteristic
39C2×D4×Dic73C2211yescharacteristic
40C2×#14556553C2211yescharacteristic
41C2×#14556551—21no—
42C2×#14556547—21no—
43C22×C4×Dic73C2211yescharacteristic
44#17988984C2218yescomplemented
45#17988958C2218yescomplemented
46#17988936C2218yescomplemented
47#17988932C2218yescomplemented
48#17988818C2218yescomplemented
49#17988816C2218yescomplemented
50#17988814C2218yescomplemented
51#17988678C2218yescomplemented
52SD16×Dic73C2218yescomplemented
53#17988674C2218yescomplemented
54#17988672C2218yescomplemented
55C2×#14556523C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556515C2211yescharacteristic
60C2×#14556514C2211yescharacteristic
61C2×#14556513C2211yescharacteristic
62C2×#14556512C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
64C2×C8×Dic73C2211yescharacteristic
65C2×C8×Dic73C2211yescharacteristic
66C2×C8×Dic73C2211yescharacteristic
67C2×C8×Dic73C2211yescharacteristic
68C2×C8×Dic73C2218yescomplemented
69C22×SD16×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#465×C73C2218yescomplemented
74C2×#106×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C2×#11924027—28no—
78C2×#11924027—48no—
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×Dic146C2311yescharacteristic
82C22×D292C2311yescharacteristic
83C22×C22⋊D73—21no—
84C22×C22⋊D73—21no—
85C22×C22⋊D73—21no—
86C23×Dic73—21no—
87C23×Dic73D411yescharacteristic
88C23×Dic73D411yescharacteristic
89C22×C4×D73—21no—
90C2×#11924017—24no—
91C2×#11924017C2314yes—
92C2×#11924016—24no—
93C2×#11924016C2314yes—
94C2×#11924015—24no—
95C2×#11924015C2314yes—
96C22×#10596831—24no—
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2314yes—
99C22×#10596831C2311yescharacteristic
100#14556590—22no—
101#14556590—22no—
102#14556590C2314yes—
103#14556590C2314yes—
104#14556589—22no—
105#14556589C2314yes—
106#14556587—22no—
107#14556587C2314yes—
108#14556581—28no—
109#14556577—28no—
110#14556570—22no—
111#14556570C2314yes—
112#14556568—28no—
113#14556565—22no—
114#14556565C2314yes—
115#14556563—28no—
116Q8×Dic73—22no—
117Q8×Dic73C2314yes—
118#14556556—22no—
119#14556556—28no—
120#14556556C2314yes—
121D4×Dic73—22no—
122D4×Dic73C2314yes—
123#14556553—22no—
124#14556553C2314yes—
125#14556551—28no—
126#14556547—28no—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×C22⋊Dic73—21no—
137C2×C22⋊Dic73—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73D414yes—
143C2×C4×Dic73D411yescharacteristic
144C2×C4×Dic73D411yescharacteristic
145C2×C4×Dic73C2311yescharacteristic
146C2×C4×Dic73C2314yes—
147C2×C4×Dic73C2311yescharacteristic
148#14556523C2314yes—
149#14556522C2314yes—
150#14556522C2314yes—
151#14556516C2314yes—
152#14556515C2314yes—
153#14556514C2314yes—
154#14556513C2314yes—
155#14556512C2314yes—
156#14556511C2314yes—
157C8×Dic73C2314yes—
158C8×Dic73C2314yes—
159C8×Dic73C2314yes—
160C8×Dic73C2314yes—
161C22×Q8×C73C2311yescharacteristic
162C22×D4×C73—21no—
163C22×D4×C73C2311yescharacteristic
164C23×C4×C73C2311yescharacteristic
165C2×SD16×C73—24no—
166C2×SD16×C73C2314yes—
167C22×C8×C73—24no—
168C22×C8×C73C2311yescharacteristic
169C22×C8×C73C2314yes—
170C22×C8×C73C2311yescharacteristic
171C22⋊Q8×C73—22no—
172C22⋊Q8×C73C2314yes—
173#121×C73—22no—
174#121×C73C2314yes—
175C2×C4⋊C4×C73—21no—
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73—21no—
180#106×C73C2314yes—
181#103×C73C2314yes—
182#102×C73C2314yes—
183C23×D73—21no—
184#11924027—432no—
185C2×Dic146—22no—
186C2×Dic146—22no—
187C2×Dic146—21no—
188C2×Dic146—24no—
189C2×Dic146—24no—
190C2×Dic146—44no—
191C2×Dic146—44no—
192C2×Dic146C2412yes—
193C2×D292—22no—
194C2×D292—22no—
195C2×D292—21no—
196C2×D292C2412yes—
197C2×C22⋊D73—24no—
198C2×C22⋊D73—24no—
199C2×C22⋊D73—24no—
200C2×C22⋊D73—44no—
201C2×C22⋊D73—44no—
202C2×C22⋊D73—44no—
203C22×Dic73—24no—
204C22×Dic73—21no—
205C22×Dic73—21no—
206C22×Dic73—21no—
207C22×Dic73—24no—
208C22×Dic73—44no—
209C22×Dic73SD1618yescomplemented
210C22×Dic73C2×D411yescharacteristic
211C22×Dic73C2×D414yes—
212C22×Dic73C2×D411yescharacteristic
213C22×Dic73C2×D411yescharacteristic
214C22×Dic73C2×D414yes—
215C22×Dic73C2×D411yescharacteristic
216C2×C4×D73—24no—
217C2×C4×D73—44no—
218#11924017—28no—
219#11924016—28no—
220#11924015—28no—
221C2×#10596831—22no—
222C2×#10596831—28no—
223C2×#10596831#4114yescomplemented
224C2×#10596831C2412yes—
225C2×#10596831C2412yes—
226C4⋊Dic73—21no—
227C4⋊Dic73—21no—
228C4⋊Dic73—24no—
229C4⋊Dic73C2412yes—
230C4⋊Dic73C2412yes—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924007—24no—
236#11924007—24no—
237C22⋊Dic73—24no—
238C22⋊Dic73—24no—
239#11924005—24no—
240#11924005—24no—
241C4×Dic73—24no—
242C4×Dic73—24no—
243C4×Dic73C2×D414yes—
244C4×Dic73C2×D412yes—
245C4×Dic73C2×D414yes—
246C4×Dic73C2×D412yes—
247C4×Dic73C2412yes—
248C4×Dic73C2412yes—
249C24×C73—21no—
250C24×C73C2×D411yescharacteristic
251C2×Q8×C73—21no—
252C2×Q8×C73—22no—
253C2×Q8×C73—22no—
254C2×Q8×C73C2412yes—
255C2×D4×C73—24no—
256C2×D4×C73—21no—
257C2×D4×C73—22no—
258C2×D4×C73—22no—
259C2×D4×C73—44no—
260C2×D4×C73C2412yes—
261C22×C4×C73—22no—
262C22×C4×C73—22no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73C2×D411yescharacteristic
267C22×C4×C73C2×D412yes—
268C22×C4×C73C2412yes—
269C22×C4×C73C2411yescharacteristic
270SD16×C73—28no—
271C2×C8×C73—22no—
272C2×C8×C73—28no—
273C2×C8×C73#4114yescomplemented
274C2×C8×C73C2412yes—
275C2×C8×C73C2412yes—
276C4⋊C4×C73—24no—
277C4⋊C4×C73—21no—
278C4⋊C4×C73—21no—
279C4⋊C4×C73C2412yes—
280C4⋊C4×C73C2412yes—
281C22⋊C4×C73—24no—
282C22⋊C4×C73—24no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—42no—
287C23×C73—42no—
288C23×C73—42no—
289C23×C73C2×SD1614yes—
290C23×C73C22×D412yes—
291C23×C73C22×D411yescharacteristic
292C22×D73—22no—
293C22×D73—42no—
294C22×D73—42no—
295C22×D73—42no—
296Q8×C73—22no—
297Q8×C73—22no—
298Q8×C73—42no—
299D4×C73—22no—
300D4×C73—22no—
301D4×C73—48no—
302D4×C73—42no—
303C2×C4×C73—22no—
304C2×C4×C73—24no—
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×D411yescharacteristic
315C2×C4×C73C2×#4112yes—
316C2×C4×C73C2×#4112yes—
317C2×C4×C73C2511yescharacteristic
318C22⋊D73—48no—
319C22⋊D73—48no—
320C22⋊D73—48no—
321C2×Dic73—22no—
322C2×Dic73—28no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—42no—
329C2×Dic73—48no—
330C2×Dic73C2×SD1614yes—
331C2×Dic73C2×SD1614yes—
332C2×Dic73C2×SD16116yescomplemented
333C2×Dic73#13514yes—
334C2×Dic73C22×D412yes—
335C2×Dic73C22×D412yes—
336C2×Dic73C22×D412yes—
337C2×Dic73C22×D412yes—
338D292—22no—
339D292—22no—
340D292—42no—
341C4×D73—48no—
342Dic146—22no—
343Dic146—22no—
344Dic146—42no—
345Dic146—48no—
346Dic146—48no—
347C8×C73—22no—
348C8×C73C2×#4114yescomplemented
349#10596831—22no—
350#10596831C2×#4114yescomplemented
351C22×C73—28no—
352C22×C73—22no—
353C22×C73—22no—
354C22×C73—42no—
355C22×C73—42no—
356C22×C73—42no—
357C22×C73—84no—
358C22×C73#53212yes—
359C22×C73C22×SD1614yes—
360C22×C73C22×SD1612yes—
361C22×C73C2×#13512yes—
362C22×C73C23×D411yescharacteristic
363C2×D73—42no—
364C2×D73—42no—
365C2×D73—42no—
366C2×D73—84no—
367C4×C73—22no—
368C4×C73—42no—
369C4×C73—42no—
370C4×C73—42no—
371C4×C73#53212yes—
372C4×C73C22×#4111yescharacteristic
373C4×C73C22×#4111yescharacteristic
374Dic73—22no—
375Dic73—42no—
376Dic73—42no—
377Dic73—42no—
378Dic73C22×SD1614yes—
379Dic73C22×SD1614yes—
380Dic73C2×#13514yes—
381C2×#3167—731nomaximal, Sylow
382C2×C73—24no—
383C2×C73—82no—
384C2×C73#316714yescomplemented
385C2×C73C2×#53211yescharacteristic
386C2×C73C23×SD1611yescharacteristic
387C2×C73C22×#13511yescharacteristic
388D73—82no—
389C2×#533—731no—
390C2×#532—731no—
391#3167—7316no—
392C2×#498—731no—
393C2×#492—731no—
394C2×#487—731no—
395C2×#486—731no—
396C2×#465—731no—
397C2×#465—731no—
398C2×#465—731no—
399C2×#465D7311yescharacteristic, complemented
400C2×C4×SD16—731no—
401C2×C4×SD16—731no—
402C2×C4×SD16—731no—
403C2×C4×SD16—731no—
404C22×C4×C8—731no—
405C73C2×#316711yescharacteristic, complemented, Sylow
406C22×#41—1461no—
407C22×SD16—731no—
408C22×SD16—731no—
409C22×SD16—731no—
410C22×SD16C2×D7311yescharacteristic
411C23×C8—731no—
412C23×C8C2×D7311yescharacteristic
413#533—738no—
414#533—1464no—
415#532—738no—
416#532—1464no—
417C2×C4⋊Q8—731no—
418C2×C4⋊Q8—731no—
419C2×C4⋊Q8—731no—
420C2×#127—731no—
421C2×#125—1461no—
422C2×#124—1461no—
423C2×C22⋊Q8—731no—
424C2×C22⋊Q8—1461no—
425C2×C22⋊Q8C2×D7311yescharacteristic
426C2×#121—731no—
427C2×#121—1461no—
428C2×#121C2×D7311yescharacteristic
429C2×C4×Q8—731no—
430C2×C4×Q8—731no—
431C2×C4×Q8—1461no—
432C2×C4×D4—731no—
433C2×C4×D4—731no—
434C2×C4×D4—1461no—
435C2×#117—1461no—
436C22×C42—731no—
437#498—738no—
438#492—738no—
439#487—738no—
440#486—738no—
441#465—738no—
442#465—738no—
443#465—738no—
444#465C2×D7318yescomplemented
445C4×SD16—738no—
446C4×SD16—738no—
447C4×SD16—738no—
448C4×SD16—738no—
449C2×#106—731no—
450C2×#106—731no—
451C2×#106—731no—
452C2×#106C2×D7311yescharacteristic
453C2×#103—731no—
454C2×#103—731no—
455C2×#103—731no—
456C2×#103C2×D7311yescharacteristic
457C2×#102—731no—
458C2×#102—731no—
459C2×#102—731no—
460C2×#102C2×D7311yescharacteristic
461C2×C4×C8—731no—
462C2×C4×C8—731no—
463C2×C4×C8—738no—
464C2×C4×C8—731no—
465C2×C4×C8—731no—
466C2×#41—2928no—
467C2×#41—1468no—
468C22×Q8—731no—
469C22×Q8—1461no—
470C22×Q8—1461no—
471C22×Q8C22×D7311yescharacteristic
472C22×D4—21no—
473C22×D4—731no—
474C22×D4—1461no—
475C22×D4—1461no—
476C22×D4—1461no—
477C22×D4C22×D7311yescharacteristic
478C23×C4—731no—
479C23×C4—731no—
480C23×C4—1461no—
481C23×C4—1461no—
482C23×C4C22×D7311yescharacteristic
483C2×SD16—24no—
484C2×SD16—734no—
485C2×SD16—734no—
486C2×SD16—734no—
487C2×SD16—1464no—
488C2×SD16—1464no—
489C2×SD16—1464no—
490C2×SD16C22×D7314yes—
491C22×C8—24no—
492C22×C8—731no—
493C22×C8—731no—
494C22×C8—734no—
495C22×C8—1464no—
496C22×C8C22×D7311yescharacteristic
497C22×C8C22×D7314yes—
498C22×C8C22×D7311yescharacteristic
499C4⋊Q8—734no—
500C4⋊Q8—734no—
501C4⋊Q8—734no—
502C4⋊Q8—1462no—
503C4⋊Q8—1462no—
504C4⋊Q8—1462no—
505#127—734no—
506#127—1462no—
507#125—1468no—
508#124—1468no—
509C22⋊Q8—22no—
510C22⋊Q8—734no—
511C22⋊Q8—1468no—
512C22⋊Q8—1462no—
513C22⋊Q8C22×D7314yes—
514#121—22no—
515#121—734no—
516#121—1468no—
517#121—1462no—
518#121C22×D7314yes—
519C4×Q8—734no—
520C4×Q8—734no—
521C4×Q8—1462no—
522C4×Q8—1468no—
523C4×Q8—1462no—
524C4×D4—734no—
525C4×D4—734no—
526C4×D4—1468no—
527C4×D4—1462no—
528C4×D4—1462no—
529#117—1468no—
530C2×C4⋊C4—21no—
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⋊C4C22×D7311yescharacteristic
541C2×C4⋊C4C22×D7311yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—1461no—
545C2×C22⋊C4—1461no—
546C2×C22⋊C4—1461no—
547C2×C22⋊C4—1461no—
548C2×C42—731no—
549C2×C42—731no—
550C2×C42—734no—
551C2×C42—731no—
552C2×C42—731no—
553C2×C42—734no—
554C2×C42—1461no—
555C2×C42—1461no—
556#106—734no—
557#106—734no—
558#106—734no—
559#106C22×D7314yes—
560#103—734no—
561#103—734no—
562#103—734no—
563#103C22×D7314yes—
564#102—734no—
565#102—734no—
566#102—734no—
567#102C22×D7314yes—
568C4×C8—734no—
569C4×C8—734no—
570C4×C8—734no—
571C4×C8—734no—
572C24—21no—
573C24—1461no—
574C24D4×D7311yescharacteristic
575#41—29232no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—2924no—
580C2×Q8—2924no—
581C2×Q8—732no—
582C2×Q8—1464no—
583C2×Q8—1464no—
584C2×Q8—1462no—
585C2×Q8—1462no—
586C2×Q8—1461no—
587C2×Q8C23×D7312yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—44no—
593C2×D4—2924no—
594C2×D4—2924no—
595C2×D4—2924no—
596C2×D4—732no—
597C2×D4—1464no—
598C2×D4—1464no—
599C2×D4—1464no—
600C2×D4—1461no—
601C2×D4—1462no—
602C2×D4—1462no—
603C2×D4C23×D7312yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—2924no—
610C22×C4—2924no—
611C22×C4—738no—
612C22×C4—734no—
613C22×C4—731no—
614C22×C4—731no—
615C22×C4—731no—
616C22×C4—734no—
617C22×C4—731no—
618C22×C4—1464no—
619C22×C4—1464no—
620C22×C4—1461no—
621C22×C4—1461no—
622C22×C4—1461no—
623C22×C4—1464no—
624C22×C4D4×D7312yes—
625C22×C4D4×D7311yescharacteristic
626C22×C4C23×D7312yes—
627C22×C4C23×D7311yescharacteristic
628SD16—28no—
629SD16—1468no—
630SD16—1468no—
631SD16—1468no—
632C2×C8—22no—
633C2×C8—28no—
634C2×C8—734no—
635C2×C8—732no—
636C2×C8—732no—
637C2×C8—1468no—
638C2×C8—1462no—
639C2×C8#1192402714yescomplemented
640C2×C8C23×D7312yes—
641C2×C8C23×D7312yes—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—732no—
646C4⋊C4—732no—
647C4⋊C4—1464no—
648C4⋊C4—1464no—
649C4⋊C4—1464no—
650C4⋊C4—1464no—
651C4⋊C4—1464no—
652C4⋊C4—1464no—
653C4⋊C4—1464no—
654C4⋊C4—1461no—
655C4⋊C4—1461no—
656C4⋊C4C23×D7312yes—
657C4⋊C4C23×D7312yes—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1464no—
661C22⋊C4—1464no—
662C22⋊C4—1464no—
663C22⋊C4—1464no—
664C42—734no—
665C42—732no—
666C42—734no—
667C42—732no—
668C42—732no—
669C42—732no—
670C42—1464no—
671C42—1464no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—2922no—
679C23—2922no—
680C23—2922no—
681C23—1462no—
682C23SD16×D7314yes—
683C23C2×D4×D7312yes—
684C23C2×D4×D7311yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—2928no—
689Q8—2928no—
690Q8—2922no—
691Q8—1462no—
692Q8—1462no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—42no—
697D4—2928no—
698D4—2928no—
699D4—2928no—
700D4—2922no—
701D4—1462no—
702D4—1462no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—2928no—
714C2×C4—2922no—
715C2×C4—2922no—
716C2×C4—2922no—
717C2×C4—2928no—
718C2×C4—732no—
719C2×C4—732no—
720C2×C4—732no—
721C2×C4—734no—
722C2×C4—734no—
723C2×C4—7316no—
724C2×C4—734no—
725C2×C4—732no—
726C2×C4—1462no—
727C2×C4—1462no—
728C2×C4—1462no—
729C2×C4—1468no—
730C2×C4—1462no—
731C2×C4C2×D4×D7312yes—
732C2×C4C2×D4×D7311yescharacteristic
733C2×C4#41×D7312yes—
734C2×C4C2×#1192402712yes—
735C2×C4C24×D7311yescharacteristic
736C8—22no—
737C8—734no—
738C8—1462no—
739C8C2×#1192402714yescomplemented
740C22—28no—
741C22—22no—
742C22—22no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22—2922no—
748C22—2922no—
749C22—2922no—
750C22—5844no—
751C22#1798913212yes—
752C22C2×SD16×D7314yes—
753C22C2×SD16×D7312yes—
754C22#135×D7312yes—
755C22C22×D4×D7311yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—2922no—
761C4—2922no—
762C4—2922no—
763C4—734no—
764C4—734no—
765C4—734no—
766C4—1462no—
767C4#1798913212yes—
768C4C2×#41×D7311yescharacteristic
769C4C22×#1192402711yescharacteristic
770C2—24no—
771C2—82no—
772C2—5842no—
773C2#2262048514yesdirect product factor
774C2C2×#1798913211yescharacteristic
775C2C22×SD16×D7311yescharacteristic
776C2C2×#135×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#465×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989132C2
hypercenterC2×#465D73
hypocenterC73C2×#3167
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#17989139C2semidirect
3. #22620485C2direct (N × H)
4. C2×#17988984C2semidirect
5. C2×#17988958C2semidirect
6. C2×#17988936C2semidirect
7. C2×#17988932C2semidirect
8. C2×#17988818C2semidirect
9. C2×#17988816C2semidirect
10. C2×#17988814C2semidirect
11. C2×#17988678C2semidirect
12. C2×SD16×Dic73C2semidirect
13. C2×#17988674C2semidirect
14. C2×#17988672C2semidirect
15. C22×C8×Dic73C2semidirect
16. C2×#465×C73C2semidirect
23. #17989139C22semidirect
44. #17988984C22semidirect
45. #17988958C22semidirect
46. #17988936C22semidirect
47. #17988932C22semidirect
48. #17988818C22semidirect
49. #17988816C22semidirect
50. #17988814C22semidirect
51. #17988678C22semidirect
52. SD16×Dic73C22semidirect
53. #17988674C22semidirect
54. #17988672C22semidirect
68. C2×C8×Dic73C22semidirect
73. #465×C73C22semidirect
209. C22×Dic73SD16semidirect
223. C2×#10596831#41semidirect
273. C2×C8×C73#41semidirect
332. C2×Dic73C2×SD16semidirect
348. C8×C73C2×#41semidirect
350. #10596831C2×#41semidirect
384. C2×C73#3167semidirect
399. C2×#465D73semidirect
405. C73C2×#3167semidirect
444. #465C2×D73semidirect
639. C2×C8#11924027semidirect
739. C8C2×#11924027semidirect
773. C2#22620485direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891392
C2×#179891322
#226204852
C2×#179889842
C2×#179889582
C2×#179889362
C2×#179889322
C2×#179888182
C2×#179888162
C2×#179888142
C2×#179886782
C2×SD16×Dic732
C2×#179886742
C2×#179886722
C22×C8×Dic732
C2×#465×C732
C2×#316773