Finite Group Databasebeta

← C2×#22620221 #33954329

Subgroups — C2×#22620221 #33954329

Order 18688.

2122 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989188C211yesmaximal, characteristic
2C2×#17989063C211yesmaximal, characteristic, complemented
3#22620221C2116yesmaximal, direct product factor
4C2×#17988914C211yesmaximal, characteristic, complemented
5C2×#17988909C211yesmaximal, characteristic, complemented
6C2×#17988896C211yesmaximal, characteristic, complemented
7C2×#17988893C211yesmaximal, characteristic, complemented
8C2×#17988786C211yesmaximal, characteristic, complemented
9C2×#17988785C211yesmaximal, characteristic, complemented
10C2×#17988727C211yesmaximal, characteristic, complemented
11C2×#17988724C211yesmaximal, characteristic, complemented
12C2×#17988689C211yesmaximal, characteristic, complemented
13C2×C4×#11924015C211yesmaximal, characteristic, complemented
14C2×C4×#11924016C211yesmaximal, characteristic, complemented
15C2×#17988649C211yesmaximal, characteristic, complemented
16C2×#440×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18C22×#11924017C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21#17989188—24no—
22#17989188C2218yes—
23C2×#14556587C2211yescharacteristic
24C2×#14556582C2211yescharacteristic
25C2×#14556574—21no—
26C2×#14556573—21no—
27C2×#14556566C2211yescharacteristic
28C2×#14556565—21no—
29C2×#14556564—21no—
30C2×#14556562C2211yescharacteristic
31#17989063—24no—
32#17989063C2218yescomplemented
33C2×Q8×Dic73C2211yescharacteristic
34C2×C4×Dic146—21no—
35C2×C4×Dic146C2211yescharacteristic
36C2×#14556556—21no—
37C2×#14556556C2211yescharacteristic
38C2×C4×D292C2211yescharacteristic
39C2×#14556549—21no—
40C2×#14556549C2211yescharacteristic
41C2×#14556548—21no—
42C2×#14556548C2211yescharacteristic
43#17988914C2218yescomplemented
44#17988909C2218yescomplemented
45#17988896C2218yescomplemented
46#17988893C2218yescomplemented
47#17988786C2218yescomplemented
48#17988785C2218yescomplemented
49#17988727C2218yescomplemented
50#17988724C2218yescomplemented
51#17988689C2218yescomplemented
52C4×#11924015C2218yescomplemented
53C4×#11924016C2218yescomplemented
54#17988649C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C4×#10596831C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72#440×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C2×Q8×D73—24no—
80C2×Q8×D73—22no—
81C2×Q8×D73—24no—
82C2×Q8×D73C2314yes—
83C22×D292—21no—
84C22×D292C2311yescharacteristic
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C22×C22⋊D73—21no—
88C22×C4×D73—21no—
89C22×C4×D73—21no—
90C22×C4×D73C2311yescharacteristic
91C2×#11924017—24no—
92C2×#11924017C2314yes—
93C2×#11924016—24no—
94C2×#11924016C2314yes—
95C2×#11924015—24no—
96C2×#11924015C2314yes—
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2311yescharacteristic
99#14556587—22no—
100#14556587C2314yes—
101#14556582—22no—
102#14556582C2314yes—
103#14556574—28no—
104#14556573—28no—
105#14556566—22no—
106#14556566C2314yes—
107#14556565—28no—
108#14556564—28no—
109#14556562—22no—
110#14556562C2314yes—
111Q8×Dic73—22no—
112Q8×Dic73C2314yes—
113C4×Dic146—28no—
114C4×Dic146—22no—
115C4×Dic146C2314yes—
116#14556556—28no—
117#14556556—22no—
118#14556556C2314yes—
119C4×D292—22no—
120C4×D292C2314yes—
121#14556549—22no—
122#14556549—28no—
123#14556549C2314yes—
124#14556548—28no—
125#14556548D414yes—
126#14556548C2314yes—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73—21no—
129C2×C4⋊Dic73C2311yescharacteristic
130C2×C4⋊Dic73C2311yescharacteristic
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007D411yescharacteristic
135C2×#11924007D411yescharacteristic
136C2×C22⋊Dic73—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005D411yescharacteristic
141C2×#11924005D411yescharacteristic
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73C2311yescharacteristic
147#14556525C2314yes—
148#14556522C2314yes—
149#14556522C2314yes—
150#14556520C2314yes—
151#14556520C2314yes—
152#14556516C2314yes—
153#14556515C2314yes—
154#14556514C2314yes—
155#14556513C2314yes—
156#14556512C2314yes—
157#14556511C2314yes—
158#14556503C2314yes—
159#14556503C2314yes—
160C4×#10596831C2314yes—
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#107×C73C2314yes—
179#103×C73C2314yes—
180#102×C73C2314yes—
181#97×C73C2314yes—
182C23×D73—21no—
183C23×D73C2×D411yescharacteristic
184C2×Dic146—28no—
185C2×Dic146—21no—
186C2×Dic146—22no—
187C2×Dic146—24no—
188C2×Dic146#4114yes—
189C2×Dic146C2412yes—
190Q8×D73—216no—
191Q8×D73—28no—
192Q8×D73—28no—
193C2×D292—22no—
194C2×D292—22no—
195C2×D292—21no—
196C2×D292—24no—
197C2×D292—82no—
198C2×D292C2412yes—
199C2×C22⋊D73—24no—
200C2×C22⋊D73—24no—
201C2×C22⋊D73—24no—
202C2×C22⋊D73—82no—
203C2×C22⋊D73—82no—
204C2×C22⋊D73—82no—
205C22×Dic73—21no—
206C22×Dic73—21no—
207C22×Dic73—21no—
208C22×Dic73C2×D411yescharacteristic
209C22×Dic73C2×D411yescharacteristic
210C22×Dic73C2×D411yescharacteristic
211C2×C4×D73—28no—
212C2×C4×D73—24no—
213C2×C4×D73—22no—
214C2×C4×D73—22no—
215C2×C4×D73—24no—
216C2×C4×D73—82no—
217C2×C4×D73C2×D412yes—
218C2×C4×D73C2412yes—
219#11924017—28no—
220#11924016—28no—
221#11924015—28no—
222C2×#10596831—22no—
223C2×#10596831—22no—
224C2×#10596831C2412yes—
225C2×#10596831C2412yes—
226C4⋊Dic73—21no—
227C4⋊Dic73—21no—
228C4⋊Dic73—24no—
229C4⋊Dic73—24no—
230C4⋊Dic73C2412yes—
231C4⋊Dic73C2412yes—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924007C2×D414yes—
236#11924007C2×D414yes—
237C22⋊Dic73—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005C2×D414yes—
242#11924005C2×D414yes—
243C4×Dic73—24no—
244C4×Dic73—24no—
245C4×Dic73—24no—
246C4×Dic73—24no—
247C4×Dic73C2×D412yes—
248C4×Dic73C2412yes—
249C24×C73—21no—
250C2×Q8×C73—21no—
251C2×Q8×C73—22no—
252C2×Q8×C73#4114yes—
253C2×Q8×C73C2412yes—
254C2×D4×C73—21no—
255C2×D4×C73—22no—
256C2×D4×C73—22no—
257C2×D4×C73C2412yes—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—24no—
262C22×C4×C73—82no—
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2411yescharacteristic
266SD16×C73—28no—
267C2×C8×C73—22no—
268C2×C8×C73—22no—
269C2×C8×C73C2412yes—
270C2×C8×C73C2412yes—
271C4⋊C4×C73—24no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73C2412yes—
275C4⋊C4×C73C2412yes—
276C22⋊C4×C73—24no—
277C42×C73—24no—
278C42×C73C2×D412yes—
279C42×C73C2412yes—
280C23×C73—22no—
281C23×C73—42no—
282C23×C73—42no—
283C23×C73—42no—
284C23×C73C22×D411yescharacteristic
285C22×D73—22no—
286C22×D73—22no—
287C22×D73—22no—
288C22×D73—22no—
289C22×D73—42no—
290C22×D73—42no—
291C22×D73—42no—
292C22×D73C22×D412yes—
293Q8×C73—24no—
294Q8×C73—22no—
295Q8×C73C2×#4114yes—
296D4×C73—22no—
297D4×C73—22no—
298D4×C73—42no—
299C2×C4×C73—24no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—42no—
306C2×C4×C73—42no—
307C2×C4×C73—84no—
308C2×C4×C73C22×D412yes—
309C2×C4×C73C22×D412yes—
310C2×C4×C73C22×D411yescharacteristic
311C2×C4×C73C2×#4112yes—
312C2×C4×C73C2×#4112yes—
313C2×C4×C73C2511yescharacteristic
314C22⋊D73—84no—
315C22⋊D73—84no—
316C22⋊D73—84no—
317C2×Dic73—24no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326C2×Dic73C22×D412yes—
327C2×Dic73C22×D412yes—
328C2×Dic73C22×D412yes—
329D292—22no—
330D292—22no—
331D292—42no—
332D292—84no—
333C4×D73—216no—
334C4×D73—24no—
335C4×D73—22no—
336C4×D73—22no—
337C4×D73—84no—
338Dic146—216no—
339Dic146—24no—
340Dic146—22no—
341Dic146C2×#4114yes—
342C8×C73—22no—
343C8×C73—22no—
344#10596831—22no—
345#10596831—22no—
346C22×C73—42no—
347C22×C73—42no—
348C22×C73—42no—
349C22×C73—84no—
350C22×C73#52512yes—
351C22×C73#57712yes—
352C22×C73#57712yes—
353C22×C73C23×D411yescharacteristic
354C2×D73—22no—
355C2×D73—22no—
356C2×D73—22no—
357C2×D73—44no—
358C2×D73—42no—
359C2×D73—42no—
360C2×D73—42no—
361C2×D73—84no—
362C4×C73—24no—
363C4×C73—22no—
364C4×C73—22no—
365C4×C73—42no—
366C4×C73—42no—
367C4×C73#52512yes—
368C4×C73C22×#4111yescharacteristic
369C4×C73C22×#4111yescharacteristic
370Dic73—22no—
371Dic73—24no—
372Dic73—22no—
373Dic73—22no—
374Dic73—42no—
375Dic73—42no—
376C2×#3126—731nomaximal, Sylow
377C2×C73—82no—
378C2×C73#312614yescomplemented
379C2×C73C2×#52511yescharacteristic
380C2×C73C2×#57711yescharacteristic
381C2×C73C2×#57711yescharacteristic
382D73—42no—
383D73—82no—
384C2×#540—731no—
385C2×#519—731no—
386#3126—7316no—
387C2×#482—731no—
388C2×#482—731no—
389C2×#479—731no—
390C2×#479—731no—
391C2×#460—731no—
392C2×#460—731no—
393C2×#448—731no—
394C2×#448—731no—
395C2×#440—731no—
396C2×#440D7311yescharacteristic, complemented
397C2×C4×SD16—731no—
398C2×C4×SD16—731no—
399C2×#433—731no—
400C73C2×#312611yescharacteristic, complemented, Sylow
401C23×Q8—731no—
402C22×SD16—731no—
403C22×SD16—731no—
404C22×SD16—731no—
405C22×SD16C2×D7311yescharacteristic
406#540—738no—
407#540—1464no—
408C2×#127—731no—
409C2×#125—731no—
410C2×#123—1461no—
411C2×#123—1461no—
412C2×#121—731no—
413C2×#121—731no—
414C2×#121—1461no—
415C2×#121—1461no—
416#519—738no—
417#519—1464no—
418C2×C4×Q8—731no—
419C2×C4×Q8—731no—
420C2×C4×Q8—731no—
421C2×C4×Q8—1461no—
422C2×C4×Q8—1461no—
423C2×C4×Q8C2×D7311yescharacteristic
424C2×C4×D4—731no—
425C2×C4×D4C2×D7311yescharacteristic
426C2×#117—731no—
427C2×#117—731no—
428C2×#117—1461no—
429C2×#117—1461no—
430#482—738no—
431#482—738no—
432#479—738no—
433#479—738no—
434#460—738no—
435#460—738no—
436#448—738no—
437#448—738no—
438#440—738no—
439#440C2×D7318yescomplemented
440C4×SD16—738no—
441C4×SD16—738no—
442#433—738no—
443C2×#107—731no—
444C2×#107C2×D7311yescharacteristic
445C2×#106—731no—
446C2×#106—731no—
447C2×C4⋊C8—731no—
448C2×C4⋊C8—731no—
449C2×#103—731no—
450C2×#103—731no—
451C2×#103—731no—
452C2×#103C2×D7311yescharacteristic
453C2×#102—731no—
454C2×#102—731no—
455C2×#102—731no—
456C2×#102C2×D7311yescharacteristic
457C2×C22⋊C8—731no—
458C2×C22⋊C8—731no—
459C2×#97C2×D7311yescharacteristic
460C2×C4×C8—731no—
461C22×Q8—734no—
462C22×Q8—731no—
463C22×Q8—1461no—
464C22×Q8—1462no—
465C22×Q8—1464no—
466C22×Q8—1464no—
467C22×Q8C22×D7311yescharacteristic
468C22×D4—731no—
469C22×D4—1461no—
470C22×D4—1461no—
471C22×D4—1461no—
472C22×D4—1461no—
473C22×D4C22×D7311yescharacteristic
474C23×C4—21no—
475C23×C4—731no—
476C23×C4—1461no—
477C23×C4—1461no—
478C2×SD16—24no—
479C2×SD16—734no—
480C2×SD16—734no—
481C2×SD16—734no—
482C2×SD16—1464no—
483C2×SD16—1464no—
484C2×SD16—1464no—
485C2×SD16C22×D7314yes—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8C22×D7311yescharacteristic
489C22×C8C22×D7311yescharacteristic
490#127—734no—
491#127—1462no—
492#125—734no—
493#125—1462no—
494#123—1468no—
495#123—1468no—
496#121—734no—
497#121—734no—
498#121—1468no—
499#121—1468no—
500#121—1462no—
501#121—1462no—
502C4×Q8—22no—
503C4×Q8—734no—
504C4×Q8—734no—
505C4×Q8—734no—
506C4×Q8—1468no—
507C4×Q8—1462no—
508C4×Q8—1462no—
509C4×Q8—1468no—
510C4×Q8—1462no—
511C4×Q8C22×D7314yes—
512C4×D4—22no—
513C4×D4—734no—
514C4×D4—1462no—
515C4×D4C22×D7314yes—
516#117—734no—
517#117—734no—
518#117—734no—
519#117—1468no—
520#117—1468no—
521#117—1462no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—731no—
524C2×C4⋊C4—731no—
525C2×C4⋊C4—731no—
526C2×C4⋊C4—731no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4—1461no—
530C2×C4⋊C4—1461no—
531C2×C4⋊C4—1461no—
532C2×C4⋊C4C22×D7311yescharacteristic
533C2×C4⋊C4C22×D7311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—731no—
536C2×C22⋊C4—731no—
537C2×C22⋊C4—1461no—
538C2×C22⋊C4—1461no—
539C2×C22⋊C4—1461no—
540C2×C22⋊C4—1461no—
541C2×C42—21no—
542C2×C42—731no—
543C2×C42—1461no—
544C2×C42—1461no—
545C2×C42—1461no—
546C2×C42—1461no—
547C2×C42C22×D7311yescharacteristic
548#107—734no—
549#107C22×D7314yes—
550#106—734no—
551#106—734no—
552C4⋊C8—734no—
553C4⋊C8—734no—
554#103—734no—
555#103—734no—
556#103—734no—
557#103C22×D7314yes—
558#102—734no—
559#102—734no—
560#102—734no—
561#102C22×D7314yes—
562C22⋊C8—734no—
563C22⋊C8—734no—
564#97C22×D7314yes—
565C4×C8—734no—
566C24—21no—
567C24—731no—
568C24—1461no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—734no—
572C2×Q8—732no—
573C2×Q8—1464no—
574C2×Q8—1468no—
575C2×Q8—1468no—
576C2×Q8—14616no—
577C2×Q8—1468no—
578C2×Q8—1461no—
579C2×Q8—1462no—
580C2×Q8#1192402814yes—
581C2×Q8C23×D7312yes—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—5842no—
586C2×D4—5842no—
587C2×D4—5842no—
588C2×D4—5842no—
589C2×D4—732no—
590C2×D4—1464no—
591C2×D4—1464no—
592C2×D4—1464no—
593C2×D4—1464no—
594C2×D4—1461no—
595C2×D4—1462no—
596C2×D4—1462no—
597C2×D4C23×D7312yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—82no—
603C22×C4—5842no—
604C22×C4—731no—
605C22×C4—731no—
606C22×C4—731no—
607C22×C4—732no—
608C22×C4—732no—
609C22×C4—1464no—
610C22×C4—1468no—
611C22×C4—1461no—
612C22×C4—1461no—
613C22×C4—1464no—
614C22×C4—1461no—
615C22×C4—1462no—
616C22×C4—1462no—
617C22×C4D4×D7311yescharacteristic
618C22×C4D4×D7311yescharacteristic
619C22×C4C23×D7311yescharacteristic
620SD16—28no—
621SD16—1468no—
622SD16—1468no—
623SD16—1468no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—732no—
627C2×C8—732no—
628C2×C8—1462no—
629C2×C8—1462no—
630C2×C8C23×D7312yes—
631C2×C8C23×D7312yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—734no—
636C4⋊C4—734no—
637C4⋊C4—732no—
638C4⋊C4—732no—
639C4⋊C4—1464no—
640C4⋊C4—1464no—
641C4⋊C4—1464no—
642C4⋊C4—1464no—
643C4⋊C4—1464no—
644C4⋊C4—1461no—
645C4⋊C4—1461no—
646C4⋊C4C23×D7312yes—
647C4⋊C4C23×D7312yes—
648C22⋊C4—24no—
649C22⋊C4—734no—
650C22⋊C4—734no—
651C22⋊C4—1464no—
652C22⋊C4—1464no—
653C22⋊C4—1464no—
654C22⋊C4—1464no—
655C42—24no—
656C42—732no—
657C42—732no—
658C42—1464no—
659C42—1464no—
660C42—1464no—
661C42—1464no—
662C42D4×D7312yes—
663C42C23×D7312yes—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—2922no—
669C23—2922no—
670C23—2922no—
671C23—732no—
672C23—1462no—
673C23—1462no—
674C23—1462no—
675C23—1462no—
676C23C2×D4×D7311yescharacteristic
677Q8—22no—
678Q8—24no—
679Q8—734no—
680Q8—14616no—
681Q8—1462no—
682Q8—1464no—
683Q8C2×#1192402814yes—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—2922no—
688D4—5844no—
689D4—5844no—
690D4—5844no—
691D4—5844no—
692D4—1462no—
693D4—1462no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—84no—
703C2×C4—2922no—
704C2×C4—2922no—
705C2×C4—5844no—
706C2×C4—732no—
707C2×C4—732no—
708C2×C4—732no—
709C2×C4—14616no—
710C2×C4—1462no—
711C2×C4—1462no—
712C2×C4—1462no—
713C2×C4—1462no—
714C2×C4—1462no—
715C2×C4—1462no—
716C2×C4—1464no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1464no—
720C2×C4C2×D4×D7312yes—
721C2×C4C2×D4×D7312yes—
722C2×C4C2×D4×D7311yescharacteristic
723C2×C4#41×D7312yes—
724C2×C4C2×#1192402812yes—
725C2×C4C24×D7311yescharacteristic
726C8—22no—
727C8—22no—
728C8—1462no—
729C8—1462no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—2924no—
735C22—2922no—
736C22—2922no—
737C22—2922no—
738C22—5844no—
739C22—1462no—
740C22—1462no—
741C22—1462no—
742C22#1798909612yes—
743C22#1798939612yes—
744C22#1798939712yes—
745C22C22×D4×D7311yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—2922no—
752C4—2922no—
753C4—1462no—
754C4—1462no—
755C4—1462no—
756C4—1464no—
757C4#1798909612yes—
758C4C2×#41×D7311yescharacteristic
759C4C22×#1192402811yescharacteristic
760C2—82no—
761C2—2922no—
762C2—5842no—
763C2#2262022114yesdirect product factor
764C2C2×#1798909611yescharacteristic
765C2C2×#1798939611yescharacteristic
766C2C2×#1798939711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#440×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989188C2
hypercenterC2×#440D73
hypocenterC73C2×#3126
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#17989063C2semidirect
3. #22620221C2direct (N × H)
4. C2×#17988914C2semidirect
5. C2×#17988909C2semidirect
6. C2×#17988896C2semidirect
7. C2×#17988893C2semidirect
8. C2×#17988786C2semidirect
9. C2×#17988785C2semidirect
10. C2×#17988727C2semidirect
11. C2×#17988724C2semidirect
12. C2×#17988689C2semidirect
13. C2×C4×#11924015C2semidirect
14. C2×C4×#11924016C2semidirect
15. C2×#17988649C2semidirect
16. C2×#440×C73C2semidirect
32. #17989063C22semidirect
43. #17988914C22semidirect
44. #17988909C22semidirect
45. #17988896C22semidirect
46. #17988893C22semidirect
47. #17988786C22semidirect
48. #17988785C22semidirect
49. #17988727C22semidirect
50. #17988724C22semidirect
51. #17988689C22semidirect
52. C4×#11924015C22semidirect
53. C4×#11924016C22semidirect
54. #17988649C22semidirect
72. #440×C73C22semidirect
378. C2×C73#3126semidirect
396. C2×#440D73semidirect
400. C73C2×#3126semidirect
439. #440C2×D73semidirect
763. C2#22620221direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891882
C2×#179890632
#226202212
C2×#179889142
C2×#179889092
C2×#179888962
C2×#179888932
C2×#179887862
C2×#179887852
C2×#179887272
C2×#179887242
C2×#179886892
C2×C4×#119240152
C2×C4×#119240162
C2×#179886492
C2×#440×C732
C2×#312673