Finite Group Databasebeta

← C2×#22619280 #33952612

Subgroups — C2×#22619280 #33952612

Order 18688.

4850 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989385C212yesmaximal, complemented
2C2×#17989133C211yesmaximal, characteristic, complemented
3#22619280C2116yesmaximal, direct product factor
4C2×#17988770C212yesmaximal, complemented
5C2×#17988760C212yesmaximal, complemented
6C2×#17988765C212yesmaximal, complemented
7C2×#17988755C212yesmaximal, complemented
8C22×#14556518C212yesmaximal, complemented
9C2×#17988571C211yesmaximal, characteristic, complemented
10C2×#585×C73C211yesmaximal, characteristic, complemented
11C22×#11924028C2211yescharacteristic, complemented
12#17989385—28no—
13#17989385C22116yescomplemented
14C2×#14556622—22no—
15C2×#14556621C2214yescomplemented
16C2×#14556617—22no—
17C2×#14556616C2214yescomplemented
18C2×#14556611—24no—
19C22×#11924012C2212yescomplemented
20#17989133—24no—
21#17989133C2218yescomplemented
22C2×#14556589C2211yescharacteristic, complemented
23C2×#14556587C2211yescharacteristic, complemented
24C2×#14556580C2211yescharacteristic, complemented
25C2×#14556578C2211yescharacteristic, complemented
26C2×#14556563—22no—
27C2×C4×C22⋊D73—22no—
28C22×C4×Dic73C2211yescharacteristic, complemented
29#17988770C22116yescomplemented
30#17988765C22116yescomplemented
31#17988760C22116yescomplemented
32#17988755C22116yescomplemented
33C2×#14556518C2214yescomplemented
34C2×#14556518C2214yescomplemented
35C2×#14556518C22116yescomplemented
36#17988571C2218yescomplemented
37C2×#14556510C2212yescomplemented
38C2×#14556508C2212yescomplemented
39#585×C73—24no—
40#585×C73—28no—
41#585×C73C2218yescomplemented
42C2×2−1+4×C73—22no—
43C2×2−1+4×C73C2212yes—
44C2×H(5,𝔽2)×C73—22no—
45C2×H(5,𝔽2)×C73—22no—
46C2×H(5,𝔽2)×C73C2212yes—
47C22×#41×C73—24no—
48C22×#41×C73—22no—
49C22×#41×C73C2212yes—
50C22×#41×C73C2211yescharacteristic
51C2×#11924028—22no—
52C2×#11924028—22no—
53C2×#11924028—24no—
54C2×#11924028—22no—
55C2×#11924028C2314yescomplemented
56C22×Dic146C2311yescharacteristic
57C22×D292C2311yescharacteristic
58C22×C22⋊D73—22no—
59C22×C22⋊D73—21no—
60C23×Dic73—21no—
61C22×C4×D73—21no—
62#14556622—216no—
63#14556621—28no—
64#14556621C23116yescomplemented
65#14556617—216no—
66#14556616—28no—
67#14556616C23116yescomplemented
68#14556611—232no—
69C2×#11924018—24no—
70C2×#11924016—24no—
71C2×#11924015—24no—
72C2×#11924013—24no—
73C2×#11924012—22no—
74C2×#11924012—24no—
75C2×#11924012C2314yes—
76C2×#11924012C2318yescomplemented
77C22×#10596831—22no—
78#14556589—22no—
79#14556589C2314yescomplemented
80#14556587—22no—
81#14556587C2314yescomplemented
82#14556580—22no—
83#14556580C2314yescomplemented
84#14556578—22no—
85#14556578C2314yescomplemented
86#14556563—216no—
87C4×C22⋊D73—216no—
88C2×#11924007—22no—
89C2×C22⋊Dic73—22no—
90C2×#11924005—22no—
91C2×C4×Dic73—22no—
92C2×C4×Dic73—21no—
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95C2×C4×Dic73C2314yescomplemented
96#14556518C23116yescomplemented
97#14556518C23116yescomplemented
98#14556510C2318yescomplemented
99#14556508C2318yescomplemented
1002−1+4×C73—216no—
1012−1+4×C73—28no—
1022−1+4×C73—24no—
1032−1+4×C73—216no—
1042−1+4×C73C2318yes—
105H(5,𝔽2)×C73—216no—
106H(5,𝔽2)×C73—216no—
107H(5,𝔽2)×C73—28no—
108H(5,𝔽2)×C73—216no—
109H(5,𝔽2)×C73—24no—
110H(5,𝔽2)×C73—216no—
111H(5,𝔽2)×C73C2318yes—
112C2×#41×C73—24no—
113C2×#41×C73—28no—
114C2×#41×C73—24no—
115C2×#41×C73—232no—
116C2×#41×C73—216no—
117C2×#41×C73—232no—
118C2×#41×C73—24no—
119C2×#41×C73—24no—
120C2×#41×C73—22no—
121C2×#41×C73—22no—
122C2×#41×C73—24no—
123C2×#41×C73—216no—
124C2×#41×C73—22no—
125C2×#41×C73—22no—
126C2×#41×C73—24no—
127C2×#41×C73—24no—
128C2×#41×C73—24no—
129C2×#41×C73D414yes—
130C2×#41×C73D414yescomplemented
131C2×#41×C73D418yescomplemented
132C2×#41×C73C2314yes—
133C2×#41×C73C2318yes—
134C2×#41×C73C2314yes—
135C22×Q8×C73—22no—
136C22×Q8×C73—24no—
137C22×Q8×C73D412yescomplemented
138C22×Q8×C73C2311yescharacteristic
139C22×D4×C73—28no—
140C22×D4×C73—22no—
141C22×D4×C73—24no—
142C22×D4×C73—22no—
143C22×D4×C73—24no—
144C22×D4×C73D412yes—
145C22×D4×C73D412yescomplemented
146C22×D4×C73C2311yescharacteristic
147C23×C4×C73—24no—
148C23×C4×C73—22no—
149C23×C4×C73D412yes—
150C23×C4×C73C2311yescharacteristic
151C23×D73—21no—
152#11924028—28no—
153#11924028—28no—
154#11924028—44no—
155#11924028—44no—
156C2×Dic146—22no—
157C2×Dic146—22no—
158C2×Dic146—21no—
159C2×Dic146C2412yes—
160C2×D292—22no—
161C2×D292—22no—
162C2×D292—21no—
163C2×D292C2412yes—
164C2×C22⋊D73—28no—
165C2×C22⋊D73—24no—
166C2×C22⋊D73—48no—
167C2×C22⋊D73—42no—
168C2×C22⋊D73—42no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—24no—
172C22×Dic73—21no—
173C22×Dic73—44no—
174C2×C4×D73—24no—
175C2×C4×D73—41no—
176C2×C4×D73—42no—
177C2×C4×D73—41no—
178#11924018—216no—
179#11924016—216no—
180#11924015—216no—
181#11924013—216no—
182#11924012—24no—
183#11924012—28no—
184#11924012C2418yes—
185C2×#10596831—24no—
186C2×#10596831—28no—
187#11924007—28no—
188C22⋊Dic73—28no—
189#11924005—28no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—24no—
193C4×Dic73C2412yes—
194C4×Dic73C2412yes—
195C24×C73—24no—
196C24×C73—22no—
197C24×C73C2×D412yes—
198C24×C73C2×D411yescharacteristic
199#41×C73—232no—
200#41×C73—264no—
201#41×C73—216no—
202#41×C73—216no—
203#41×C73—216no—
204#41×C73—232no—
205#41×C73—216no—
206#41×C73—216no—
207#41×C73—28no—
208#41×C73—28no—
209#41×C73—28no—
210#41×C73—28no—
211#41×C73—28no—
212#41×C73—28no—
213#41×C73—28no—
214#41×C73—216no—
215#41×C73—24no—
216#41×C73—28no—
217#41×C73—24no—
218#41×C73—28no—
219#41×C73C2×D418yes—
220#41×C73C2×D4116yescomplemented
221#41×C73C2418yes—
222C2×Q8×C73—24no—
223C2×Q8×C73—216no—
224C2×Q8×C73—216no—
225C2×Q8×C73—216no—
226C2×Q8×C73—22no—
227C2×Q8×C73—24no—
228C2×Q8×C73—22no—
229C2×Q8×C73—22no—
230C2×Q8×C73C2×D414yes—
231C2×Q8×C73C2×D412yes—
232C2×Q8×C73C2×D418yescomplemented
233C2×Q8×C73C2412yes—
234C2×D4×C73—28no—
235C2×D4×C73—24no—
236C2×D4×C73—216no—
237C2×D4×C73—264no—
238C2×D4×C73—216no—
239C2×D4×C73—216no—
240C2×D4×C73—24no—
241C2×D4×C73—24no—
242C2×D4×C73—28no—
243C2×D4×C73—24no—
244C2×D4×C73—24no—
245C2×D4×C73—216no—
246C2×D4×C73—28no—
247C2×D4×C73—216no—
248C2×D4×C73—22no—
249C2×D4×C73—24no—
250C2×D4×C73—22no—
251C2×D4×C73—22no—
252C2×D4×C73C2×D418yes—
253C2×D4×C73C2×D412yes—
254C2×D4×C73C2×D414yes—
255C2×D4×C73C2×D418yescomplemented
256C2×D4×C73C2412yes—
257C22×C4×C73—24no—
258C22×C4×C73—28no—
259C22×C4×C73—232no—
260C22×C4×C73—22no—
261C22×C4×C73—24no—
262C22×C4×C73—22no—
263C22×C4×C73—28no—
264C22×C4×C73—22no—
265C22×C4×C73—24no—
266C22×C4×C73—24no—
267C22×C4×C73—28no—
268C22×C4×C73C2×D412yes—
269C22×C4×C73C2×D418yes—
270C22×C4×C73C2×D411yescharacteristic
271C22×C4×C73C2×D412yes—
272C22×C4×C73C2×D412yes—
273C22×C4×C73C2×D412yes—
274C22×C4×C73C2×D414yes—
275C22×C4×C73C2411yescharacteristic
276C22×C4×C73C2412yes—
277C23×C73—216no—
278C23×C73—22no—
279C23×C73—24no—
280C23×C73—22no—
281C23×C73—28no—
282C23×C73—42no—
283C23×C73—44no—
284C23×C73—84no—
285C23×C73—88no—
286C23×C73#12012yes—
287C23×C73#12012yes—
288C23×C73C22×D411yescharacteristic
289C23×C73C22×D414yes—
290C23×C73C22×D412yes—
291C22×D73—22no—
292C22×D73—44no—
293C22×D73—41no—
294C22×D73—41no—
295Q8×C73—216no—
296Q8×C73—24no—
297Q8×C73—24no—
298Q8×C73—28no—
299Q8×C73—24no—
300Q8×C73C22×D418yes—
301D4×C73—232no—
302D4×C73—216no—
303D4×C73—28no—
304D4×C73—216no—
305D4×C73—216no—
306D4×C73—28no—
307D4×C73—24no—
308D4×C73—24no—
309D4×C73—28no—
310D4×C73—24no—
311D4×C73C22×D418yes—
312C2×C4×C73—216no—
313C2×C4×C73—232no—
314C2×C4×C73—24no—
315C2×C4×C73—22no—
316C2×C4×C73—28no—
317C2×C4×C73—22no—
318C2×C4×C73—216no—
319C2×C4×C73—28no—
320C2×C4×C73—28no—
321C2×C4×C73—28no—
322C2×C4×C73—28no—
323C2×C4×C73#12011yescharacteristic
324C2×C4×C73#12012yes—
325C2×C4×C73#12014yes—
326C2×C4×C73#12014yes—
327C2×C4×C73#12011yescharacteristic
328C2×C4×C73C22×D414yes—
329C2×C4×C73C22×D412yes—
330C2×C4×C73C22×D411yescharacteristic
331C2×C4×C73C22×D412yes—
332C2×C4×C73C22×D414yes—
333C2×C4×C73C22×D412yes—
334C2×C4×C73C22×D414yes—
335C2×C4×C73C2511yescharacteristic
336C22⋊D73—416no—
337C22⋊D73—48no—
338C2×Dic73—24no—
339C2×Dic73—22no—
340C2×Dic73—22no—
341C2×Dic73—22no—
342C2×Dic73—48no—
343C2×Dic73—42no—
344C2×Dic73—41no—
345C2×Dic73—41no—
346D292—24no—
347D292—42no—
348C4×D73—44no—
349C4×D73—44no—
350Dic146—24no—
351Dic146—42no—
352#10596831—28no—
353C22×C73—22no—
354C22×C73—24no—
355C22×C73—24no—
356C22×C73—28no—
357C22×C73—42no—
358C22×C73—42no—
359C22×C73—44no—
360C22×C73—44no—
361C22×C73—48no—
362C22×C73—82no—
363C22×C73—88no—
364C22×C73—816no—
365C22×C73C2×#12011yescharacteristic
366C22×C73C2×#12014yes—
367C22×C73C2×#12011yescharacteristic
368C22×C73C23×D411yescharacteristic
369C2×D73—44no—
370C2×D73—42no—
371C2×D73—82no—
372C2×D73—82no—
373C4×C73—28no—
374C4×C73—24no—
375C4×C73C2×#12012yes—
376C4×C73C2×#12012yes—
377C4×C73C2×#12012yes—
378C4×C73C23×D412yes—
379Dic73—24no—
380Dic73—42no—
381Dic73—42no—
382C2×#3018—731nomaximal, Sylow
383C2×C73—21no—
384C2×C73—21no—
385C2×C73—24no—
386C2×C73—44no—
387C2×C73—48no—
388C2×C73#301812yescomplemented
389C2×C73C22×#12011yescharacteristic
390D73—82no—
391C2×#585D7311yescharacteristic, complemented
392C2×#575—732no—
393C2×#532—731no—
394#3018—7316no—
395C2×#456—732no—
396C2×#454—732no—
397C2×#455—732no—
398C2×#453—732no—
399C22×#104—732no—
400C2×#413—731no—
401C73C2×#301811yescharacteristic, complemented, Sylow
402#585—24no—
403#585—28no—
404#585C2×D7318yescomplemented
405C2×2−1+4—22no—
406C2×2−1+4C2×D7312yes—
407C2×H(5,𝔽2)—22no—
408C2×H(5,𝔽2)—22no—
409C2×H(5,𝔽2)C2×D7312yes—
410C22×#41—24no—
411C22×#41—22no—
412C22×#41—731no—
413C22×#41C2×D7312yes—
414C22×#41C2×D7311yescharacteristic
415#575—7316no—
416#575—1468no—
417C2×#137—734no—
418C2×#137—1462no—
419C2×AGL(1,ℤ/8)—734no—
420C2×AGL(1,ℤ/8)—1462no—
421C2×#135—1464no—
422C22×M16—732no—
423#532—738no—
424#532—1464no—
425C2×C4⋊Q8—731no—
426C2×#127—731no—
427C2×#124—731no—
428C2×#124—731no—
429C2×#121—1462no—
430C2×C4×D4—1462no—
431C22×C42—731no—
432#456—7316no—
433#455—7316no—
434#454—7316no—
435#453—7316no—
436C2×#104—734no—
437C2×#104—734no—
438C2×#104—7316no—
439#413—738no—
440C2×#101—732no—
441C2×#100—732no—
4422−1+4—216no—
4432−1+4—28no—
4442−1+4—24no—
4452−1+4—216no—
4462−1+4C22×D7318yes—
447H(5,𝔽2)—216no—
448H(5,𝔽2)—216no—
449H(5,𝔽2)—28no—
450H(5,𝔽2)—216no—
451H(5,𝔽2)—24no—
452H(5,𝔽2)—216no—
453H(5,𝔽2)C22×D7318yes—
454C2×#41—24no—
455C2×#41—28no—
456C2×#41—24no—
457C2×#41—232no—
458C2×#41—216no—
459C2×#41—232no—
460C2×#41—24no—
461C2×#41—24no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—24no—
465C2×#41—216no—
466C2×#41—22no—
467C2×#41—22no—
468C2×#41—24no—
469C2×#41—24no—
470C2×#41—24no—
471C2×#41—734no—
472C2×#41—1462no—
473C2×#41—1462no—
474C2×#41—1464no—
475C2×#41—1462no—
476C2×#41C22⋊D7314yes—
477C2×#41C22⋊D7314yescomplemented
478C2×#41C22⋊D7318yescomplemented
479C2×#41C22×D7314yes—
480C2×#41C22×D7318yes—
481C2×#41C22×D7314yes—
482C22×Q8—22no—
483C22×Q8—24no—
484C22×Q8—731no—
485C22×Q8C22⋊D7312yescomplemented
486C22×Q8C22×D7311yescharacteristic
487C22×D4—28no—
488C22×D4—22no—
489C22×D4—24no—
490C22×D4—22no—
491C22×D4—24no—
492C22×D4—731no—
493C22×D4—1462no—
494C22×D4—1461no—
495C22×D4C22⋊D7312yes—
496C22×D4C22⋊D7312yescomplemented
497C22×D4C22×D7311yescharacteristic
498C23×C4—24no—
499C23×C4—22no—
500C23×C4—1461no—
501C23×C4—1461no—
502C23×C4C22⋊D7312yes—
503C23×C4C22×D7311yescharacteristic
504#137—7316no—
505#137—1468no—
506#137—14616no—
507AGL(1,ℤ/8)—7316no—
508AGL(1,ℤ/8)—1468no—
509AGL(1,ℤ/8)—14616no—
510#135—14632no—
511C2×Q16—1464no—
512C2×SD16—1464no—
513C2×SD16—1464no—
514C2×D8—1464no—
515C2×M16—734no—
516C2×M16—738no—
517C2×M16—1462no—
518C2×M16—1464no—
519C22×C8—1462no—
520C4⋊Q8—734no—
521C4⋊Q8—1462no—
522#127—734no—
523#127—1462no—
524#124—734no—
525#124—734no—
526#124—1462no—
527#124—1462no—
528#121—14616no—
529C4×D4—14616no—
530C2×C4⋊C4—1462no—
531C2×C22⋊C4—1462no—
532C2×C22⋊C4—1462no—
533C2×C42—731no—
534C2×C42—731no—
535C2×C42—734no—
536C2×C42—1461no—
537C2×C42—1462no—
538#104—7316no—
539#104—7316no—
540#101—738no—
541#100—738no—
542C24—24no—
543C24—22no—
544C24—1461no—
545C24C2×C22⋊D7312yes—
546C24C2×C22⋊D7311yescharacteristic
547#41—232no—
548#41—264no—
549#41—216no—
550#41—216no—
551#41—216no—
552#41—232no—
553#41—216no—
554#41—216no—
555#41—28no—
556#41—28no—
557#41—28no—
558#41—28no—
559#41—28no—
560#41—28no—
561#41—28no—
562#41—216no—
563#41—24no—
564#41—28no—
565#41—24no—
566#41—28no—
567#41—2924no—
568#41—2924no—
569#41—1468no—
570#41—1468no—
571#41C2×C22⋊D7318yes—
572#41C2×C22⋊D73116yescomplemented
573#41C23×D7318yes—
574C2×Q8—24no—
575C2×Q8—216no—
576C2×Q8—216no—
577C2×Q8—216no—
578C2×Q8—22no—
579C2×Q8—24no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—732no—
583C2×Q8—1462no—
584C2×Q8—1462no—
585C2×Q8—1461no—
586C2×Q8C2×C22⋊D7314yes—
587C2×Q8C2×C22⋊D7312yes—
588C2×Q8C2×C22⋊D7318yescomplemented
589C2×Q8C23×D7312yes—
590C2×D4—28no—
591C2×D4—24no—
592C2×D4—216no—
593C2×D4—264no—
594C2×D4—216no—
595C2×D4—216no—
596C2×D4—24no—
597C2×D4—24no—
598C2×D4—28no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—216no—
602C2×D4—28no—
603C2×D4—216no—
604C2×D4—22no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—2922no—
609C2×D4—2922no—
610C2×D4—2928no—
611C2×D4—732no—
612C2×D4—1468no—
613C2×D4—1464no—
614C2×D4—1461no—
615C2×D4—1462no—
616C2×D4—1462no—
617C2×D4C2×C22⋊D7318yes—
618C2×D4C2×C22⋊D7312yes—
619C2×D4C2×C22⋊D7314yes—
620C2×D4C2×C22⋊D7318yescomplemented
621C2×D4C23×D7312yes—
622C22×C4—24no—
623C22×C4—28no—
624C22×C4—232no—
625C22×C4—22no—
626C22×C4—28no—
627C22×C4—22no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—28no—
633C22×C4—2924no—
634C22×C4—2921no—
635C22×C4—2922no—
636C22×C4—2921no—
637C22×C4—1461no—
638C22×C4—1464no—
639C22×C4—1461no—
640C22×C4—1464no—
641C22×C4—1461no—
642C22×C4C2×C22⋊D7312yes—
643C22×C4C2×C22⋊D7318yes—
644C22×C4C2×C22⋊D7312yes—
645C22×C4C2×C22⋊D7311yescharacteristic
646C22×C4C2×C22⋊D7312yes—
647C22×C4C2×C22⋊D7314yes—
648C22×C4C2×C22⋊D7312yes—
649C22×C4C23×D7311yescharacteristic
650C22×C4C23×D7312yes—
651Q16—14616no—
652SD16—14616no—
653SD16—14616no—
654D8—14616no—
655M16—738no—
656M16—1464no—
657M16—1468no—
658C2×C8—1464no—
659C2×C8—1468no—
660C4⋊C4—1468no—
661C22⋊C4—1468no—
662C22⋊C4—1468no—
663C42—732no—
664C42—732no—
665C42—1464no—
666C42—1461no—
667C42—1461no—
668C23—216no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—28no—
673C23—42no—
674C23—44no—
675C23—84no—
676C23—88no—
677C23—2924no—
678C23—2921no—
679C23—2921no—
680C23—1462no—
681C23#1455656012yes—
682C23#1455656012yes—
683C23C22×C22⋊D7311yescharacteristic
684C23C22×C22⋊D7314yes—
685C23C22×C22⋊D7312yes—
686Q8—216no—
687Q8—24no—
688Q8—24no—
689Q8—24no—
690Q8—28no—
691Q8—2922no—
692Q8—1464no—
693Q8C22×C22⋊D7318yes—
694D4—232no—
695D4—216no—
696D4—28no—
697D4—28no—
698D4—216no—
699D4—216no—
700D4—24no—
701D4—24no—
702D4—24no—
703D4—28no—
704D4—2928no—
705D4—29216no—
706D4—2922no—
707D4—1464no—
708D4C22×C22⋊D7318yes—
709C2×C4—216no—
710C2×C4—232no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—28no—
714C2×C4—22no—
715C2×C4—28no—
716C2×C4—216no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—2922no—
721C2×C4—2921no—
722C2×C4—2921no—
723C2×C4—2928no—
724C2×C4—2924no—
725C2×C4—2924no—
726C2×C4—1462no—
727C2×C4—1462no—
728C2×C4—1464no—
729C2×C4—1462no—
730C2×C4#1455656011yescharacteristic
731C2×C4#1455656012yes—
732C2×C4#1455656014yes—
733C2×C4#1455656014yes—
734C2×C4#1455656011yescharacteristic
735C2×C4C22×C22⋊D7314yes—
736C2×C4C22×C22⋊D7312yes—
737C2×C4C22×C22⋊D7314yes—
738C2×C4C22×C22⋊D7312yes—
739C2×C4C22×C22⋊D7314yes—
740C2×C4C22×C22⋊D7312yes—
741C2×C4C22×C22⋊D7311yescharacteristic
742C2×C4C24×D7311yescharacteristic
743C8—1468no—
744C22—22no—
745C22—24no—
746C22—24no—
747C22—28no—
748C22—42no—
749C22—42no—
750C22—44no—
751C22—44no—
752C22—48no—
753C22—82no—
754C22—88no—
755C22—816no—
756C22—2924no—
757C22—2922no—
758C22—5842no—
759C22—5842no—
760C22C2×#1455656011yescharacteristic
761C22C2×#1455656014yes—
762C22C2×#1455656011yescharacteristic
763C22C23×C22⋊D7311yescharacteristic
764C4—28no—
765C4—24no—
766C4—2922no—
767C4—2922no—
768C4—1464no—
769C4C2×#1455656012yes—
770C4C2×#1455656012yes—
771C4C2×#1455656012yes—
772C4C23×C22⋊D7312yes—
773C2—21no—
774C2—21no—
775C2—24no—
776C2—44no—
777C2—48no—
778C2—5842no—
779C2#2261928012yesdirect product factor
780C2C22×#1455656011yescharacteristic
subgroupG/H
centerC2×C4#14556560
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#585×C73C2
socleC22×C73C2×#120
hypercenterC2×#585D73
hypocenterC73C2×#3018
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. C2×#17989385C2semidirect
2. C2×#17989133C2semidirect
3. #22619280C2direct (N × H)
4. C2×#17988770C2semidirect
5. C2×#17988760C2semidirect
6. C2×#17988765C2semidirect
7. C2×#17988755C2semidirect
8. C22×#14556518C2semidirect
9. C2×#17988571C2semidirect
10. C2×#585×C73C2semidirect
11. C22×#11924028C22semidirect
13. #17989385C22semidirect
15. C2×#14556621C22semidirect
17. C2×#14556616C22semidirect
19. C22×#11924012C22semidirect
21. #17989133C22semidirect
22. C2×#14556589C22semidirect
23. C2×#14556587C22semidirect
24. C2×#14556580C22semidirect
25. C2×#14556578C22semidirect
28. C22×C4×Dic73C22semidirect
29. #17988770C22semidirect
30. #17988765C22semidirect
31. #17988760C22semidirect
32. #17988755C22semidirect
33. C2×#14556518C22semidirect
34. C2×#14556518C22semidirect
35. C2×#14556518C22semidirect
36. #17988571C22semidirect
37. C2×#14556510C22semidirect
38. C2×#14556508C22semidirect
41. #585×C73C22semidirect
55. C2×#11924028C23semidirect
64. #14556621C23semidirect
67. #14556616C23semidirect
76. C2×#11924012C23semidirect
79. #14556589C23semidirect
81. #14556587C23semidirect
83. #14556580C23semidirect
85. #14556578C23semidirect
95. C2×C4×Dic73C23semidirect
96. #14556518C23semidirect
97. #14556518C23semidirect
98. #14556510C23semidirect
99. #14556508C23semidirect
130. C2×#41×C73D4semidirect
131. C2×#41×C73D4semidirect
137. C22×Q8×C73D4semidirect
145. C22×D4×C73D4semidirect
220. #41×C73C2×D4semidirect
232. C2×Q8×C73C2×D4semidirect
255. C2×D4×C73C2×D4semidirect
388. C2×C73#3018semidirect
391. C2×#585D73semidirect
401. C73C2×#3018semidirect
404. #585C2×D73semidirect
477. C2×#41C22⋊D73semidirect
478. C2×#41C22⋊D73semidirect
485. C22×Q8C22⋊D73semidirect
496. C22×D4C22⋊D73semidirect
572. #41C2×C22⋊D73semidirect
588. C2×Q8C2×C22⋊D73semidirect
620. C2×D4C2×C22⋊D73semidirect
779. C2#22619280direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893852
C2×#179891332
#226192802
C2×#179887702
C2×#179887602
C2×#179887652
C2×#179887552
C22×#145565182
C2×#179885712
C2×#585×C732
C2×#301873