Finite Group Databasebeta

← C2×#22620209 #33954316

Subgroups — C2×#22620209 #33954316

Order 18688.

2134 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×#17989204C211yesmaximal, characteristic, complemented
2C2×#17989070C211yesmaximal, characteristic, complemented
3#22620209C2116yesmaximal, direct product factor
4C2×#17988903C211yesmaximal, characteristic, complemented
5C2×#17988918C211yesmaximal, characteristic, complemented
6C2×#17988870C211yesmaximal, characteristic, complemented
7C2×#17988875C211yesmaximal, characteristic, complemented
8C2×#17988807C211yesmaximal, characteristic, complemented
9C2×#17988800C211yesmaximal, characteristic, complemented
10C2×#17988749C211yesmaximal, characteristic, complemented
11C2×#17988699C211yesmaximal, characteristic, complemented
12C2×#17988691C211yesmaximal, characteristic, complemented
13C2×#17988678C211yesmaximal, characteristic, complemented
14C2×SD16×Dic73C211yesmaximal, characteristic, complemented
15C2×#17988645C211yesmaximal, characteristic, complemented
16C2×#449×C73C211yesmaximal, characteristic
17C22×#11924018C2211yescharacteristic
18C22×#11924016C2211yescharacteristic
19#17989204—24no—
20#17989204C2218yescomplemented
21C2×#14556590C2211yescharacteristic
22C2×#14556584—21no—
23C2×#14556578—21no—
24C2×#14556578C2211yescharacteristic
25C2×#14556572—21no—
26C2×#14556570C2211yescharacteristic
27C2×#14556568—21no—
28#17989070—24no—
29#17989070C2218yescomplemented
30C2×Q8×Dic73C2211yescharacteristic
31C2×Q8×Dic73C2211yescharacteristic
32C2×#14556556C2211yescharacteristic
33C2×D4×Dic73—21no—
34C2×D4×Dic73—21no—
35C2×D4×Dic73C2211yescharacteristic
36C2×D4×Dic73C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic
38C2×#14556550—21no—
39C2×#14556550C2211yescharacteristic
40C22×C4⋊Dic73—21no—
41C22×C4⋊Dic73C2211yescharacteristic
42#17988918C2218yescomplemented
43#17988903C2218yescomplemented
44#17988875C2218yescomplemented
45#17988870C2218yescomplemented
46#17988807C2218yescomplemented
47#17988800C2218yescomplemented
48#17988749C2218yescomplemented
49#17988699C2218yescomplemented
50#17988691C2218yescomplemented
51#17988678C2218yescomplemented
52SD16×Dic73C2218yescomplemented
53#17988645C2218yescomplemented
54C2×#14556523C2211yescharacteristic
55C2×#14556523C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×#41×C73C2211yescharacteristic
70C22×SD16×C73C2211yescharacteristic
71C22×D8×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#449×C73C2218yes—
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C23×Dic73—21no—
80C23×Dic73—21no—
81C23×Dic73—21no—
82C23×Dic73—21no—
83C2×#11924018—24no—
84C2×#11924018C2314yes—
85C2×#11924016—24no—
86C2×#11924016C2314yes—
87C22×#10596831C2311yescharacteristic
88C22×#10596831C2311yescharacteristic
89#14556590—22no—
90#14556590C2314yes—
91#14556584—28no—
92#14556578—28no—
93#14556578—22no—
94#14556578C2314yes—
95#14556572—28no—
96#14556570—22no—
97#14556570C2314yes—
98#14556568—28no—
99Q8×Dic73—22no—
100Q8×Dic73—22no—
101Q8×Dic73C2314yes—
102Q8×Dic73C2314yes—
103#14556556—22no—
104#14556556C2314yes—
105D4×Dic73—28no—
106D4×Dic73—28no—
107D4×Dic73—22no—
108D4×Dic73—22no—
109D4×Dic73—22no—
110D4×Dic73C2314yes—
111D4×Dic73C2314yes—
112D4×Dic73C2314yes—
113#14556550—28no—
114#14556550D414yes—
115#14556550C2314yes—
116C2×C4⋊Dic73—21no—
117C2×C4⋊Dic73—21no—
118C2×C4⋊Dic73—28no—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73—22no—
121C2×C4⋊Dic73D411yescharacteristic
122C2×C4⋊Dic73D411yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2314yes—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×C22⋊Dic73—21no—
131C2×C22⋊Dic73—21no—
132C2×C22⋊Dic73—21no—
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73D411yescharacteristic
137C2×C22⋊Dic73D411yescharacteristic
138C2×C4×Dic73—21no—
139C2×C4×Dic73—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73C2311yescharacteristic
142C2×C4×Dic73C2311yescharacteristic
143#14556523C2314yes—
144#14556523C2314yes—
145#14556522C2314yes—
146#14556522C2314yes—
147#14556520C2314yes—
148#14556520C2314yes—
149#14556516C2314yes—
150#14556516C2314yes—
151#14556515C2314yes—
152#14556512C2314yes—
153#14556512C2314yes—
154#14556512C2314yes—
155C22⋊#10596831C2314yes—
156#14556501C2314yes—
157C8×Dic73C2314yes—
158C2×#41×C73—24no—
159C2×#41×C73—24no—
160C2×#41×C73—22no—
161C2×#41×C73C2314yes—
162C22×Q8×C73C2311yescharacteristic
163C22×D4×C73—21no—
164C22×D4×C73—21no—
165C22×D4×C73C2311yescharacteristic
166C22×D4×C73C2311yescharacteristic
167C23×C4×C73—21no—
168C23×C4×C73C2311yescharacteristic
169C2×SD16×C73—24no—
170C2×SD16×C73C2314yes—
171C2×D8×C73—24no—
172C2×D8×C73C2314yes—
173C22×C8×C73C2311yescharacteristic
174C22×C8×C73C2311yescharacteristic
175#121×C73—22no—
176#121×C73C2314yes—
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C22⋊C4×C73—21no—
179#103×C73C2314yes—
180#102×C73C2314yes—
181C22⋊C8×C73C2314yes—
182C2×Dic146—22no—
183C2×Dic146—22no—
184C2×Dic146—21no—
185C2×Dic146—24no—
186C2×Dic146—82no—
187C2×Dic146C2412yes—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—24no—
193C22×Dic73—24no—
194C22×Dic73—24no—
195C22×Dic73—24no—
196C22×Dic73—82no—
197C22×Dic73—82no—
198C22×Dic73—82no—
199C22×Dic73—82no—
200C22×Dic73C2×D411yescharacteristic
201C22×Dic73C2×D411yescharacteristic
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204#11924018—28no—
205#11924016—28no—
206C2×#10596831—22no—
207C2×#10596831—22no—
208C2×#10596831C2412yes—
209C2×#10596831C2412yes—
210C4⋊Dic73—24no—
211C4⋊Dic73—21no—
212C4⋊Dic73—21no—
213C4⋊Dic73—21no—
214C4⋊Dic73—24no—
215C4⋊Dic73—24no—
216C4⋊Dic73C2×D414yes—
217C4⋊Dic73C2×D414yes—
218C4⋊Dic73C2412yes—
219C4⋊Dic73C2412yes—
220C4⋊Dic73C2412yes—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224C22⋊Dic73—24no—
225C22⋊Dic73—24no—
226C22⋊Dic73—24no—
227C22⋊Dic73—24no—
228C22⋊Dic73—24no—
229C22⋊Dic73—24no—
230C22⋊Dic73C2×D414yes—
231C22⋊Dic73C2×D414yes—
232C4×Dic73—24no—
233C4×Dic73—24no—
234C4×Dic73—24no—
235C4×Dic73C2×D412yes—
236C4×Dic73C2×D412yes—
237C4×Dic73C2412yes—
238C4×Dic73C2412yes—
239C24×C73—21no—
240C24×C73—21no—
241C24×C73C2×D411yescharacteristic
242#41×C73—216no—
243#41×C73—28no—
244#41×C73—28no—
245C2×Q8×C73—21no—
246C2×Q8×C73—22no—
247C2×Q8×C73#4114yes—
248C2×Q8×C73C2412yes—
249C2×D4×C73—28no—
250C2×D4×C73—24no—
251C2×D4×C73—24no—
252C2×D4×C73—21no—
253C2×D4×C73—21no—
254C2×D4×C73—22no—
255C2×D4×C73—22no—
256C2×D4×C73—22no—
257C2×D4×C73—82no—
258C2×D4×C73#4114yes—
259C2×D4×C73C2412yes—
260C2×D4×C73C2412yes—
261C22×C4×C73—28no—
262C22×C4×C73—21no—
263C22×C4×C73—24no—
264C22×C4×C73—22no—
265C22×C4×C73—22no—
266C22×C4×C73—21no—
267C22×C4×C73C2×D411yescharacteristic
268C22×C4×C73C2×D412yes—
269C22×C4×C73C2412yes—
270C22×C4×C73C2411yescharacteristic
271SD16×C73—28no—
272D8×C73—28no—
273C2×C8×C73—22no—
274C2×C8×C73—22no—
275C2×C8×C73C2412yes—
276C2×C8×C73C2412yes—
277C4⋊C4×C73—21no—
278C4⋊C4×C73C2412yes—
279C22⋊C4×C73—24no—
280C23×C73—22no—
281C23×C73—24no—
282C23×C73—22no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—42no—
287C23×C73—42no—
288C23×C73—42no—
289C23×C73—42no—
290C23×C73—42no—
291C23×C73C22×D412yes—
292C23×C73C22×D411yescharacteristic
293Q8×C73—24no—
294Q8×C73—22no—
295Q8×C73C2×#4114yes—
296D4×C73—216no—
297D4×C73—24no—
298D4×C73—22no—
299D4×C73—22no—
300D4×C73—22no—
301D4×C73—42no—
302D4×C73—84no—
303D4×C73C2×#4114yes—
304C2×C4×C73—216no—
305C2×C4×C73—22no—
306C2×C4×C73—24no—
307C2×C4×C73—22no—
308C2×C4×C73—24no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—42no—
313C2×C4×C73C22×D412yes—
314C2×C4×C73C22×D411yescharacteristic
315C2×C4×C73C2×#4112yes—
316C2×C4×C73C2×#4112yes—
317C2×C4×C73C2511yescharacteristic
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—42no—
329C2×Dic73—42no—
330C2×Dic73—84no—
331C2×Dic73—84no—
332C2×Dic73—84no—
333C2×Dic73—84no—
334C2×Dic73C22×D412yes—
335C2×Dic73C22×D412yes—
336C2×Dic73C22×D412yes—
337C2×Dic73C22×D412yes—
338Dic146—22no—
339Dic146—22no—
340Dic146—42no—
341Dic146—84no—
342C8×C73—22no—
343C8×C73—22no—
344#10596831—22no—
345#10596831—22no—
346C22×C73—22no—
347C22×C73—24no—
348C22×C73—22no—
349C22×C73—22no—
350C22×C73—44no—
351C22×C73—48no—
352C22×C73—42no—
353C22×C73—42no—
354C22×C73—42no—
355C22×C73—42no—
356C22×C73—42no—
357C22×C73—84no—
358C22×C73#52512yes—
359C22×C73#57712yes—
360C22×C73#57712yes—
361C22×C73C23×D411yescharacteristic
362C4×C73—22no—
363C4×C73—24no—
364C4×C73—42no—
365C4×C73#52512yes—
366C4×C73C22×#4111yescharacteristic
367C4×C73C22×#4111yescharacteristic
368Dic73—22no—
369Dic73—22no—
370Dic73—22no—
371Dic73—22no—
372Dic73—42no—
373Dic73—42no—
374Dic73—42no—
375Dic73—42no—
376C2×#3125—731nomaximal, Sylow
377C2×C73—42no—
378C2×C73—44no—
379C2×C73—82no—
380C2×C73#312514yescomplemented
381C2×C73C2×#52511yescharacteristic
382C2×C73C2×#57711yescharacteristic
383C2×C73C2×#57711yescharacteristic
384C2×#542—731no—
385C2×#520—731no—
386#3125—7316no—
387C2×#481—731no—
388C2×#483—731no—
389C2×#475—731no—
390C2×#476—731no—
391C2×#464—731no—
392C2×#463—731no—
393C2×#452—731no—
394C2×#449D7311yescharacteristic
395C2×#442—731no—
396C2×#441—731no—
397C2×C4×SD16—731no—
398C2×C4×SD16—731no—
399C2×#433—731no—
400C73C2×#312511yescharacteristic, complemented, Sylow
401C22×#41C2×D7311yescharacteristic
402C22×Q16—731no—
403C22×SD16—731no—
404C22×SD16C2×D7311yescharacteristic
405C22×D8C2×D7311yescharacteristic
406#542—738no—
407#542—1464no—
408C2×C4⋊Q8—731no—
409C2×#126—1461no—
410C2×#124—731no—
411C2×#124—1461no—
412C2×#123—1461no—
413C2×C22⋊Q8—731no—
414C2×C22⋊Q8—1461no—
415C2×#121C2×D7311yescharacteristic
416#520—738no—
417#520—1464no—
418C2×C4×Q8—731no—
419C2×C4×Q8—731no—
420C2×C4×Q8—731no—
421C2×C4×D4—731no—
422C2×C4×D4—731no—
423C2×C4×D4—731no—
424C2×C4×D4—1461no—
425C2×C4×D4—1461no—
426C2×#117—731no—
427C2×#117—1461no—
428C22×C4⋊C4—731no—
429C22×C4⋊C4—1461no—
430#483—738no—
431#481—738no—
432#476—738no—
433#475—738no—
434#464—738no—
435#463—738no—
436#452—738no—
437#449C2×D7318yes—
438#442—738no—
439#441—738no—
440C4×SD16—738no—
441C4×SD16—738no—
442#433—738no—
443C2×#106—731no—
444C2×#106—731no—
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⋊C8C2×D7311yescharacteristic
459C2×#97—731no—
460C2×C4×C8—731no—
461C2×#41—24no—
462C2×#41—24no—
463C2×#41—22no—
464C2×#41C22×D7314yes—
465C22×Q8—731no—
466C22×Q8—1461no—
467C22×Q8C22×D7311yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4C22×D7311yescharacteristic
471C22×D4C22×D7311yescharacteristic
472C23×C4—21no—
473C23×C4—1461no—
474C23×C4—1461no—
475C23×C4—1461no—
476C23×C4—1461no—
477C23×C4C22×D7311yescharacteristic
478C2×Q16—734no—
479C2×Q16—1464no—
480C2×SD16—24no—
481C2×SD16—734no—
482C2×SD16—1464no—
483C2×SD16C22×D7314yes—
484C2×D8—24no—
485C2×D8C22×D7314yes—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8C22×D7311yescharacteristic
489C22×C8C22×D7311yescharacteristic
490C4⋊Q8—734no—
491C4⋊Q8—1462no—
492#126—1468no—
493#124—734no—
494#124—1462no—
495#124—1468no—
496#123—1468no—
497C22⋊Q8—734no—
498C22⋊Q8—1468no—
499C22⋊Q8—1462no—
500#121—22no—
501#121C22×D7314yes—
502C4×Q8—734no—
503C4×Q8—734no—
504C4×Q8—734no—
505C4×Q8—1462no—
506C4×Q8—1462no—
507C4×Q8—1462no—
508C4×D4—734no—
509C4×D4—734no—
510C4×D4—734no—
511C4×D4—1462no—
512C4×D4—1462no—
513C4×D4—1462no—
514C4×D4—1468no—
515C4×D4—1468no—
516#117—734no—
517#117—734no—
518#117—1468no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—734no—
524C2×C4⋊C4—731no—
525C2×C4⋊C4—1468no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4—1461no—
530C2×C4⋊C4—1461no—
531C2×C4⋊C4—1462no—
532C2×C4⋊C4—1461no—
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×C22⋊C4—1461no—
542C2×C22⋊C4—1461no—
543C2×C42—731no—
544C2×C42—731no—
545C2×C42—1461no—
546C2×C42—1461no—
547C2×C42—1461no—
548#106—734no—
549#106—734no—
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⋊C8C22×D7314yes—
564#97—734no—
565C4×C8—734no—
566C24—21no—
567C24—21no—
568C24D4×D7311yescharacteristic
569#41—216no—
570#41—28no—
571#41—28no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—5842no—
575C2×Q8—732no—
576C2×Q8—1464no—
577C2×Q8—1462no—
578C2×Q8—1462no—
579C2×Q8—1461no—
580C2×Q8#1192402714yes—
581C2×Q8C23×D7312yes—
582C2×D4—28no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—82no—
591C2×D4#1192402714yes—
592C2×D4C23×D7312yes—
593C2×D4C23×D7312yes—
594C22×C4—28no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—5842no—
601C22×C4—5842no—
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—1461no—
612C22×C4—1464no—
613C22×C4—1464no—
614C22×C4—1464no—
615C22×C4—1464no—
616C22×C4D4×D7312yes—
617C22×C4D4×D7311yescharacteristic
618C22×C4C23×D7312yes—
619C22×C4C23×D7311yescharacteristic
620Q16—1468no—
621SD16—28no—
622SD16—1468no—
623D8—28no—
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—21no—
633C4⋊C4—734no—
634C4⋊C4—734no—
635C4⋊C4—732no—
636C4⋊C4—732no—
637C4⋊C4—732no—
638C4⋊C4—1464no—
639C4⋊C4—1464no—
640C4⋊C4—1464no—
641C4⋊C4—1464no—
642C4⋊C4—1464no—
643C4⋊C4—1464no—
644C4⋊C4—1461no—
645C4⋊C4—1461no—
646C4⋊C4—1461no—
647C4⋊C4C23×D7312yes—
648C22⋊C4—24no—
649C22⋊C4—734no—
650C22⋊C4—734no—
651C22⋊C4—1464no—
652C22⋊C4—1464no—
653C22⋊C4—1464no—
654C22⋊C4—1464no—
655C22⋊C4—1464no—
656C22⋊C4—1464no—
657C42—732no—
658C42—732no—
659C42—732no—
660C42—732no—
661C42—1464no—
662C42—1464no—
663C42—1464no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23C2×D4×D7312yes—
676C23C2×D4×D7311yescharacteristic
677Q8—22no—
678Q8—24no—
679Q8—2922no—
680Q8—5844no—
681Q8—1462no—
682Q8—1462no—
683Q8C2×#1192402714yes—
684D4—216no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—24no—
689D4—42no—
690D4—84no—
691D4C2×#1192402714yes—
692C2×C4—216no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—2922no—
702C2×C4—2922no—
703C2×C4—2922no—
704C2×C4—2922no—
705C2×C4—5844no—
706C2×C4—5844no—
707C2×C4—5844no—
708C2×C4—5844no—
709C2×C4—732no—
710C2×C4—732no—
711C2×C4—732no—
712C2×C4—732no—
713C2×C4—1462no—
714C2×C4—1462no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4—1462no—
721C2×C4C2×D4×D7312yes—
722C2×C4C2×D4×D7311yescharacteristic
723C2×C4C2×#1192402712yes—
724C2×C4C2×#1192402712yes—
725C2×C4C24×D7311yescharacteristic
726C8—22no—
727C8—22no—
728C8—1462no—
729C8—1462no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—44no—
735C22—48no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—84no—
742C22#1798909312yes—
743C22#1798939412yes—
744C22#1798939712yes—
745C22C22×D4×D7311yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—2922no—
750C4—2922no—
751C4—2922no—
752C4—2922no—
753C4—1462no—
754C4—1462no—
755C4—1462no—
756C4—1462no—
757C4#1798909312yes—
758C4C22×#1192402711yescharacteristic
759C4C22×#1192402711yescharacteristic
760C2—42no—
761C2—44no—
762C2—82no—
763C2#2262020914yesdirect product factor
764C2C2×#1798909311yescharacteristic
765C2C2×#1798939411yescharacteristic
766C2C2×#1798939711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
Fitting, prime radicalC2×#449×C73C2
socleC23×C73C22×D4
hypercenterC2×#449D73
hypocenterC73C2×#3125
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#17989204C2semidirect
2. C2×#17989070C2semidirect
3. #22620209C2direct (N × H)
4. C2×#17988903C2semidirect
5. C2×#17988918C2semidirect
6. C2×#17988870C2semidirect
7. C2×#17988875C2semidirect
8. C2×#17988807C2semidirect
9. C2×#17988800C2semidirect
10. C2×#17988749C2semidirect
11. C2×#17988699C2semidirect
12. C2×#17988691C2semidirect
13. C2×#17988678C2semidirect
14. C2×SD16×Dic73C2semidirect
15. C2×#17988645C2semidirect
20. #17989204C22semidirect
29. #17989070C22semidirect
42. #17988918C22semidirect
43. #17988903C22semidirect
44. #17988875C22semidirect
45. #17988870C22semidirect
46. #17988807C22semidirect
47. #17988800C22semidirect
48. #17988749C22semidirect
49. #17988699C22semidirect
50. #17988691C22semidirect
51. #17988678C22semidirect
52. SD16×Dic73C22semidirect
53. #17988645C22semidirect
380. C2×C73#3125semidirect
400. C73C2×#3125semidirect
763. C2#22620209direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892042
C2×#179890702
#226202092
C2×#179889032
C2×#179889182
C2×#179888702
C2×#179888752
C2×#179888072
C2×#179888002
C2×#179887492
C2×#179886992
C2×#179886912
C2×#179886782
C2×SD16×Dic732
C2×#179886452
C2×#449×C732
C2×#312573