Finite Group Databasebeta

← C2×#22623834 #33994353

Subgroups — C2×#22623834 #33994353

Order 18688.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623834C2132yesmaximal, direct product factor
2C2×#17989305C212yesmaximal, complemented
3C2×#17989300C212yesmaximal, complemented
4C2×#17989292C212yesmaximal, complemented
5C2×#17989286C214yesmaximal, complemented
6C2×#17989246C214yesmaximal, complemented
7C2×#17989238C212yesmaximal, complemented
8C2×#17989209C212yesmaximal, complemented
9C2×#17989202C212yesmaximal, complemented
10C2×#17989168C211yesmaximal, characteristic, complemented
11C2×#17989165C211yesmaximal, characteristic, complemented
12C2×#17989141C212yesmaximal, complemented
13C2×#17989134C212yesmaximal, complemented
14C2×#17989133C211yesmaximal, characteristic, complemented
15C22×#14556590C211yesmaximal, characteristic, complemented
16C2×#17989067C211yesmaximal, characteristic, complemented
17C2×#17989055C211yesmaximal, characteristic, complemented
18C2×#520×C73C211yesmaximal, characteristic, complemented
19C22×#11924028C2211yescharacteristic
20C22×#11924028C2211yescharacteristic
21C22×#11924028C2214yes—
22C23×Dic146C2212yes—
23#17989305C22132yescomplemented
24#17989300C22132yescomplemented
25#17989292C22132yescomplemented
26#17989286C22164yescomplemented
27#17989246C22164yescomplemented
28#17989238C22132yescomplemented
29#17989209C22132yescomplemented
30#17989202C22132yescomplemented
31#17989168C22116yescomplemented
32#17989165C22116yescomplemented
33#17989141C22132yescomplemented
34#17989134C22132yescomplemented
35#17989133C22116yescomplemented
36C2×#14556590C2212yes—
37C2×#14556590C2212yes—
38C2×#14556590C2212yes—
39C2×#14556590C2212yes—
40C2×#14556590C22116yescomplemented
41C2×#14556589C2211yescharacteristic
42C2×#14556587C2211yescharacteristic
43C2×#14556585C2214yes—
44C2×#14556584C2214yes—
45C2×#14556581C2214yes—
46C2×#14556580C2211yescharacteristic
47C2×#14556579C2214yes—
48C2×#14556578C2211yescharacteristic
49C2×#14556577C2214yes—
50C2×#14556577C2214yes—
51C2×#14556576C2214yes—
52C2×#14556574C2214yes—
53C2×#14556571C2212yes—
54C2×#14556571C2212yes—
55C2×#14556570C2212yes—
56C2×#14556570C2214yes—
57C2×#14556569C2214yes—
58C2×#14556569C2214yes—
59C2×#14556567C2212yes—
60C2×#14556566C2212yes—
61C2×#14556566C2212yes—
62C2×#14556565C2212yes—
63C2×#14556565C2214yes—
64C2×#14556564C2214yes—
65C2×#14556563C2214yes—
66C2×#14556563C2212yes—
67C2×#14556563C2212yes—
68C2×#14556562C2212yes—
69#17989067C22116yescomplemented
70#17989055C22116yescomplemented
71C2×C4×Dic146C2212yes—
72C2×C4×Dic146C2214yes—
73C2×#14556556C2211yescharacteristic
74C2×#14556556C2211yescharacteristic
75C2×C4×D292C2212yes—
76C2×#14556553C2211yescharacteristic
77C2×#14556553C2211yescharacteristic
78C2×C4×C22⋊D73C2212yes—
79C2×C4×C22⋊D73C2214yes—
80C2×C4×C22⋊D73C2212yes—
81C2×#14556551C2212yes—
82C2×#14556551C2212yes—
83C2×#14556551C2214yes—
84C2×#14556549C2212yes—
85C2×#14556548C2212yes—
86C2×#14556548C2214yes—
87C22×C4⋊Dic73C2211yescharacteristic
88C22×#11924007C2212yes—
89C2×C4⋊C4×D73C2212yes—
90C22×C4×Dic73C2211yescharacteristic
91C2×C42×D73C2212yes—
92C22×#41×C73C2211yescharacteristic
93#520×C73C22116yescomplemented
94C2×C4×Q8×C73C2212yes—
95C2×C4×D4×C73C2212yes—
96C2×C4×D4×C73C2214yes—
97C2×#117×C73C2211yescharacteristic
98C2×#117×C73C2212yes—
99C22×C4⋊C4×C73C2211yescharacteristic
100C22×C4⋊C4×C73C2212yes—
101C2×#11924028—28no—
102C2×#11924028—28no—
103C2×#11924028—416no—
104C2×#11924028C2318yes—
105C2×#11924028C2318yes—
106C2×#11924028C23132yes—
107C22×Dic146—48no—
108C22×Dic146C2311yescharacteristic
109C22×Dic146C2314yes—
110C22×Dic146C2311yescharacteristic
111C22×Dic146C2314yes—
112C22×Dic146C23116yes—
113C22×D292C2311yescharacteristic
114C22×D292C2311yescharacteristic
115C22×D292C2314yes—
116C22×C22⋊D73C2312yes—
117C22×C22⋊D73C2312yes—
118C22×C22⋊D73C2312yes—
119C22×C22⋊D73C2312yes—
120C22×C22⋊D73C2314yes—
121C23×Dic73C2311yescharacteristic
122C23×Dic73C2311yescharacteristic
123C23×Dic73C2312yes—
124C22×C4×D73C2312yes—
125C22×C4×D73C2312yes—
126C22×C4×D73C2312yes—
127C22×C4×D73C2312yes—
128C22×C4×D73C2314yes—
129#14556590C23116yes—
130#14556590C23116yes—
131#14556590C23116yes—
132#14556590C23116yes—
133#14556589C2318yes—
134#14556587C2318yes—
135#14556585C23132yes—
136#14556584C23132yes—
137#14556581C23132yes—
138#14556580C2318yes—
139#14556579C23132yes—
140#14556578C2318yes—
141#14556577C23132yes—
142#14556577C23132yes—
143#14556576C23132yes—
144#14556574C23132yes—
145#14556571C23116yes—
146#14556571C23116yes—
147#14556570C23116yes—
148#14556570C23132yes—
149#14556569C23132yes—
150#14556569C23132yes—
151#14556567C23116yes—
152#14556566C23116yes—
153#14556566C23116yes—
154#14556565C23116yes—
155#14556565C23132yes—
156#14556564C23132yes—
157#14556563C23116yes—
158#14556563C23116yes—
159#14556563C23132yes—
160#14556562C23116yes—
161C4×Dic146C23116yes—
162C4×Dic146C23132yes—
163#14556556C2318yes—
164#14556556C2318yes—
165C4×D292C23116yes—
166#14556553C2318yes—
167#14556553C2318yes—
168C4×C22⋊D73C23116yes—
169C4×C22⋊D73C23116yes—
170C4×C22⋊D73C23132yes—
171#14556551C23116yes—
172#14556551C23132yes—
173#14556551C23116yes—
174#14556549C23116yes—
175#14556548C23132yes—
176#14556548C23116yes—
177C2×C4⋊Dic73C2312yes—
178C2×C4⋊Dic73C2312yes—
179C2×C4⋊Dic73C2318yes—
180C2×C4⋊Dic73C2314yes—
181C2×#11924007C2312yes—
182C2×#11924007C2312yes—
183C2×#11924007C2314yes—
184C2×#11924007C2314yes—
185C2×#11924007C23116yes—
186C2×#11924007C2314yes—
187C2×#11924007C2312yes—
188C2×#11924007C2312yes—
189C2×#11924007C2314yes—
190C4⋊C4×D73C23116yes—
191C2×C22⋊Dic73C2314yes—
192C2×C22⋊Dic73C2312yes—
193C2×C22⋊Dic73C2312yes—
194C2×#11924005C2312yes—
195C2×#11924005C2312yes—
196C2×#11924005C2314yes—
197C2×#11924005C2314yes—
198C2×#11924005C2314yes—
199C2×#11924005C2312yes—
200C2×#11924005C2312yes—
201C2×#11924005C2314yes—
202C2×C4×Dic73C2311yescharacteristic
203C2×C4×Dic73C2311yescharacteristic
204C2×C4×Dic73C2311yescharacteristic
205C2×C4×Dic73C2311yescharacteristic
206C2×C4×Dic73C2318yes—
207C2×C4×Dic73C2312yes—
208C2×C4×Dic73C2312yes—
209C2×C4×Dic73C2314yes—
210C42×D73C23116yes—
211C2×#41×C73—28no—
212C2×#41×C73C2318yes—
213C22×Q8×C73C2311yescharacteristic
214C22×D4×C73C2311yescharacteristic
215C22×D4×C73C2312yes—
216C23×C4×C73C2312yes—
217C23×C4×C73C2312yes—
218C23×C4×C73C2314yes—
219C23×C4×C73C2311yescharacteristic
220C4×Q8×C73C23116yes—
221C4×D4×C73C23116yes—
222C4×D4×C73C23132yes—
223#117×C73C23116yes—
224#117×C73C2318yes—
225C2×C4⋊C4×C73C2312yes—
226C2×C4⋊C4×C73C2312yes—
227C2×C4⋊C4×C73C2318yes—
228C2×C4⋊C4×C73C23116yes—
229C2×C4⋊C4×C73C2311yescharacteristic
230C2×C4⋊C4×C73C2314yes—
231C2×C4⋊C4×C73C2311yescharacteristic
232C2×C22⋊C4×C73C2312yes—
233C2×C22⋊C4×C73C2314yes—
234C2×C42×C73C2312yes—
235C2×C42×C73C2314yes—
236C23×D73C2412yes—
237C23×D73C2412yes—
238#11924028—232no—
239#11924028—232no—
240#11924028—464no—
241C2×Dic146—24no—
242C2×Dic146—24no—
243C2×Dic146—216no—
244C2×Dic146—432no—
245C2×Dic146—48no—
246C2×Dic146C2414yes—
247C2×Dic146C2414yes—
248C2×Dic146C24116yes—
249C2×Dic146C24116yes—
250C2×D292—24no—
251C2×D292—24no—
252C2×D292—48no—
253C2×D292C2414yes—
254C2×D292C2414yes—
255C2×D292C24116yes—
256C2×C22⋊D73—28no—
257C2×C22⋊D73—28no—
258C2×C22⋊D73—28no—
259C2×C22⋊D73—28no—
260C2×C22⋊D73—48no—
261C2×C22⋊D73C2418yes—
262C2×C22⋊D73C2418yes—
263C2×C22⋊D73C2418yes—
264C2×C22⋊D73C2418yes—
265C2×C22⋊D73C24116yes—
266C22×Dic73—24no—
267C22×Dic73—24no—
268C22×Dic73—44no—
269C22×Dic73C2411yescharacteristic
270C22×Dic73C2411yescharacteristic
271C22×Dic73C2412yes—
272C22×Dic73C2412yes—
273C22×Dic73C2414yes—
274C22×Dic73C2414yes—
275C22×Dic73C2414yes—
276C22×Dic73C2418yes—
277C22×Dic73C2411yescharacteristic
278C22×Dic73C2411yescharacteristic
279C2×C4×D73—28no—
280C2×C4×D73—28no—
281C2×C4×D73—28no—
282C2×C4×D73—28no—
283C2×C4×D73—48no—
284C2×C4×D73C2418yes—
285C2×C4×D73C2418yes—
286C2×C4×D73C2418yes—
287C2×C4×D73C2418yes—
288C2×C4×D73C24116yes—
289C4⋊Dic73C2418yes—
290C4⋊Dic73C2418yes—
291C4⋊Dic73C24116yes—
292#11924007C24116yes—
293#11924007C24116yes—
294#11924007C24116yes—
295#11924007C2418yes—
296#11924007C2418yes—
297#11924007C2418yes—
298#11924007C2418yes—
299#11924007C24116yes—
300C22⋊Dic73C24116yes—
301C22⋊Dic73C2418yes—
302C22⋊Dic73C2418yes—
303#11924005C2418yes—
304#11924005C2418yes—
305#11924005C24116yes—
306#11924005C24116yes—
307#11924005C24116yes—
308#11924005C2418yes—
309#11924005C2418yes—
310#11924005C24116yes—
311C4×Dic73C2414yes—
312C4×Dic73C2418yes—
313C4×Dic73C2418yes—
314C4×Dic73C2414yes—
315C4×Dic73C2414yes—
316C4×Dic73C2414yes—
317C4×Dic73C24116yes—
318C24×C73C2412yes—
319C24×C73C2411yescharacteristic
320#41×C73—232no—
321C2×Q8×C73—24no—
322C2×Q8×C73C2414yes—
323C2×D4×C73—28no—
324C2×D4×C73—24no—
325C2×D4×C73C2414yes—
326C2×D4×C73C2418yes—
327C22×C4×C73—28no—
328C22×C4×C73—44no—
329C22×C4×C73—48no—
330C22×C4×C73#4118yescomplemented
331C22×C4×C73C2412yes—
332C22×C4×C73C2412yes—
333C22×C4×C73C2412yes—
334C22×C4×C73C2414yes—
335C22×C4×C73C2418yes—
336C22×C4×C73C2418yes—
337C22×C4×C73C24116yes—
338C22×C4×C73C2411yescharacteristic
339C22×C4×C73C2411yescharacteristic
340C22×C4×C73C2414yes—
341C4⋊C4×C73C2414yes—
342C4⋊C4×C73C2418yes—
343C4⋊C4×C73C2418yes—
344C4⋊C4×C73C24116yes—
345C4⋊C4×C73C2414yes—
346C22⋊C4×C73C2418yes—
347C22⋊C4×C73C24116yes—
348C42×C73C2418yes—
349C42×C73C24116yes—
350C23×C73—22no—
351C23×C73—22no—
352C23×C73—24no—
353C23×C73—24no—
354C23×C73—24no—
355C23×C73C2×#4114yes—
356C23×C73C2514yes—
357C23×C73C2512yes—
358C23×C73C2511yescharacteristic
359C22×D73—24no—
360C22×D73—24no—
361C22×D73—24no—
362C22×D73—24no—
363C22×D73—24no—
364C22×D73—24no—
365C22×D73C2514yes—
366C22×D73C2514yes—
367Q8×C73—28no—
368D4×C73—216no—
369D4×C73—28no—
370C2×C4×C73—24no—
371C2×C4×C73—24no—
372C2×C4×C73—28no—
373C2×C4×C73—24no—
374C2×C4×C73—216no—
375C2×C4×C73—48no—
376C2×C4×C73—416no—
377C2×C4×C73C2×#4114yes—
378C2×C4×C73C2×#4114yes—
379C2×C4×C73C2×#41116yescomplemented
380C2×C4×C73C2514yes—
381C2×C4×C73C2514yes—
382C2×C4×C73C2514yes—
383C2×C4×C73C2518yes—
384C2×C4×C73C2512yes—
385C2×C4×C73C2512yes—
386C22⋊D73—216no—
387C22⋊D73—216no—
388C22⋊D73—216no—
389C22⋊D73—216no—
390C22⋊D73—416no—
391C2×Dic73—24no—
392C2×Dic73—24no—
393C2×Dic73—28no—
394C2×Dic73—22no—
395C2×Dic73—22no—
396C2×Dic73—28no—
397C2×Dic73—28no—
398C2×Dic73—48no—
399C2×Dic73H(5,𝔽2)14yes—
400C2×Dic732−1+414yes—
401C2×Dic73C2512yes—
402C2×Dic73C2512yes—
403C2×Dic73C2514yes—
404C2×Dic73C2514yes—
405C2×Dic73C2518yes—
406C2×Dic73C2512yes—
407C2×Dic73C2512yes—
408D292—28no—
409D292—28no—
410D292—416no—
411C4×D73—216no—
412C4×D73—216no—
413C4×D73—216no—
414C4×D73—216no—
415C4×D73—416no—
416Dic146—28no—
417Dic146—28no—
418Dic146—232no—
419Dic146—416no—
420C22×C73—22no—
421C22×C73—22no—
422C22×C73—28no—
423C22×C73—24no—
424C22×C73—24no—
425C22×C73—24no—
426C22×C73—48no—
427C22×C73C22×#4114yes—
428C22×C73C22×#4112yes—
429C22×C73C2×H(5,𝔽2)12yes—
430C22×C73C2×2−1+412yes—
431C22×C73C2611yescharacteristic
432C2×D73—24no—
433C2×D73—24no—
434C2×D73—24no—
435C2×D73—24no—
436C2×D73—24no—
437C2×D73—24no—
438C2×D73—48no—
439C2×D73—48no—
440C4×C73—24no—
441C4×C73—28no—
442C4×C73—24no—
443C4×C73—24no—
444C4×C73C22×#4114yes—
445C4×C73C22×#4114yes—
446Dic73—24no—
447Dic73—24no—
448Dic73—28no—
449Dic73—22no—
450Dic73—22no—
451Dic73C2×H(5,𝔽2)14yes—
452Dic73C2×2−1+414yes—
453C2×#3511—731nomaximal, Sylow
454C2×C73—24no—
455C2×C73—44no—
456C2×C73#351114yescomplemented
457C2×C73C23×#4111yescharacteristic
458C2×C73C22×H(5,𝔽2)11yescharacteristic
459C2×C73C22×2−1+411yescharacteristic
460D73—44no—
461D73—44no—
462#3511—7332no—
463C2×#556—732no—
464C2×#555—732no—
465C2×#554—732no—
466C2×#553—734no—
467C2×#548—734no—
468C2×#547—732no—
469C2×#542—732no—
470C2×#542—732no—
471C2×#537—731no—
472C2×#537—731no—
473C2×#533—732no—
474C2×#532—731no—
475C2×#532—732no—
476C22×C4⋊Q8—731no—
477C2×#520—731no—
478C2×#520D7311yescharacteristic, complemented
479C2×C4×#41—731no—
480C73C2×#351111yescharacteristic, complemented, Sylow
481C22×#41—734no—
482C22×#41—731no—
483C22×#41—731no—
484C22×#41C2×D7311yescharacteristic
485C23×Q8—732no—
486#556—7332no—
487#555—7332no—
488#554—7332no—
489#553—7364no—
490#548—7364no—
491#547—7332no—
492#542—7332no—
493#542—7332no—
494#537—7316no—
495#537—7316no—
496#533—7332no—
497#532—7316no—
498#532—7332no—
499C2×C4⋊Q8—731no—
500C2×C4⋊Q8—732no—
501C2×C4⋊Q8—732no—
502C2×C4⋊Q8—732no—
503C2×C4⋊Q8—732no—
504C2×C4⋊Q8—7316no—
505C2×#127—731no—
506C2×#126—734no—
507C2×#126—734no—
508C2×#125—734no—
509C2×#124—731no—
510C2×#124—731no—
511C2×#124—734no—
512C2×#124—734no—
513C2×#124—734no—
514C2×#123—734no—
515C2×#123—734no—
516C2×C22⋊Q8—732no—
517C2×C22⋊Q8—732no—
518C2×C22⋊Q8—734no—
519C2×C22⋊Q8—732no—
520C2×C22⋊Q8—734no—
521C2×C22⋊Q8—732no—
522C2×C22⋊Q8—734no—
523C2×#121—732no—
524C2×#121—732no—
525C2×#121—732no—
526C2×#121—734no—
527C2×#121—732no—
528C2×#121—734no—
529C2×#121—732no—
530C2×#121—732no—
531C2×#121—734no—
532#520—7316no—
533#520C2×D73116yescomplemented
534C4×#41—7316no—
535C2×C4×Q8—731no—
536C2×C4×Q8—731no—
537C2×C4×Q8—732no—
538C2×C4×Q8—734no—
539C2×C4×Q8C2×D7312yes—
540C2×C4×D4—732no—
541C2×C4×D4—734no—
542C2×C4×D4—732no—
543C2×C4×D4—731no—
544C2×C4×D4—731no—
545C2×C4×D4—732no—
546C2×C4×D4—732no—
547C2×C4×D4—734no—
548C2×C4×D4—732no—
549C2×C4×D4C2×D7312yes—
550C2×C4×D4C2×D7314yes—
551C2×#117—732no—
552C2×#117—732no—
553C2×#117—734no—
554C2×#117C2×D7311yescharacteristic
555C2×#117C2×D7312yes—
556C22×C4⋊C4—731no—
557C22×C4⋊C4—732no—
558C22×C4⋊C4—732no—
559C22×C4⋊C4C2×D7311yescharacteristic
560C22×C4⋊C4C2×D7312yes—
561C22×C42—731no—
562C22×C42—732no—
563C2×#41—28no—
564C2×#41—29216no—
565C2×#41—7332no—
566C2×#41—738no—
567C2×#41—738no—
568C2×#41—1468no—
569C2×#41—1468no—
570C2×#41C22×D7318yes—
571C22×Q8—2928no—
572C22×Q8—734no—
573C22×Q8—7316no—
574C22×Q8—731no—
575C22×Q8—731no—
576C22×Q8—734no—
577C22×Q8C22×D7311yescharacteristic
578C22×D4—734no—
579C22×D4—732no—
580C22×D4—732no—
581C22×D4—732no—
582C22×D4—732no—
583C22×D4—734no—
584C22×D4—731no—
585C22×D4—731no—
586C22×D4C22×D7312yes—
587C22×D4C22×D7311yescharacteristic
588C23×C4—732no—
589C23×C4—734no—
590C23×C4—731no—
591C23×C4—731no—
592C23×C4—732no—
593C23×C4—732no—
594C23×C4—732no—
595C23×C4—732no—
596C23×C4C22×D7312yes—
597C23×C4C22×D7312yes—
598C23×C4C22×D7314yes—
599C23×C4C22×D7311yescharacteristic
600C4⋊Q8—738no—
601C4⋊Q8—7316no—
602C4⋊Q8—7316no—
603C4⋊Q8—7316no—
604C4⋊Q8—7316no—
605#127—738no—
606#126—7332no—
607#126—7332no—
608#125—7332no—
609#124—738no—
610#124—738no—
611#124—7332no—
612#124—7332no—
613#124—7332no—
614#123—7332no—
615#123—7332no—
616C22⋊Q8—7316no—
617C22⋊Q8—7316no—
618C22⋊Q8—7332no—
619C22⋊Q8—7316no—
620C22⋊Q8—7332no—
621C22⋊Q8—7316no—
622C22⋊Q8—7332no—
623#121—7316no—
624#121—7316no—
625#121—7316no—
626#121—7332no—
627#121—7316no—
628#121—7332no—
629#121—7316no—
630#121—7316no—
631#121—7332no—
632C4×Q8—738no—
633C4×Q8—738no—
634C4×Q8—7316no—
635C4×Q8—7332no—
636C4×Q8C22×D73116yes—
637C4×D4—7316no—
638C4×D4—7332no—
639C4×D4—7316no—
640C4×D4—738no—
641C4×D4—738no—
642C4×D4—7316no—
643C4×D4—7316no—
644C4×D4—7332no—
645C4×D4—7316no—
646C4×D4C22×D73116yes—
647C4×D4C22×D73132yes—
648#117—7316no—
649#117—7316no—
650#117—7332no—
651#117C22×D7318yes—
652#117C22×D73116yes—
653C2×C4⋊C4—732no—
654C2×C4⋊C4—734no—
655C2×C4⋊C4—732no—
656C2×C4⋊C4—734no—
657C2×C4⋊C4—738no—
658C2×C4⋊C4—734no—
659C2×C4⋊C4—7316no—
660C2×C4⋊C4—732no—
661C2×C4⋊C4—732no—
662C2×C4⋊C4—732no—
663C2×C4⋊C4—732no—
664C2×C4⋊C4—734no—
665C2×C4⋊C4—734no—
666C2×C4⋊C4—7316no—
667C2×C4⋊C4C22×D7311yescharacteristic
668C2×C4⋊C4C22×D7312yes—
669C2×C4⋊C4C22×D7312yes—
670C2×C4⋊C4C22×D7314yes—
671C2×C4⋊C4C22×D7318yes—
672C2×C4⋊C4C22×D73116yes—
673C2×C4⋊C4C22×D7311yescharacteristic
674C2×C22⋊C4—734no—
675C2×C22⋊C4—732no—
676C2×C22⋊C4—732no—
677C2×C22⋊C4—734no—
678C2×C22⋊C4—732no—
679C2×C22⋊C4—732no—
680C2×C22⋊C4—734no—
681C2×C22⋊C4—734no—
682C2×C22⋊C4—734no—
683C2×C22⋊C4—732no—
684C2×C22⋊C4—732no—
685C2×C22⋊C4C22×D7312yes—
686C2×C22⋊C4C22×D7314yes—
687C2×C42—734no—
688C2×C42—731no—
689C2×C42—732no—
690C2×C42—731no—
691C2×C42—731no—
692C2×C42—732no—
693C2×C42—738no—
694C2×C42—731no—
695C2×C42—7316no—
696C2×C42C22×D7312yes—
697C2×C42C22×D7314yes—
698C24—732no—
699C24—732no—
700C24C23×D7312yes—
701C24C23×D7311yescharacteristic
702#41—232no—
703#41—29264no—
704#41—14632no—
705#41—14632no—
706C2×Q8—24no—
707C2×Q8—2928no—
708C2×Q8—29232no—
709C2×Q8—7316no—
710C2×Q8—734no—
711C2×Q8—734no—
712C2×Q8—7316no—
713C2×Q8—14616no—
714C2×Q8—1464no—
715C2×Q8—1464no—
716C2×Q8C23×D7314yes—
717C2×D4—28no—
718C2×D4—24no—
719C2×D4—2928no—
720C2×D4—2928no—
721C2×D4—7316no—
722C2×D4—738no—
723C2×D4—738no—
724C2×D4—738no—
725C2×D4—738no—
726C2×D4—7316no—
727C2×D4—734no—
728C2×D4—734no—
729C2×D4—1468no—
730C2×D4—1468no—
731C2×D4—1468no—
732C2×D4—1468no—
733C2×D4—1464no—
734C2×D4—1464no—
735C2×D4C23×D7318yes—
736C2×D4C23×D7314yes—
737C22×C4—28no—
738C22×C4—44no—
739C22×C4—48no—
740C22×C4—2928no—
741C22×C4—2924no—
742C22×C4—738no—
743C22×C4—7316no—
744C22×C4—731no—
745C22×C4—731no—
746C22×C4—734no—
747C22×C4—734no—
748C22×C4—731no—
749C22×C4—731no—
750C22×C4—732no—
751C22×C4—732no—
752C22×C4—734no—
753C22×C4—738no—
754C22×C4—738no—
755C22×C4—738no—
756C22×C4—738no—
757C22×C4—1468no—
758C22×C4—1468no—
759C22×C4—1464no—
760C22×C4—1464no—
761C22×C4—1468no—
762C22×C4—1468no—
763C22×C4#1192402818yescomplemented
764C22×C4C23×D7318yes—
765C22×C4C23×D7312yes—
766C22×C4C23×D7312yes—
767C22×C4C23×D7312yes—
768C22×C4C23×D7314yes—
769C22×C4C23×D7318yes—
770C22×C4C23×D73116yes—
771C22×C4C23×D7311yescharacteristic
772C22×C4C23×D7311yescharacteristic
773C22×C4C23×D7314yes—
774C4⋊C4—7316no—
775C4⋊C4—7316no—
776C4⋊C4—7316no—
777C4⋊C4—738no—
778C4⋊C4—738no—
779C4⋊C4—738no—
780C4⋊C4—738no—
781C4⋊C4—7316no—
782C4⋊C4—738no—
783C4⋊C4—738no—
784C4⋊C4—7316no—
785C4⋊C4C23×D7314yes—
786C4⋊C4C23×D7318yes—
787C4⋊C4C23×D7318yes—
788C4⋊C4C23×D73116yes—
789C4⋊C4C23×D7314yes—
790C22⋊C4—7316no—
791C22⋊C4—738no—
792C22⋊C4—738no—
793C22⋊C4—7316no—
794C22⋊C4—738no—
795C22⋊C4—738no—
796C22⋊C4—7316no—
797C22⋊C4—7316no—
798C22⋊C4—7316no—
799C22⋊C4—738no—
800C22⋊C4—738no—
801C22⋊C4C23×D7318yes—
802C22⋊C4C23×D73116yes—
803C42—734no—
804C42—734no—
805C42—738no—
806C42—734no—
807C42—734no—
808C42—738no—
809C42—7316no—
810C42C23×D7318yes—
811C42C23×D73116yes—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—734no—
818C23—734no—
819C23—1464no—
820C23—1464no—
821C23—1464no—
822C23—1464no—
823C23—1464no—
824C23—1464no—
825C23C2×#1192402814yes—
826C23C24×D7314yes—
827C23C24×D7312yes—
828C23C24×D7311yescharacteristic
829Q8—28no—
830Q8—29216no—
831Q8—14632no—
832Q8—1468no—
833Q8—1468no—
834D4—216no—
835D4—28no—
836D4—29216no—
837D4—29216no—
838D4—14616no—
839D4—14616no—
840D4—14616no—
841D4—14616no—
842D4—1468no—
843D4—1468no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—24no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—416no—
851C2×C4—29216no—
852C2×C4—2928no—
853C2×C4—734no—
854C2×C4—734no—
855C2×C4—732no—
856C2×C4—732no—
857C2×C4—732no—
858C2×C4—732no—
859C2×C4—734no—
860C2×C4—734no—
861C2×C4—738no—
862C2×C4—14616no—
863C2×C4—14616no—
864C2×C4—1468no—
865C2×C4—1468no—
866C2×C4—1464no—
867C2×C4—1464no—
868C2×C4—1468no—
869C2×C4—1462no—
870C2×C4—1462no—
871C2×C4—14616no—
872C2×C4—14616no—
873C2×C4C2×#1192402814yes—
874C2×C4C2×#1192402814yes—
875C2×C4C2×#11924028116yescomplemented
876C2×C4C24×D7314yes—
877C2×C4C24×D7314yes—
878C2×C4C24×D7314yes—
879C2×C4C24×D7318yes—
880C2×C4C24×D7312yes—
881C2×C4C24×D7312yes—
882C22—28no—
883C22—22no—
884C22—22no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—48no—
889C22—2928no—
890C22—2928no—
891C22—1464no—
892C22—1464no—
893C22—1464no—
894C22—1464no—
895C22—1464no—
896C22—1464no—
897C22C22×#1192402814yes—
898C22C22×#1192402812yes—
899C22H(5,𝔽2)×D7312yes—
900C222−1+4×D7312yes—
901C22C25×D7311yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—24no—
906C4—734no—
907C4—734no—
908C4—1464no—
909C4—1464no—
910C4—1468no—
911C4—1462no—
912C4—1462no—
913C4C22×#1192402814yes—
914C4C22×#1192402814yes—
915C2—24no—
916C2—44no—
917C2—2924no—
918C2—2924no—
919C2#2262383414yesdirect product factor
920C2C23×#1192402811yescharacteristic
921C2C2×H(5,𝔽2)×D7311yescharacteristic
922C2C2×2−1+4×D7311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#520×C73C2
socleC23×C73C25
hypercenterC2×#520D73
hypocenterC73C2×#3511
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #22623834C2direct (N × H)
2. C2×#17989305C2semidirect
3. C2×#17989300C2semidirect
4. C2×#17989292C2semidirect
5. C2×#17989286C2semidirect
6. C2×#17989246C2semidirect
7. C2×#17989238C2semidirect
8. C2×#17989209C2semidirect
9. C2×#17989202C2semidirect
10. C2×#17989168C2semidirect
11. C2×#17989165C2semidirect
12. C2×#17989141C2semidirect
13. C2×#17989134C2semidirect
14. C2×#17989133C2semidirect
15. C22×#14556590C2semidirect
16. C2×#17989067C2semidirect
17. C2×#17989055C2semidirect
18. C2×#520×C73C2semidirect
23. #17989305C22semidirect
24. #17989300C22semidirect
25. #17989292C22semidirect
26. #17989286C22semidirect
27. #17989246C22semidirect
28. #17989238C22semidirect
29. #17989209C22semidirect
30. #17989202C22semidirect
31. #17989168C22semidirect
32. #17989165C22semidirect
33. #17989141C22semidirect
34. #17989134C22semidirect
35. #17989133C22semidirect
40. C2×#14556590C22semidirect
69. #17989067C22semidirect
70. #17989055C22semidirect
93. #520×C73C22semidirect
330. C22×C4×C73#41semidirect
379. C2×C4×C73C2×#41semidirect
456. C2×C73#3511semidirect
478. C2×#520D73semidirect
480. C73C2×#3511semidirect
533. #520C2×D73semidirect
763. C22×C4#11924028semidirect
875. C2×C4C2×#11924028semidirect
919. C2#22623834direct (N × H)

Maximal subgroups

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

subgroupindex
#226238342
C2×#179893052
C2×#179893002
C2×#179892922
C2×#179892862
C2×#179892462
C2×#179892382
C2×#179892092
C2×#179892022
C2×#179891682
C2×#179891652
C2×#179891412
C2×#179891342
C2×#179891332
C22×#145565902
C2×#179890672
C2×#179890552
C2×#520×C732
C2×#351173