Finite Group Databasebeta

← C2×#22623840 #33994357

Subgroups — C2×#22623840 #33994357

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#22623840C2132yesmaximal, direct product factor
2C2×#17989308C212yesmaximal, complemented
3C2×#17989301C212yesmaximal, complemented
4C2×#17989295C212yesmaximal, complemented
5C2×#17989280C214yesmaximal, complemented
6C2×#17989243C214yesmaximal, complemented
7C2×#17989237C212yesmaximal, complemented
8C2×#17989210C212yesmaximal, complemented
9C2×#17989204C212yesmaximal, complemented
10C2×#17989165C211yesmaximal, characteristic, complemented
11C2×#17989139C212yesmaximal, complemented
12C2×#17989133C211yesmaximal, characteristic, complemented
13C2×#17989132C212yesmaximal, complemented
14C22×#14556590C211yesmaximal, characteristic, complemented
15C2×#17989070C211yesmaximal, characteristic, complemented
16C2×#17989068C211yesmaximal, characteristic, complemented
17C2×#41×Dic73C211yesmaximal, characteristic, complemented
18C2×#537×C73C211yesmaximal, characteristic, complemented
19C22×#11924028C2211yescharacteristic
20C22×#11924027C2214yes—
21C23×Dic146C2212yes—
22#17989308C22132yescomplemented
23#17989301C22132yescomplemented
24#17989295C22132yescomplemented
25#17989280C22164yescomplemented
26#17989243C22164yescomplemented
27#17989237C22132yescomplemented
28#17989210C22132yescomplemented
29#17989204C22132yescomplemented
30#17989165C22116yescomplemented
31#17989139C22132yescomplemented
32#17989133C22116yescomplemented
33#17989132C22132yescomplemented
34C2×#14556590C2212yes—
35C2×#14556590C2212yes—
36C2×#14556590C2212yes—
37C2×#14556590C2212yes—
38C2×#14556590C22116yescomplemented
39C2×#14556589C2211yescharacteristic
40C2×#14556587C2211yescharacteristic
41C2×#14556586C2214yes—
42C2×#14556584C2214yes—
43C2×#14556581C2214yes—
44C2×#14556580C2211yescharacteristic
45C2×#14556578C2211yescharacteristic
46C2×#14556578C2214yes—
47C2×#14556577C2214yes—
48C2×#14556577C2214yes—
49C2×#14556573C2214yes—
50C2×#14556572C2214yes—
51C2×#14556571C2214yes—
52C2×#14556570C2212yes—
53C2×#14556568C2214yes—
54C2×#14556568C2214yes—
55C2×#14556567C2212yes—
56C2×#14556565C2212yes—
57C2×#14556563C2214yes—
58C2×#14556563C2212yes—
59C2×#14556563C2212yes—
60C2×#14556563C2214yes—
61C2×#14556562C2212yes—
62#17989070C22116yescomplemented
63#17989068C22116yescomplemented
64#41×Dic73C22116yescomplemented
65C2×Q8×Dic73C2212yes—
66C2×Q8×Dic73C2211yescharacteristic
67C2×Q8×Dic73C2211yescharacteristic
68C2×#14556556C2212yes—
69C2×#14556556C2214yes—
70C2×D4×Dic73C2212yes—
71C2×D4×Dic73C2211yescharacteristic
72C2×D4×Dic73C2212yes—
73C2×D4×Dic73C2212yes—
74C2×D4×Dic73C2211yescharacteristic
75C2×D4×Dic73C2214yes—
76C2×#14556553C2212yes—
77C2×C4×C22⋊D73C2214yes—
78C2×C4×C22⋊D73C2212yes—
79C2×C4×C22⋊D73C2212yes—
80C2×#14556551C2214yes—
81C2×#14556550C2212yes—
82C2×#14556550C2211yescharacteristic
83C2×#14556550C2212yes—
84C2×#14556549C2212yes—
85C2×#14556547C2214yes—
86C22×C4⋊Dic73C2211yescharacteristic
87C22×C4⋊Dic73C2212yes—
88C22×#11924007C2212yes—
89C2×C4⋊C4×D73C2212yes—
90C22×C4×Dic73C2211yescharacteristic
91C22×C4×Dic73C2212yes—
92C22×#41×C73C2211yescharacteristic
93C22×#41×C73C2211yescharacteristic
94#537×C73C22116yescomplemented
95C2×C22⋊Q8×C73C2212yes—
96C2×C22⋊Q8×C73C2212yes—
97C2×#121×C73C2212yes—
98C2×#121×C73C2212yes—
99C2×#121×C73C2214yes—
100C22×C4⋊C4×C73C2211yescharacteristic
101C2×#11924028—28no—
102C2×#11924028C2318yes—
103C2×#11924027—416no—
104C2×#11924027C23132yes—
105C22×Dic146—48no—
106C22×Dic146C2311yescharacteristic
107C22×Dic146C2314yes—
108C22×Dic146C2314yes—
109C22×Dic146C23116yes—
110C22×D292C2311yescharacteristic
111C22×C22⋊D73C2312yes—
112C22×C22⋊D73C2312yes—
113C22×C22⋊D73C2312yes—
114C22×C22⋊D73C2314yes—
115C23×Dic73C2311yescharacteristic
116C23×Dic73C2312yes—
117C23×Dic73C2311yescharacteristic
118C23×Dic73C2312yes—
119C23×Dic73C2312yes—
120C23×Dic73C2314yes—
121C22×C4×D73C2312yes—
122C22×C4×D73C2314yes—
123#14556590C23116yes—
124#14556590C23116yes—
125#14556590C23116yes—
126#14556590C23116yes—
127#14556589C2318yes—
128#14556587C2318yes—
129#14556586C23132yes—
130#14556584C23132yes—
131#14556581C23132yes—
132#14556580C2318yes—
133#14556578C2318yes—
134#14556578C23132yes—
135#14556577C23132yes—
136#14556577C23132yes—
137#14556573C23132yes—
138#14556572C23132yes—
139#14556571C23132yes—
140#14556570C23116yes—
141#14556568C23132yes—
142#14556568C23132yes—
143#14556567C23116yes—
144#14556565C23116yes—
145#14556563C23132yes—
146#14556563C23116yes—
147#14556563C23116yes—
148#14556563C23132yes—
149#14556562C23116yes—
150Q8×Dic73C23116yes—
151Q8×Dic73C2318yes—
152Q8×Dic73C2318yes—
153#14556556C23116yes—
154#14556556C23132yes—
155D4×Dic73C23116yes—
156D4×Dic73C2318yes—
157D4×Dic73C23116yes—
158D4×Dic73C23132yes—
159D4×Dic73C23116yes—
160D4×Dic73C2318yes—
161#14556553C23116yes—
162C4×C22⋊D73C23116yes—
163C4×C22⋊D73C23116yes—
164C4×C22⋊D73C23132yes—
165#14556551C23132yes—
166#14556550C23116yes—
167#14556550C23116yes—
168#14556550C2318yes—
169#14556549C23116yes—
170#14556547C23132yes—
171C2×C4⋊Dic73C2312yes—
172C2×C4⋊Dic73C2312yes—
173C2×C4⋊Dic73C2318yes—
174C2×C4⋊Dic73C23116yes—
175C2×C4⋊Dic73C2311yescharacteristic
176C2×C4⋊Dic73C2314yes—
177C2×C4⋊Dic73C2311yescharacteristic
178C2×C4⋊Dic73C2312yes—
179C2×C4⋊Dic73C2312yes—
180C2×#11924007C2312yes—
181C2×#11924007C2312yes—
182C2×#11924007C2314yes—
183C2×#11924007C2314yes—
184C2×#11924007C23116yes—
185C2×#11924007C2314yes—
186C2×#11924007C2314yes—
187C4⋊C4×D73C23116yes—
188C2×C22⋊Dic73C2314yes—
189C2×C22⋊Dic73C2312yes—
190C2×C22⋊Dic73C2314yes—
191C2×C22⋊Dic73C2312yes—
192C2×C22⋊Dic73C2312yes—
193C2×C22⋊Dic73C2312yes—
194C2×C22⋊Dic73C2312yes—
195C2×#11924005C2314yes—
196C2×#11924005C2314yes—
197C2×#11924005C2312yes—
198C2×#11924005C2312yes—
199C2×C4×Dic73C2311yescharacteristic
200C2×C4×Dic73C2311yescharacteristic
201C2×C4×Dic73C2311yescharacteristic
202C2×C4×Dic73C2311yescharacteristic
203C2×C4×Dic73C2318yes—
204C2×C4×Dic73C23116yes—
205C2×C4×Dic73C2312yes—
206C2×C4×Dic73C2312yes—
207C2×C4×Dic73C2312yes—
208C2×C4×Dic73C2314yes—
209C2×C4×Dic73C2314yes—
210C2×#41×C73—28no—
211C2×#41×C73—28no—
212C2×#41×C73C2318yes—
213C2×#41×C73C2318yes—
214C22×Q8×C73C2311yescharacteristic
215C22×Q8×C73C2311yescharacteristic
216C22×D4×C73C2311yescharacteristic
217C22×D4×C73C2311yescharacteristic
218C22×D4×C73C2312yes—
219C22×D4×C73C2312yes—
220C22×D4×C73C2314yes—
221C23×C4×C73C2312yes—
222C23×C4×C73C2312yes—
223C23×C4×C73C2312yes—
224C23×C4×C73C2311yescharacteristic
225C22⋊Q8×C73C23116yes—
226C22⋊Q8×C73C23116yes—
227#121×C73C23116yes—
228#121×C73C23116yes—
229#121×C73C23132yes—
230C2×C4⋊C4×C73C2312yes—
231C2×C4⋊C4×C73C2312yes—
232C2×C4⋊C4×C73C2318yes—
233C2×C4⋊C4×C73C2314yes—
234C2×C22⋊C4×C73C2314yes—
235C2×C22⋊C4×C73C2314yes—
236C23×D73C2412yes—
237#11924028—232no—
238#11924027—464no—
239C2×Dic146—24no—
240C2×Dic146—216no—
241C2×Dic146—432no—
242C2×Dic146—48no—
243C2×Dic146C2414yes—
244C2×Dic146C24116yes—
245C2×Dic146C24116yes—
246C2×D292—24no—
247C2×D292C2414yes—
248C2×C22⋊D73—28no—
249C2×C22⋊D73—28no—
250C2×C22⋊D73—28no—
251C2×C22⋊D73—48no—
252C2×C22⋊D73C2418yes—
253C2×C22⋊D73C2418yes—
254C2×C22⋊D73C2418yes—
255C2×C22⋊D73C24116yes—
256C22×Dic73—24no—
257C22×Dic73—28no—
258C22×Dic73—24no—
259C22×Dic73—28no—
260C22×Dic73—44no—
261C22×Dic73—48no—
262C22×Dic73C2412yes—
263C22×Dic73C2411yescharacteristic
264C22×Dic73C2411yescharacteristic
265C22×Dic73C2412yes—
266C22×Dic73C2412yes—
267C22×Dic73C2414yes—
268C22×Dic73C2418yes—
269C22×Dic73C2414yes—
270C22×Dic73C2418yes—
271C22×Dic73C2414yes—
272C22×Dic73C2418yes—
273C22×Dic73C24116yes—
274C22×Dic73C2411yescharacteristic
275C22×Dic73C2411yescharacteristic
276C2×C4×D73—28no—
277C2×C4×D73—48no—
278C2×C4×D73C2418yes—
279C2×C4×D73C24116yes—
280C4⋊Dic73C2414yes—
281C4⋊Dic73C2418yes—
282C4⋊Dic73C2418yes—
283C4⋊Dic73C24116yes—
284C4⋊Dic73C2414yes—
285C4⋊Dic73C2418yes—
286C4⋊Dic73C2418yes—
287#11924007C24116yes—
288#11924007C24116yes—
289#11924007C24116yes—
290#11924007C2418yes—
291#11924007C2418yes—
292#11924007C24116yes—
293C22⋊Dic73C24116yes—
294C22⋊Dic73C2418yes—
295C22⋊Dic73C24116yes—
296C22⋊Dic73C2418yes—
297C22⋊Dic73C2418yes—
298C22⋊Dic73C2418yes—
299C22⋊Dic73C2418yes—
300#11924005C24116yes—
301#11924005C24116yes—
302#11924005C2418yes—
303#11924005C2418yes—
304C4×Dic73C2414yes—
305C4×Dic73C2418yes—
306C4×Dic73C2414yes—
307C4×Dic73C2418yes—
308C4×Dic73C2414yes—
309C4×Dic73C2414yes—
310C4×Dic73C2418yes—
311C4×Dic73C24116yes—
312C4×Dic73C24116yes—
313C24×C73C2412yes—
314C24×C73C2412yes—
315C24×C73C2411yescharacteristic
316#41×C73—232no—
317#41×C73—232no—
318C2×Q8×C73—24no—
319C2×Q8×C73—24no—
320C2×Q8×C73C2414yes—
321C2×Q8×C73C2414yes—
322C2×D4×C73—28no—
323C2×D4×C73—28no—
324C2×D4×C73—24no—
325C2×D4×C73—24no—
326C2×D4×C73—48no—
327C2×D4×C73C2414yes—
328C2×D4×C73C2418yes—
329C2×D4×C73C2418yes—
330C2×D4×C73C2414yes—
331C2×D4×C73C24116yes—
332C22×C4×C73—28no—
333C22×C4×C73—28no—
334C22×C4×C73—44no—
335C22×C4×C73#4118yescomplemented
336C22×C4×C73C2414yes—
337C22×C4×C73C2412yes—
338C22×C4×C73C2412yes—
339C22×C4×C73C2418yes—
340C22×C4×C73C2418yes—
341C22×C4×C73C2418yes—
342C22×C4×C73C2411yescharacteristic
343C22×C4×C73C2411yescharacteristic
344C22×C4×C73C2414yes—
345C4⋊C4×C73C2418yes—
346C4⋊C4×C73C2418yes—
347C4⋊C4×C73C24116yes—
348C22⋊C4×C73C24116yes—
349C22⋊C4×C73C24116yes—
350C23×C73—22no—
351C23×C73—22no—
352C23×C73—24no—
353C23×C73—24no—
354C23×C73—24no—
355C23×C73—24no—
356C23×C73—24no—
357C23×C73—24no—
358C23×C73C2×#4114yes—
359C23×C73C2514yes—
360C23×C73C2514yes—
361C23×C73C2512yes—
362C23×C73C2511yescharacteristic
363C22×D73—24no—
364C22×D73—24no—
365C22×D73—24no—
366C22×D73C2514yes—
367Q8×C73—28no—
368Q8×C73—28no—
369D4×C73—216no—
370D4×C73—216no—
371D4×C73—28no—
372D4×C73—28no—
373D4×C73—416no—
374C2×C4×C73—24no—
375C2×C4×C73—24no—
376C2×C4×C73—28no—
377C2×C4×C73—216no—
378C2×C4×C73—216no—
379C2×C4×C73—48no—
380C2×C4×C73C2×#4114yes—
381C2×C4×C73C2×#4114yes—
382C2×C4×C73C2×#41116yescomplemented
383C2×C4×C73C2518yes—
384C2×C4×C73C2514yes—
385C2×C4×C73C2514yes—
386C2×C4×C73C2512yes—
387C2×C4×C73C2512yes—
388C22⋊D73—216no—
389C22⋊D73—216no—
390C22⋊D73—216no—
391C22⋊D73—416no—
392C2×Dic73—24no—
393C2×Dic73—24no—
394C2×Dic73—22no—
395C2×Dic73—28no—
396C2×Dic73—24no—
397C2×Dic73—22no—
398C2×Dic73—28no—
399C2×Dic73—216no—
400C2×Dic73—28no—
401C2×Dic73—216no—
402C2×Dic73—48no—
403C2×Dic73—416no—
404C2×Dic73H(5,𝔽2)14yes—
405C2×Dic732−1+414yes—
406C2×Dic73C2514yes—
407C2×Dic73C2512yes—
408C2×Dic73C2512yes—
409C2×Dic73C2514yes—
410C2×Dic73C2514yes—
411C2×Dic73C2518yes—
412C2×Dic73C2512yes—
413C2×Dic73C2512yes—
414D292—28no—
415C4×D73—216no—
416C4×D73—416no—
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—24no—
427C22×C73—24no—
428C22×C73—24no—
429C22×C73—48no—
430C22×C73—48no—
431C22×C73C22×#4114yes—
432C22×C73C22×#4112yes—
433C22×C73C2×H(5,𝔽2)12yes—
434C22×C73C2×2−1+412yes—
435C22×C73C2611yescharacteristic
436C2×D73—24no—
437C2×D73—24no—
438C2×D73—24no—
439C2×D73—48no—
440C4×C73—24no—
441C4×C73—24no—
442C4×C73—28no—
443C4×C73C22×#4114yes—
444C4×C73C22×#4114yes—
445Dic73—24no—
446Dic73—28no—
447Dic73—22no—
448Dic73—24no—
449Dic73—24no—
450Dic73—22no—
451Dic73C2×H(5,𝔽2)14yes—
452Dic73C2×2−1+414yes—
453C2×#3511—731nomaximal, Sylow
454C2×C73—24no—
455C2×C73—44no—
456C2×C73—44no—
457C2×C73#351114yescomplemented
458C2×C73C23×#4111yescharacteristic
459C2×C73C22×H(5,𝔽2)11yescharacteristic
460C2×C73C22×2−1+411yescharacteristic
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×#537D7311yescharacteristic, complemented
473C2×#533—732no—
474C2×#532—731no—
475C2×#532—732no—
476C22×C4⋊Q8—731no—
477C2×#520—731no—
478C2×#520—731no—
479C2×C4×#41—731no—
480C73C2×#351111yescharacteristic, complemented, Sylow
481C22×#41—734no—
482C22×#41—731no—
483C22×#41C2×D7311yescharacteristic
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#537C2×D73116yescomplemented
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—734no—
520C2×C22⋊Q8—734no—
521C2×C22⋊Q8C2×D7312yes—
522C2×C22⋊Q8C2×D7312yes—
523C2×#121—732no—
524C2×#121—732no—
525C2×#121—734no—
526C2×#121—732no—
527C2×#121—734no—
528C2×#121—732no—
529C2×#121C2×D7312yes—
530C2×#121C2×D7312yes—
531C2×#121C2×D7314yes—
532#520—7316no—
533#520—7316no—
534C4×#41—7316no—
535C2×C4×Q8—731no—
536C2×C4×Q8—731no—
537C2×C4×Q8—732no—
538C2×C4×Q8—732no—
539C2×C4×Q8—734no—
540C2×C4×D4—731no—
541C2×C4×D4—732no—
542C2×C4×D4—732no—
543C2×C4×D4—731no—
544C2×C4×D4—732no—
545C2×C4×D4—734no—
546C2×C4×D4—734no—
547C2×C4×D4—732no—
548C2×C4×D4—732no—
549C2×C4×D4—732no—
550C2×C4×D4—734no—
551C2×#117—731no—
552C2×#117—732no—
553C2×#117—732no—
554C2×#117—732no—
555C2×#117—734no—
556C22×C4⋊C4—731no—
557C22×C4⋊C4—732no—
558C22×C4⋊C4—732no—
559C22×C4⋊C4—732no—
560C22×C4⋊C4C2×D7311yescharacteristic
561C22×C42—731no—
562C22×C42—732no—
563C2×#41—28no—
564C2×#41—28no—
565C2×#41—29216no—
566C2×#41—7332no—
567C2×#41—738no—
568C2×#41—1468no—
569C2×#41C22×D7318yes—
570C2×#41C22×D7318yes—
571C22×Q8—2928no—
572C22×Q8—734no—
573C22×Q8—7316no—
574C22×Q8—731no—
575C22×Q8—734no—
576C22×Q8C22×D7311yescharacteristic
577C22×Q8C22×D7311yescharacteristic
578C22×D4—734no—
579C22×D4—732no—
580C22×D4—732no—
581C22×D4—732no—
582C22×D4—731no—
583C22×D4C22×D7312yes—
584C22×D4C22×D7312yes—
585C22×D4C22×D7311yescharacteristic
586C22×D4C22×D7311yescharacteristic
587C22×D4C22×D7314yes—
588C23×C4—732no—
589C23×C4—734no—
590C23×C4—734no—
591C23×C4—731no—
592C23×C4—732no—
593C23×C4—731no—
594C23×C4—732no—
595C23×C4—732no—
596C23×C4C22×D7312yes—
597C23×C4C22×D7312yes—
598C23×C4C22×D7312yes—
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—7332no—
620C22⋊Q8—7332no—
621C22⋊Q8C22×D73116yes—
622C22⋊Q8C22×D73116yes—
623#121—7316no—
624#121—7316no—
625#121—7332no—
626#121—7316no—
627#121—7332no—
628#121—7316no—
629#121C22×D73116yes—
630#121C22×D73116yes—
631#121C22×D73132yes—
632C4×Q8—738no—
633C4×Q8—738no—
634C4×Q8—7316no—
635C4×Q8—7316no—
636C4×Q8—7332no—
637C4×D4—738no—
638C4×D4—7316no—
639C4×D4—7316no—
640C4×D4—738no—
641C4×D4—7316no—
642C4×D4—7332no—
643C4×D4—7332no—
644C4×D4—7316no—
645C4×D4—7316no—
646C4×D4—7316no—
647C4×D4—7332no—
648#117—738no—
649#117—7316no—
650#117—7316no—
651#117—7316no—
652#117—7332no—
653C2×C4⋊C4—731no—
654C2×C4⋊C4—732no—
655C2×C4⋊C4—734no—
656C2×C4⋊C4—732no—
657C2×C4⋊C4—734no—
658C2×C4⋊C4—734no—
659C2×C4⋊C4—738no—
660C2×C4⋊C4—7316no—
661C2×C4⋊C4—734no—
662C2×C4⋊C4—7316no—
663C2×C4⋊C4—731no—
664C2×C4⋊C4—732no—
665C2×C4⋊C4—732no—
666C2×C4⋊C4—732no—
667C2×C4⋊C4—732no—
668C2×C4⋊C4—734no—
669C2×C4⋊C4—7316no—
670C2×C4⋊C4C22×D7312yes—
671C2×C4⋊C4C22×D7312yes—
672C2×C4⋊C4C22×D7318yes—
673C2×C4⋊C4C22×D7314yes—
674C2×C22⋊C4—732no—
675C2×C22⋊C4—734no—
676C2×C22⋊C4—732no—
677C2×C22⋊C4—732no—
678C2×C22⋊C4—734no—
679C2×C22⋊C4—732no—
680C2×C22⋊C4—732no—
681C2×C22⋊C4—734no—
682C2×C22⋊C4—734no—
683C2×C22⋊C4—732no—
684C2×C22⋊C4—732no—
685C2×C22⋊C4C22×D7314yes—
686C2×C22⋊C4C22×D7314yes—
687C2×C42—732no—
688C2×C42—734no—
689C2×C42—734no—
690C2×C42—731no—
691C2×C42—732no—
692C2×C42—731no—
693C2×C42—731no—
694C2×C42—732no—
695C2×C42—738no—
696C2×C42—7316no—
697C2×C42—731no—
698C24—732no—
699C24C23×D7312yes—
700C24C23×D7312yes—
701C24C23×D7311yescharacteristic
702#41—232no—
703#41—232no—
704#41—29264no—
705#41—14632no—
706C2×Q8—24no—
707C2×Q8—24no—
708C2×Q8—2928no—
709C2×Q8—29232no—
710C2×Q8—7316no—
711C2×Q8—734no—
712C2×Q8—7316no—
713C2×Q8—14616no—
714C2×Q8—1464no—
715C2×Q8C23×D7314yes—
716C2×Q8C23×D7314yes—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—48no—
722C2×D4—2928no—
723C2×D4—7316no—
724C2×D4—738no—
725C2×D4—738no—
726C2×D4—738no—
727C2×D4—734no—
728C2×D4—1468no—
729C2×D4—1468no—
730C2×D4—1468no—
731C2×D4—1464no—
732C2×D4C23×D7318yes—
733C2×D4C23×D7318yes—
734C2×D4C23×D7314yes—
735C2×D4C23×D7314yes—
736C2×D4C23×D73116yes—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—44no—
740C22×C4—2928no—
741C22×C4—2924no—
742C22×C4—2928no—
743C22×C4—738no—
744C22×C4—7316no—
745C22×C4—7316no—
746C22×C4—731no—
747C22×C4—731no—
748C22×C4—734no—
749C22×C4—738no—
750C22×C4—734no—
751C22×C4—738no—
752C22×C4—732no—
753C22×C4—731no—
754C22×C4—731no—
755C22×C4—732no—
756C22×C4—732no—
757C22×C4—734no—
758C22×C4—738no—
759C22×C4—1464no—
760C22×C4—1468no—
761C22×C4—1464no—
762C22×C4—1468no—
763C22×C4—1468no—
764C22×C4#1192402718yescomplemented
765C22×C4C23×D7318yes—
766C22×C4C23×D7318yes—
767C22×C4C23×D7312yes—
768C22×C4C23×D7312yes—
769C22×C4C23×D7314yes—
770C22×C4C23×D7318yes—
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—7316no—
780C4⋊C4—734no—
781C4⋊C4—738no—
782C4⋊C4—738no—
783C4⋊C4—7316no—
784C4⋊C4—734no—
785C4⋊C4—738no—
786C4⋊C4—738no—
787C4⋊C4C23×D7318yes—
788C4⋊C4C23×D7318yes—
789C4⋊C4C23×D73116yes—
790C22⋊C4—738no—
791C22⋊C4—7316no—
792C22⋊C4—738no—
793C22⋊C4—738no—
794C22⋊C4—7316no—
795C22⋊C4—738no—
796C22⋊C4—738no—
797C22⋊C4—7316no—
798C22⋊C4—7316no—
799C22⋊C4—738no—
800C22⋊C4—738no—
801C22⋊C4C23×D73116yes—
802C22⋊C4C23×D73116yes—
803C42—734no—
804C42—738no—
805C42—734no—
806C42—738no—
807C42—734no—
808C42—734no—
809C42—738no—
810C42—7316no—
811C42—7316no—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—734no—
821C23—1464no—
822C23—1464no—
823C23—1464no—
824C23C2×#1192402714yes—
825C23C24×D7314yes—
826C23C24×D7314yes—
827C23C24×D7312yes—
828C23C24×D7311yescharacteristic
829Q8—28no—
830Q8—28no—
831Q8—29216no—
832Q8—14632no—
833Q8—1468no—
834D4—216no—
835D4—216no—
836D4—28no—
837D4—28no—
838D4—416no—
839D4—29216no—
840D4—14616no—
841D4—14616no—
842D4—14616no—
843D4—1468no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—216no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—29216no—
851C2×C4—2928no—
852C2×C4—29216no—
853C2×C4—734no—
854C2×C4—734no—
855C2×C4—732no—
856C2×C4—732no—
857C2×C4—734no—
858C2×C4—732no—
859C2×C4—732no—
860C2×C4—734no—
861C2×C4—734no—
862C2×C4—738no—
863C2×C4—1468no—
864C2×C4—14616no—
865C2×C4—1468no—
866C2×C4—14616no—
867C2×C4—1464no—
868C2×C4—1464no—
869C2×C4—1468no—
870C2×C4—1462no—
871C2×C4—1464no—
872C2×C4—1462no—
873C2×C4—14616no—
874C2×C4C2×#1192402714yes—
875C2×C4C2×#1192402714yes—
876C2×C4C2×#11924027116yescomplemented
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—24no—
889C22—24no—
890C22—24no—
891C22—48no—
892C22—48no—
893C22—2928no—
894C22—1464no—
895C22—1464no—
896C22—1464no—
897C22C22×#1192402714yes—
898C22C22×#1192402712yes—
899C22H(5,𝔽2)×D7312yes—
900C222−1+4×D7312yes—
901C22C25×D7311yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—734no—
906C4—734no—
907C4—1464no—
908C4—1464no—
909C4—1468no—
910C4—1462no—
911C4—1464no—
912C4—1462no—
913C4C22×#1192402714yes—
914C4C22×#1192402714yes—
915C2—24no—
916C2—44no—
917C2—44no—
918C2—2924no—
919C2#2262384014yesdirect product factor
920C2C23×#1192402711yescharacteristic
921C2C2×H(5,𝔽2)×D7311yescharacteristic
922C2C2×2−1+4×D7311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#537×C73C2
socleC23×C73C25
hypercenterC2×#537D73
hypocenterC73C2×#3511
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #22623840C2direct (N × H)
2. C2×#17989308C2semidirect
3. C2×#17989301C2semidirect
4. C2×#17989295C2semidirect
5. C2×#17989280C2semidirect
6. C2×#17989243C2semidirect
7. C2×#17989237C2semidirect
8. C2×#17989210C2semidirect
9. C2×#17989204C2semidirect
10. C2×#17989165C2semidirect
11. C2×#17989139C2semidirect
12. C2×#17989133C2semidirect
13. C2×#17989132C2semidirect
14. C22×#14556590C2semidirect
15. C2×#17989070C2semidirect
16. C2×#17989068C2semidirect
17. C2×#41×Dic73C2semidirect
18. C2×#537×C73C2semidirect
22. #17989308C22semidirect
23. #17989301C22semidirect
24. #17989295C22semidirect
25. #17989280C22semidirect
26. #17989243C22semidirect
27. #17989237C22semidirect
28. #17989210C22semidirect
29. #17989204C22semidirect
30. #17989165C22semidirect
31. #17989139C22semidirect
32. #17989133C22semidirect
33. #17989132C22semidirect
38. C2×#14556590C22semidirect
62. #17989070C22semidirect
63. #17989068C22semidirect
64. #41×Dic73C22semidirect
94. #537×C73C22semidirect
335. C22×C4×C73#41semidirect
382. C2×C4×C73C2×#41semidirect
457. C2×C73#3511semidirect
472. C2×#537D73semidirect
480. C73C2×#3511semidirect
495. #537C2×D73semidirect
764. C22×C4#11924027semidirect
876. C2×C4C2×#11924027semidirect
919. C2#22623840direct (N × H)

Maximal subgroups

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

subgroupindex
#226238402
C2×#179893082
C2×#179893012
C2×#179892952
C2×#179892802
C2×#179892432
C2×#179892372
C2×#179892102
C2×#179892042
C2×#179891652
C2×#179891392
C2×#179891332
C2×#179891322
C22×#145565902
C2×#179890702
C2×#179890682
C2×#41×Dic732
C2×#537×C732
C2×#351173