Finite Group Databasebeta

← C2×#22624714 #33999829

Subgroups — C2×#22624714 #33999829

Order 18688.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989423C211yesmaximal, characteristic, complemented
2C22×#14556639C211yesmaximal, characteristic, complemented
3#22624714C2132yesmaximal, direct product factor
4C2×#17989403C214yesmaximal, complemented
5C2×#17989400C214yesmaximal, complemented
6C2×#17989396C214yesmaximal, complemented
7C2×#17989393C214yesmaximal, complemented
8C2×#17989387C211yesmaximal, characteristic, complemented
9C2×#17989386C214yesmaximal, complemented
10C2×#17989385C211yesmaximal, characteristic, complemented
11C22×#14556622C211yesmaximal, characteristic, complemented
12C2×#137×D73C214yesmaximal, complemented
13C2×#17989353C211yesmaximal, characteristic, complemented
14C22×#137×C73C211yesmaximal, characteristic, complemented
15#17989423—28no—
16#17989423C22116yescomplemented
17C2×#14556639—22no—
18C2×#14556639—22no—
19C2×#14556639—28no—
20C2×#14556639C2214yescomplemented
21C2×#14556639C2214yescomplemented
22C2×#14556639C2212yescomplemented
23C2×#14556639C22116yescomplemented
24C2×#14556638—21no—
25C2×#14556638C2212yescomplemented
26C2×#14556637—21no—
27C2×#14556637C2212yescomplemented
28C2×#14556636—22no—
29C2×#14556636C2212yescomplemented
30C22×#11924029—21no—
31C22×#11924029C2212yescomplemented
32C22×#11924028—22no—
33C22×#11924028—22no—
34C22×#11924028C2211yescharacteristic
35C22×#11924028C2211yescharacteristic
36C22×#11924028C2211yescharacteristic, complemented
37C2×#41×D73—22no—
38C2×#41×D73C2214yes—
39C22×Q8×D73—21no—
40C22×Q8×D73C2212yescomplemented
41#17989403C22164yescomplemented
42#17989400C22164yescomplemented
43#17989396C22164yescomplemented
44#17989393C22164yescomplemented
45#17989387C22116yescomplemented
46#17989386C22164yescomplemented
47#17989385C22116yescomplemented
48C2×#14556624C2212yescomplemented
49C2×#14556624C2212yescomplemented
50C2×#14556623C2218yescomplemented
51C2×#14556623C2218yescomplemented
52C2×#14556622C2214yescomplemented
53C2×#14556622C2214yescomplemented
54C2×#14556622C2212yescomplemented
55C2×#14556622C22116yescomplemented
56C2×#14556621C2212yescomplemented
57C2×#14556620C2218yescomplemented
58#137×D73C22164yescomplemented
59C2×#14556619C2212yescomplemented
60C2×#14556619C2212yescomplemented
61C2×#14556618C2218yescomplemented
62C2×#14556617C2212yescomplemented
63C2×#14556616C2212yescomplemented
64C2×#14556614C2218yescomplemented
65C2×#14556613C2214yescomplemented
66C2×#14556612C2218yescomplemented
67C2×#14556611C2214yescomplemented
68C22×#11924018C2212yescomplemented
69C2×Q16×D73C2218yescomplemented
70C22×#11924015C2212yescomplemented
71C2×SD16×D73C2218yescomplemented
72#17989353C22116yescomplemented
73C2×#14556599C2214yescomplemented
74C2×#14556597C2214yescomplemented
75C22×#11924012C2211yescharacteristic, complemented
76C2×M16×D73C2214yescomplemented
77C22×#41×C73C2211yescharacteristic
78C23×Q8×C73C2211yescharacteristic, complemented
79C2×#137×C73C2214yescomplemented
80C2×#137×C73C2214yescomplemented
81C2×#137×C73C22116yescomplemented
82C22×Q16×C73C2212yescomplemented
83C22×SD16×C73C2212yescomplemented
84C22×M16×C73C2211yescharacteristic, complemented
85#14556639—216no—
86#14556639—216no—
87#14556639—232no—
88#14556639—232no—
89#14556639—28no—
90#14556639C23132yescomplemented
91#14556639C23132yescomplemented
92#14556639C23116yescomplemented
93#14556638—28no—
94#14556638—216no—
95#14556638C23116yescomplemented
96#14556637—28no—
97#14556637—216no—
98#14556637C23116yescomplemented
99#14556636—28no—
100#14556636—232no—
101#14556636C23116yescomplemented
102C2×#11924029—22no—
103C2×#11924029—24no—
104C2×#11924029—24no—
105C2×#11924029—216no—
106C2×#11924029—24no—
107C2×#11924029—28no—
108C2×#11924029C2314yes—
109C2×#11924029C2318yes—
110C2×#11924029C23116yescomplemented
111C2×#11924028—232no—
112C2×#11924028—22no—
113C2×#11924028—22no—
114C2×#11924028—24no—
115C2×#11924028—28no—
116C2×#11924028—28no—
117C2×#11924028—232no—
118C2×#11924028—24no—
119C2×#11924028—21no—
120C2×#11924028—21no—
121C2×#11924028—24no—
122C2×#11924028—21no—
123C2×#11924028—21no—
124C2×#11924028—24no—
125C2×#11924028D412yes—
126C2×#11924028D412yes—
127C2×#11924028D418yes—
128C2×#11924028C2312yes—
129C2×#11924028C2312yes—
130C2×#11924028C2318yes—
131C2×#11924028C2312yes—
132C2×#11924028C2312yes—
133C2×#11924028C2312yes—
134C2×#11924028C2312yes—
135C2×#11924028C2318yes—
136C2×#11924028C2318yescomplemented
137C2×#11924027—22no—
138C2×#11924027—24no—
139C2×#11924027—24no—
140C2×#11924027C2314yes—
141#41×D73—232no—
142#41×D73—216no—
143#41×D73C23132yes—
144C22×Dic146—22no—
145C22×Dic146—22no—
146C22×Dic146D411yescharacteristic
147C22×Dic146C2311yescharacteristic
148C22×Dic146C2311yescharacteristic
149C2×Q8×D73—24no—
150C2×Q8×D73—24no—
151C2×Q8×D73—216no—
152C2×Q8×D73—22no—
153C2×Q8×D73—24no—
154C2×Q8×D73—28no—
155C2×Q8×D73C2318yes—
156C2×Q8×D73C2314yes—
157C2×Q8×D73C23116yescomplemented
158C22×D292—22no—
159C22×D292—22no—
160C22×D292D411yescharacteristic
161C22×D292C2311yescharacteristic
162C22×D292C2311yescharacteristic
163C22×C22⋊D73—24no—
164C22×C22⋊D73—21no—
165C22×C22⋊D73—21no—
166C22×C22⋊D73D412yes—
167C2×D4×D73—24no—
168C2×D4×D73—22no—
169C2×D4×D73—24no—
170C2×D4×D73C2314yes—
171C22×C4×D73—22no—
172C22×C4×D73—22no—
173C22×C4×D73—24no—
174C22×C4×D73—21no—
175C22×C4×D73—21no—
176C22×C4×D73C2312yes—
177#14556624C23116yescomplemented
178#14556624C23116yescomplemented
179#14556623C23164yescomplemented
180#14556623C23164yescomplemented
181#14556622C23132yescomplemented
182#14556622C23132yescomplemented
183#14556622C23116yescomplemented
184#14556621C23116yescomplemented
185#14556620C23164yescomplemented
186#14556619C23116yescomplemented
187#14556619C23116yescomplemented
188#14556618C23164yescomplemented
189#14556617C23116yescomplemented
190#14556616C23116yescomplemented
191#14556614C23164yescomplemented
192#14556613C23132yescomplemented
193#14556612C23164yescomplemented
194#14556611C23132yescomplemented
195C2×Dic292C2314yes—
196C2×#11924018C2318yes—
197C2×#11924018C2314yes—
198C2×#11924018C23116yescomplemented
199Q16×D73C23164yescomplemented
200C2×#11924017C2314yes—
201C2×#11924017C2314yes—
202C2×#11924016C2314yes—
203C2×#11924015C2318yes—
204C2×#11924015C2314yes—
205C2×#11924015C23116yescomplemented
206SD16×D73C23164yescomplemented
207C2×D584C2314yes—
208C2×#11924013C2314yes—
209#14556599C23132yescomplemented
210#14556597C23132yescomplemented
211C2×#11924012C2312yes—
212C2×#11924012C2312yes—
213C2×#11924012C2318yescomplemented
214C2×#11924011C2318yes—
215M16×D73C23132yescomplemented
216C22×#10596831C2312yes—
217C2×C8×D73C2318yes—
218C2×#41×C73—21no—
219C2×#41×C73—21no—
220C2×#41×C73—24no—
221C2×#41×C73C2312yes—
222C2×#41×C73C2318yes—
223C2×#41×C73C2312yes—
224C22×Q8×C73—21no—
225C22×Q8×C73—21no—
226C22×Q8×C73—21no—
227C22×Q8×C73—24no—
228C22×Q8×C73C2312yes—
229C22×Q8×C73C2312yes—
230C22×Q8×C73C2311yescharacteristic
231C22×Q8×C73C2312yes—
232C22×Q8×C73C2318yescomplemented
233C22×D4×C73—21no—
234C22×D4×C73C2311yescharacteristic
235C23×C4×C73—21no—
236C23×C4×C73—21no—
237C23×C4×C73C2311yescharacteristic
238#137×C73C23132yescomplemented
239#137×C73C23132yescomplemented
240C2×Q16×C73C2318yes—
241C2×Q16×C73C23116yescomplemented
242C2×SD16×C73C2318yes—
243C2×SD16×C73C23116yescomplemented
244C2×M16×C73C2312yes—
245C2×M16×C73C2312yes—
246C2×M16×C73C2318yescomplemented
247C22×C8×C73C2312yes—
248C23×D73—21no—
249C23×D73—21no—
250C23×D73—24no—
251C23×D73C2×D412yes—
252#11924029—216no—
253#11924029—232no—
254#11924029—232no—
255#11924029—28no—
256#11924029—216no—
257#11924029—232no—
258#11924029C24132yes—
259#11924029C24116yes—
260#11924028—24no—
261#11924028—28no—
262#11924028—24no—
263#11924028—28no—
264#11924028—24no—
265#11924028—24no—
266#11924028—28no—
267#11924028—28no—
268#11924028—232no—
269#11924028—264no—
270#11924028—264no—
271#11924028—216no—
272#11924028—232no—
273#11924028—216no—
274#11924028C2×D4116yes—
275#11924028C2×D4116yes—
276#11924028C2×D418yes—
277#11924028C2×D418yes—
278#11924028C2418yes—
279#11924028C2418yes—
280#11924028C2418yes—
281#11924028C2418yes—
282#11924028C2418yes—
283#11924028C2418yes—
284#11924027—232no—
285#11924027—232no—
286#11924027—28no—
287#11924027—216no—
288#11924027C24116yes—
289C2×Dic146—21no—
290C2×Dic146—22no—
291C2×Dic146—21no—
292C2×Dic146—22no—
293C2×Dic146—28no—
294C2×Dic146—216no—
295C2×Dic146—24no—
296C2×Dic146—216no—
297C2×Dic146C2×D412yes—
298C2×Dic146C2×D412yes—
299C2×Dic146C2×D418yes—
300C2×Dic146C2412yes—
301C2×Dic146C2412yes—
302C2×Dic146C2414yes—
303C2×Dic146C2414yes—
304Q8×D73—216no—
305Q8×D73—232no—
306Q8×D73—28no—
307Q8×D73—232no—
308Q8×D73—232no—
309Q8×D73—216no—
310Q8×D73C24132yes—
311Q8×D73C24116yes—
312C2×D292—24no—
313C2×D292—28no—
314C2×D292—216no—
315C2×D292—21no—
316C2×D292—21no—
317C2×D292—22no—
318C2×D292—22no—
319C2×D292—216no—
320C2×D292C2×D412yes—
321C2×D292C2×D412yes—
322C2×D292C2×D418yes—
323C2×D292C2412yes—
324C2×D292C2412yes—
325C2×D292C2414yes—
326C2×D292C2414yes—
327C2×C22⋊D73—22no—
328C2×C22⋊D73—22no—
329C2×C22⋊D73—22no—
330C2×C22⋊D73—22no—
331C2×C22⋊D73—28no—
332C2×C22⋊D73—28no—
333C2×C22⋊D73—24no—
334C2×C22⋊D73—232no—
335C2×C22⋊D73—24no—
336C2×C22⋊D73C2×D414yes—
337C2×C22⋊D73C2×D414yes—
338C2×C22⋊D73C2×D4116yes—
339D4×D73—232no—
340D4×D73—232no—
341D4×D73—216no—
342D4×D73—28no—
343D4×D73C24116yes—
344C22×Dic73—21no—
345C22×Dic73—21no—
346C22×Dic73—24no—
347C22×Dic73C2×D412yes—
348C2×C4×D73—24no—
349C2×C4×D73—28no—
350C2×C4×D73—216no—
351C2×C4×D73—22no—
352C2×C4×D73—22no—
353C2×C4×D73—22no—
354C2×C4×D73—22no—
355C2×C4×D73—28no—
356C2×C4×D73—28no—
357C2×C4×D73—24no—
358C2×C4×D73—28no—
359C2×C4×D73—216no—
360C2×C4×D73—232no—
361C2×C4×D73C2×D414yes—
362C2×C4×D73C2×D418yes—
363C2×C4×D73C2414yes—
364C2×C4×D73C2418yes—
365Dic292C24116yes—
366#11924018C24116yes—
367#11924018C24132yes—
368#11924017C24116yes—
369#11924017C24116yes—
370#11924016C24116yes—
371#11924015C24132yes—
372#11924015C24116yes—
373D584C24116yes—
374#11924013C24116yes—
375#11924012C2418yes—
376#11924012C2418yes—
377#11924011C24132yes—
378C2×#10596831C2414yes—
379C2×#10596831C2418yes—
380C8×D73C24132yes—
381C24×C73—21no—
382C24×C73C2×D411yescharacteristic
383#41×C73—28no—
384#41×C73—24no—
385#41×C73—28no—
386#41×C73—24no—
387#41×C73C2418yes—
388#41×C73C2418yes—
389C2×Q8×C73—22no—
390C2×Q8×C73—22no—
391C2×Q8×C73—22no—
392C2×Q8×C73—24no—
393C2×Q8×C73—24no—
394C2×Q8×C73—24no—
395C2×Q8×C73—28no—
396C2×Q8×C73—28no—
397C2×Q8×C73—28no—
398C2×Q8×C73—21no—
399C2×Q8×C73—22no—
400C2×Q8×C73C2414yes—
401C2×Q8×C73C2418yes—
402C2×Q8×C73C2412yes—
403C2×Q8×C73C2414yes—
404C2×Q8×C73C2418yes—
405C2×Q8×C73C2418yes—
406C2×D4×C73—22no—
407C2×D4×C73—22no—
408C2×D4×C73—28no—
409C2×D4×C73—21no—
410C2×D4×C73—22no—
411C2×D4×C73C2412yes—
412C2×D4×C73C2414yes—
413C22×C4×C73—21no—
414C22×C4×C73—22no—
415C22×C4×C73—22no—
416C22×C4×C73—22no—
417C22×C4×C73—28no—
418C22×C4×C73—22no—
419C22×C4×C73—22no—
420C22×C4×C73—28no—
421C22×C4×C73C2×D411yescharacteristic
422C22×C4×C73C2×D411yescharacteristic
423C22×C4×C73C2×D411yescharacteristic
424C22×C4×C73C2×D414yes—
425C22×C4×C73C2411yescharacteristic
426C22×C4×C73C2411yescharacteristic
427C22×C4×C73C2411yescharacteristic
428C22×C4×C73C2414yes—
429Q16×C73C24132yes—
430SD16×C73C24132yes—
431M16×C73C2418yes—
432M16×C73C2418yes—
433C2×C8×C73C2414yes—
434C2×C8×C73C2418yes—
435C23×C73—22no—
436C23×C73—24no—
437C23×C73—42no—
438C23×C73—82no—
439C23×C73C22×D411yescharacteristic
440C23×C73C22×D411yescharacteristic
441C23×C73C22×D411yescharacteristic
442C23×C73C22×D414yes—
443C22×D73—24no—
444C22×D73—22no—
445C22×D73—22no—
446C22×D73—24no—
447C22×D73—216no—
448C22×D73—44no—
449C22×D73—44no—
450C22×D73—88no—
451C22×D73—82no—
452C22×D73C22×D414yes—
453C22×D73C22×D418yes—
454Q8×C73—24no—
455Q8×C73—28no—
456Q8×C73—28no—
457Q8×C73—28no—
458Q8×C73—22no—
459Q8×C73—24no—
460Q8×C73C2518yes—
461Q8×C73C2514yes—
462D4×C73—28no—
463D4×C73—28no—
464D4×C73—22no—
465D4×C73—24no—
466D4×C73C2514yes—
467C2×C4×C73—22no—
468C2×C4×C73—24no—
469C2×C4×C73—28no—
470C2×C4×C73—24no—
471C2×C4×C73—28no—
472C2×C4×C73—28no—
473C2×C4×C73—28no—
474C2×C4×C73—28no—
475C2×C4×C73C22×D411yescharacteristic
476C2×C4×C73C22×D411yescharacteristic
477C2×C4×C73C22×D414yes—
478C2×C4×C73C22×D411yescharacteristic
479C2×C4×C73C22×D412yes—
480C2×C4×C73C22×D414yes—
481C2×C4×C73C22×D414yes—
482C2×C4×C73C22×D412yes—
483C2×C4×C73C22×D412yes—
484C2×C4×C73C2511yescharacteristic
485C2×C4×C73C2512yes—
486C2×C4×C73C2512yes—
487C2×C4×C73C2512yes—
488C22⋊D73—28no—
489C22⋊D73—28no—
490C22⋊D73—28no—
491C22⋊D73—28no—
492C22⋊D73—216no—
493C22⋊D73—216no—
494C22⋊D73C22×D4116yes—
495C22⋊D73C22×D4116yes—
496C2×Dic73—24no—
497C2×Dic73—22no—
498C2×Dic73—22no—
499C2×Dic73—24no—
500C2×Dic73—216no—
501C2×Dic73C22×D414yes—
502C2×Dic73C22×D418yes—
503D292—216no—
504D292—232no—
505D292—22no—
506D292—24no—
507D292—22no—
508D292—24no—
509D292C22×D418yes—
510D292C22×D418yes—
511D292C2514yes—
512D292C2514yes—
513C4×D73—216no—
514C4×D73—232no—
515C4×D73—28no—
516C4×D73—28no—
517C4×D73—28no—
518C4×D73—28no—
519C4×D73—216no—
520C4×D73—232no—
521C4×D73C22×D4116yes—
522C4×D73C22×D418yes—
523C4×D73C2518yes—
524Dic146—22no—
525Dic146—24no—
526Dic146—22no—
527Dic146—24no—
528Dic146—232no—
529Dic146—216no—
530Dic146C22×D418yes—
531Dic146C22×D418yes—
532Dic146C2514yes—
533Dic146C2514yes—
534C8×C73C2518yes—
535#10596831C2518yes—
536C22×C73—22no—
537C22×C73—22no—
538C22×C73—22no—
539C22×C73—24no—
540C22×C73—44no—
541C22×C73—44no—
542C22×C73—84no—
543C22×C73C23×D412yes—
544C22×C73C23×D412yes—
545C22×C73C23×D412yes—
546C22×C73C23×D411yescharacteristic
547C2×D73—28no—
548C2×D73—24no—
549C2×D73—24no—
550C2×D73—48no—
551C2×D73—48no—
552C2×D73—44no—
553C2×D73—44no—
554C2×D73—816no—
555C2×D73—84no—
556C2×D73C23×D418yes—
557C4×C73—24no—
558C4×C73—28no—
559C4×C73C23×D411yescharacteristic
560C4×C73C23×D412yes—
561C4×C73C23×D412yes—
562C4×C73C23×D412yes—
563C4×C73C2611yescharacteristic
564Dic73—24no—
565Dic73—24no—
566Dic73C23×D418yes—
567C2×#3586—731nomaximal, Sylow
568C2×C73—22no—
569C2×C73—22no—
570C2×C73—22no—
571C2×C73—44no—
572C2×C73#358612yescomplemented
573C2×C73C24×D411yescharacteristic
574D73—28no—
575D73—44no—
576D73—44no—
577C2×#585—731no—
578C22×2−1+4—731no—
579#3586—7332no—
580C2×#578—734no—
581C2×#578—734no—
582C2×#577—734no—
583C2×#577—734no—
584C2×#575—731no—
585C2×#575—734no—
586C2×#575—731no—
587C22×#137—731no—
588C22×#137—734no—
589C22×#137D7311yescharacteristic, complemented
590C2×#568—731no—
591C73C2×#358611yescharacteristic, complemented, Sylow
592#585—7316no—
593#585—1468no—
594C2×2−1+4—732no—
595C2×2−1+4—734no—
596C2×2−1+4—734no—
597C2×2−1+4—732no—
598C2×2−1+4—7316no—
599C2×2−1+4—1462no—
600C2×2−1+4—1462no—
601C2×2−1+4—1468no—
602C2×2−1+4—1461no—
603C2×H(5,𝔽2)—732no—
604C2×H(5,𝔽2)—732no—
605C2×H(5,𝔽2)—1462no—
606C2×H(5,𝔽2)—1461no—
607C22×#41—731no—
608C22×#41—734no—
609C22×#41—732no—
610C22×#41—731no—
611C22×#41—731no—
612C22×#41—1462no—
613C22×#41—1462no—
614C22×#41—1461no—
615C22×#41—1462no—
616C22×#41C2×D7311yescharacteristic
617C23×Q8—732no—
618C23×Q8—1461no—
619C23×Q8C2×D7311yescharacteristic, complemented
620#578—7364no—
621#578—7364no—
622#577—7364no—
623#577—7364no—
624#575—7316no—
625#575—7364no—
626#575—7316no—
627C2×#137—732no—
628C2×#137—734no—
629C2×#137—734no—
630C2×#137—732no—
631C2×#137—7316no—
632C2×#137—7364no—
633C2×#137—738no—
634C2×#137—738no—
635C2×#137—738no—
636C2×#137—732no—
637C2×#137—732no—
638C2×#137C2×D7314yescomplemented
639C2×#137C2×D7314yescomplemented
640C2×#137C2×D73116yescomplemented
641C2×AGL(1,ℤ/8)—732no—
642C2×AGL(1,ℤ/8)—732no—
643C2×AGL(1,ℤ/8)—738no—
644C2×AGL(1,ℤ/8)—732no—
645C2×AGL(1,ℤ/8)—732no—
646C2×#135—734no—
647C2×#135—738no—
648C2×#135—738no—
649C2×#135—734no—
650C22×Q16—732no—
651C22×Q16—738no—
652C22×Q16C2×D7312yescomplemented
653C22×SD16—732no—
654C22×SD16—738no—
655C22×SD16C2×D7312yescomplemented
656#568—7316no—
657C2×#131—734no—
658C2×#131—734no—
659C22×M16—731no—
660C22×M16—734no—
661C22×M16C2×D7311yescharacteristic, complemented
6622−1+4—7316no—
6632−1+4—7332no—
6642−1+4—7332no—
6652−1+4—7316no—
6662−1+4—14616no—
6672−1+4—14616no—
6682−1+4—14632no—
6692−1+4—14632no—
6702−1+4—1468no—
6712−1+4—14616no—
6722−1+4—1468no—
673H(5,𝔽2)—7316no—
674H(5,𝔽2)—7316no—
675H(5,𝔽2)—14632no—
676H(5,𝔽2)—1468no—
677H(5,𝔽2)—14616no—
678H(5,𝔽2)—1468no—
679C2×#41—21no—
680C2×#41—21no—
681C2×#41—24no—
682C2×#41—732no—
683C2×#41—732no—
684C2×#41—738no—
685C2×#41—732no—
686C2×#41—732no—
687C2×#41—738no—
688C2×#41—7332no—
689C2×#41—738no—
690C2×#41—734no—
691C2×#41—7316no—
692C2×#41—734no—
693C2×#41—732no—
694C2×#41—732no—
695C2×#41—732no—
696C2×#41—732no—
697C2×#41—738no—
698C2×#41—738no—
699C2×#41—1464no—
700C2×#41—1464no—
701C2×#41—1462no—
702C2×#41—1468no—
703C2×#41—1468no—
704C2×#41—14632no—
705C2×#41—1462no—
706C2×#41—14632no—
707C2×#41—1464no—
708C2×#41—1464no—
709C2×#41—1468no—
710C2×#41—14616no—
711C2×#41—1464no—
712C2×#41—1462no—
713C2×#41—1462no—
714C2×#41—1464no—
715C2×#41—1464no—
716C2×#41—14616no—
717C2×#41—14632no—
718C2×#41—1461no—
719C2×#41—1461no—
720C2×#41—1461no—
721C2×#41—1461no—
722C2×#41—1464no—
723C2×#41—1464no—
724C2×#41C22×D7312yes—
725C2×#41C22×D7312yes—
726C2×#41C22×D7318yes—
727C22×Q8—21no—
728C22×Q8—21no—
729C22×Q8—21no—
730C22×Q8—24no—
731C22×Q8—731no—
732C22×Q8—738no—
733C22×Q8—734no—
734C22×Q8—7316no—
735C22×Q8—731no—
736C22×Q8—731no—
737C22×Q8—1462no—
738C22×Q8—1462no—
739C22×Q8—1464no—
740C22×Q8—1468no—
741C22×Q8—1464no—
742C22×Q8—1464no—
743C22×Q8—14616no—
744C22×Q8—1462no—
745C22×Q8C22×D7312yes—
746C22×Q8C22×D7312yes—
747C22×Q8C22×D7311yescharacteristic
748C22×Q8C22×D7312yes—
749C22×Q8C22×D7318yescomplemented
750C22×D4—21no—
751C22×D4—732no—
752C22×D4—734no—
753C22×D4—731no—
754C22×D4—731no—
755C22×D4—731no—
756C22×D4—1462no—
757C22×D4—1462no—
758C22×D4—1464no—
759C22×D4—1462no—
760C22×D4—1464no—
761C22×D4—1464no—
762C22×D4—1461no—
763C22×D4—1461no—
764C22×D4C22×D7311yescharacteristic
765C23×C4—21no—
766C23×C4—21no—
767C23×C4—732no—
768C23×C4—1462no—
769C23×C4—1464no—
770C23×C4—1462no—
771C23×C4—1461no—
772C23×C4—1461no—
773C23×C4C22×D7311yescharacteristic
774#137—7316no—
775#137—7332no—
776#137—7332no—
777#137—7316no—
778#137—7364no—
779#137—7364no—
780#137—7364no—
781#137—7316no—
782#137—7316no—
783#137C22×D73132yescomplemented
784#137C22×D73132yescomplemented
785AGL(1,ℤ/8)—7316no—
786AGL(1,ℤ/8)—7316no—
787AGL(1,ℤ/8)—7364no—
788AGL(1,ℤ/8)—7316no—
789AGL(1,ℤ/8)—7316no—
790#135—7332no—
791#135—7364no—
792#135—7364no—
793#135—7332no—
794C2×Q16—734no—
795C2×Q16—738no—
796C2×Q16—7316no—
797C2×Q16—7364no—
798C2×Q16—734no—
799C2×Q16C22×D7318yes—
800C2×Q16C22×D73116yescomplemented
801C2×SD16—738no—
802C2×SD16—7316no—
803C2×SD16—734no—
804C2×SD16—734no—
805C2×SD16—7364no—
806C2×SD16—734no—
807C2×SD16—734no—
808C2×SD16C22×D7318yes—
809C2×SD16C22×D73116yescomplemented
810C2×D8—734no—
811C2×D8—734no—
812#131—7332no—
813#131—7332no—
814C2×M16—732no—
815C2×M16—732no—
816C2×M16—738no—
817C2×M16—7332no—
818C2×M16—738no—
819C2×M16C22×D7312yes—
820C2×M16C22×D7312yes—
821C2×M16C22×D7318yescomplemented
822C22×C8—732no—
823C22×C8—738no—
824C22×C8C22×D7312yes—
825C24—21no—
826C24—732no—
827C24—1464no—
828C24—1461no—
829C24—1461no—
830C24D4×D7311yescharacteristic
831#41—24no—
832#41—28no—
833#41—28no—
834#41—24no—
835#41—7316no—
836#41—7316no—
837#41—738no—
838#41—738no—
839#41—738no—
840#41—738no—
841#41—7332no—
842#41—7316no—
843#41—7316no—
844#41—738no—
845#41—738no—
846#41—738no—
847#41—738no—
848#41—14632no—
849#41—14632no—
850#41—14616no—
851#41—14664no—
852#41—14664no—
853#41—14616no—
854#41—14632no—
855#41—1468no—
856#41—1468no—
857#41—14632no—
858#41—14616no—
859#41—14632no—
860#41—14616no—
861#41—14616no—
862#41—14632no—
863#41—14632no—
864#41—1468no—
865#41—1464no—
866#41—1468no—
867#41—1464no—
868#41—1468no—
869#41—1468no—
870#41—1464no—
871#41—1464no—
872#41C23×D7318yes—
873#41C23×D7318yes—
874C2×Q8—24no—
875C2×Q8—22no—
876C2×Q8—22no—
877C2×Q8—22no—
878C2×Q8—28no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—28no—
882C2×Q8—28no—
883C2×Q8—21no—
884C2×Q8—22no—
885C2×Q8—732no—
886C2×Q8—732no—
887C2×Q8—738no—
888C2×Q8—7332no—
889C2×Q8—7316no—
890C2×Q8—732no—
891C2×Q8—732no—
892C2×Q8—734no—
893C2×Q8—734no—
894C2×Q8—14616no—
895C2×Q8—1468no—
896C2×Q8—1464no—
897C2×Q8—14616no—
898C2×Q8—14632no—
899C2×Q8—14616no—
900C2×Q8—1468no—
901C2×Q8—14632no—
902C2×Q8—14632no—
903C2×Q8—14616no—
904C2×Q8—1462no—
905C2×Q8—1461no—
906C2×Q8—1461no—
907C2×Q8—1462no—
908C2×Q8C23×D7314yes—
909C2×Q8C23×D7312yes—
910C2×Q8C23×D7318yes—
911C2×Q8C23×D7318yes—
912C2×Q8C23×D7314yes—
913C2×Q8C23×D7318yes—
914C2×D4—22no—
915C2×D4—22no—
916C2×D4—28no—
917C2×D4—21no—
918C2×D4—22no—
919C2×D4—734no—
920C2×D4—734no—
921C2×D4—7316no—
922C2×D4—7316no—
923C2×D4—732no—
924C2×D4—732no—
925C2×D4—738no—
926C2×D4—732no—
927C2×D4—732no—
928C2×D4—734no—
929C2×D4—734no—
930C2×D4—14616no—
931C2×D4—1464no—
932C2×D4—14616no—
933C2×D4—1468no—
934C2×D4—1468no—
935C2×D4—1464no—
936C2×D4—14632no—
937C2×D4—14616no—
938C2×D4—14632no—
939C2×D4—14632no—
940C2×D4—1464no—
941C2×D4—1462no—
942C2×D4—1462no—
943C2×D4—1468no—
944C2×D4—1462no—
945C2×D4—1462no—
946C2×D4—1468no—
947C2×D4—1461no—
948C2×D4—1462no—
949C2×D4—1461no—
950C2×D4—1462no—
951C2×D4C23×D7312yes—
952C2×D4C23×D7314yes—
953C22×C4—22no—
954C22×C4—21no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—28no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—28no—
961C22×C4—732no—
962C22×C4—734no—
963C22×C4—738no—
964C22×C4—734no—
965C22×C4—738no—
966C22×C4—1464no—
967C22×C4—14616no—
968C22×C4—1468no—
969C22×C4—14632no—
970C22×C4—1464no—
971C22×C4—14616no—
972C22×C4—1468no—
973C22×C4—1464no—
974C22×C4—1461no—
975C22×C4—1461no—
976C22×C4—1462no—
977C22×C4—1462no—
978C22×C4—1468no—
979C22×C4—1462no—
980C22×C4—1462no—
981C22×C4—1468no—
982C22×C4D4×D7311yescharacteristic
983C22×C4D4×D7311yescharacteristic
984C22×C4D4×D7311yescharacteristic
985C22×C4D4×D7314yes—
986C22×C4C23×D7311yescharacteristic
987C22×C4C23×D7311yescharacteristic
988C22×C4C23×D7311yescharacteristic
989C22×C4C23×D7314yes—
990Q16—7316no—
991Q16—7332no—
992Q16—7316no—
993Q16C23×D73132yes—
994SD16—7332no—
995SD16—7316no—
996SD16—7316no—
997SD16—7316no—
998SD16—7316no—
999SD16C23×D73132yes—
1000D8—7316no—
1001D8—7316no—
1002M16—738no—
1003M16—738no—
1004M16—7332no—
1005M16C23×D7318yes—
1006M16C23×D7318yes—
1007C2×C8—734no—
1008C2×C8—738no—
1009C2×C8—7332no—
1010C2×C8C23×D7314yes—
1011C2×C8C23×D7318yes—
1012C23—22no—
1013C23—24no—
1014C23—42no—
1015C23—82no—
1016C23—2924no—
1017C23—2924no—
1018C23—5842no—
1019C23—5848no—
1020C23—738no—
1021C23—734no—
1022C23—14616no—
1023C23—1464no—
1024C23—1462no—
1025C23—1462no—
1026C23—1464no—
1027C23C2×D4×D7311yescharacteristic
1028C23C2×D4×D7311yescharacteristic
1029C23C2×D4×D7311yescharacteristic
1030C23C2×D4×D7314yes—
1031Q8—28no—
1032Q8—28no—
1033Q8—24no—
1034Q8—28no—
1035Q8—22no—
1036Q8—24no—
1037Q8—738no—
1038Q8—738no—
1039Q8—734no—
1040Q8—734no—
1041Q8—14632no—
1042Q8—14616no—
1043Q8—1464no—
1044Q8—1462no—
1045Q8—1464no—
1046Q8—1462no—
1047Q8C24×D7318yes—
1048Q8C24×D7314yes—
1049D4—28no—
1050D4—28no—
1051D4—22no—
1052D4—24no—
1053D4—7316no—
1054D4—7316no—
1055D4—738no—
1056D4—738no—
1057D4—734no—
1058D4—734no—
1059D4—14616no—
1060D4—14632no—
1061D4—14616no—
1062D4—14616no—
1063D4—1468no—
1064D4—1468no—
1065D4—1468no—
1066D4—1468no—
1067D4—1464no—
1068D4—1462no—
1069D4—1464no—
1070D4—1462no—
1071D4C24×D7314yes—
1072C2×C4—28no—
1073C2×C4—24no—
1074C2×C4—28no—
1075C2×C4—28no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—28no—
1079C2×C4—28no—
1080C2×C4—738no—
1081C2×C4—734no—
1082C2×C4—7316no—
1083C2×C4—738no—
1084C2×C4—738no—
1085C2×C4—14616no—
1086C2×C4—14632no—
1087C2×C4—14616no—
1088C2×C4—14632no—
1089C2×C4—14616no—
1090C2×C4—1464no—
1091C2×C4—1464no—
1092C2×C4—1462no—
1093C2×C4—1462no—
1094C2×C4—1468no—
1095C2×C4—1468no—
1096C2×C4—1468no—
1097C2×C4—1468no—
1098C2×C4C2×D4×D7314yes—
1099C2×C4C2×D4×D7312yes—
1100C2×C4C2×D4×D7314yes—
1101C2×C4C2×D4×D7314yes—
1102C2×C4C2×D4×D7312yes—
1103C2×C4C2×D4×D7312yes—
1104C2×C4C2×D4×D7311yescharacteristic
1105C2×C4C2×D4×D7311yescharacteristic
1106C2×C4C2×D4×D7311yescharacteristic
1107C2×C4C24×D7312yes—
1108C2×C4C24×D7312yes—
1109C2×C4C24×D7312yes—
1110C2×C4C24×D7311yescharacteristic
1111C8—738no—
1112C8C24×D7318yes—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22—24no—
1117C22—44no—
1118C22—44no—
1119C22—84no—
1120C22—2928no—
1121C22—2928no—
1122C22—2924no—
1123C22—2924no—
1124C22—5844no—
1125C22—58416no—
1126C22—738no—
1127C22—1464no—
1128C22—1464no—
1129C22—1468no—
1130C22C22×D4×D7312yes—
1131C22C22×D4×D7312yes—
1132C22C22×D4×D7312yes—
1133C22C22×D4×D7311yescharacteristic
1134C4—24no—
1135C4—28no—
1136C4—738no—
1137C4—1464no—
1138C4—1464no—
1139C4C22×D4×D7312yes—
1140C4C22×D4×D7312yes—
1141C4C22×D4×D7311yescharacteristic
1142C4C22×D4×D7312yes—
1143C4C25×D7311yescharacteristic
1144C2—22no—
1145C2—22no—
1146C2—22no—
1147C2—44no—
1148C2—2924no—
1149C2—2924no—
1150C2—1468no—
1151C2#2262471412yesdirect product factor
1152C2C23×D4×D7311yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC4×C73C26
FrattiniC4C25×D73
FittingC22×#137×C73C2
socleC22×C73C23×D4
hypercenterC22×#137D73
hypocenterC73C2×#3586
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C2×#17989423C2semidirect
2. C22×#14556639C2semidirect
3. #22624714C2direct (N × H)
4. C2×#17989403C2semidirect
5. C2×#17989400C2semidirect
6. C2×#17989396C2semidirect
7. C2×#17989393C2semidirect
8. C2×#17989387C2semidirect
9. C2×#17989386C2semidirect
10. C2×#17989385C2semidirect
11. C22×#14556622C2semidirect
12. C2×#137×D73C2semidirect
13. C2×#17989353C2semidirect
14. C22×#137×C73C2semidirect
16. #17989423C22semidirect
20. C2×#14556639C22semidirect
21. C2×#14556639C22semidirect
22. C2×#14556639C22semidirect
23. C2×#14556639C22semidirect
25. C2×#14556638C22semidirect
27. C2×#14556637C22semidirect
29. C2×#14556636C22semidirect
31. C22×#11924029C22semidirect
36. C22×#11924028C22semidirect
40. C22×Q8×D73C22semidirect
41. #17989403C22semidirect
42. #17989400C22semidirect
43. #17989396C22semidirect
44. #17989393C22semidirect
45. #17989387C22semidirect
46. #17989386C22semidirect
47. #17989385C22semidirect
48. C2×#14556624C22semidirect
49. C2×#14556624C22semidirect
50. C2×#14556623C22semidirect
51. C2×#14556623C22semidirect
52. C2×#14556622C22semidirect
53. C2×#14556622C22semidirect
54. C2×#14556622C22semidirect
55. C2×#14556622C22semidirect
56. C2×#14556621C22semidirect
57. C2×#14556620C22semidirect
58. #137×D73C22semidirect
59. C2×#14556619C22semidirect
60. C2×#14556619C22semidirect
61. C2×#14556618C22semidirect
62. C2×#14556617C22semidirect
63. C2×#14556616C22semidirect
64. C2×#14556614C22semidirect
65. C2×#14556613C22semidirect
66. C2×#14556612C22semidirect
67. C2×#14556611C22semidirect
68. C22×#11924018C22semidirect
69. C2×Q16×D73C22semidirect
70. C22×#11924015C22semidirect
71. C2×SD16×D73C22semidirect
72. #17989353C22semidirect
73. C2×#14556599C22semidirect
74. C2×#14556597C22semidirect
75. C22×#11924012C22semidirect
76. C2×M16×D73C22semidirect
78. C23×Q8×C73C22semidirect
79. C2×#137×C73C22semidirect
80. C2×#137×C73C22semidirect
81. C2×#137×C73C22semidirect
82. C22×Q16×C73C22semidirect
83. C22×SD16×C73C22semidirect
84. C22×M16×C73C22semidirect
90. #14556639C23semidirect
91. #14556639C23semidirect
92. #14556639C23semidirect
95. #14556638C23semidirect
98. #14556637C23semidirect
101. #14556636C23semidirect
110. C2×#11924029C23semidirect
136. C2×#11924028C23semidirect
157. C2×Q8×D73C23semidirect
177. #14556624C23semidirect
178. #14556624C23semidirect
179. #14556623C23semidirect
180. #14556623C23semidirect
181. #14556622C23semidirect
182. #14556622C23semidirect
183. #14556622C23semidirect
184. #14556621C23semidirect
185. #14556620C23semidirect
186. #14556619C23semidirect
187. #14556619C23semidirect
188. #14556618C23semidirect
189. #14556617C23semidirect
190. #14556616C23semidirect
191. #14556614C23semidirect
192. #14556613C23semidirect
193. #14556612C23semidirect
194. #14556611C23semidirect
198. C2×#11924018C23semidirect
199. Q16×D73C23semidirect
205. C2×#11924015C23semidirect
206. SD16×D73C23semidirect
209. #14556599C23semidirect
210. #14556597C23semidirect
213. C2×#11924012C23semidirect
215. M16×D73C23semidirect
232. C22×Q8×C73C23semidirect
238. #137×C73C23semidirect
239. #137×C73C23semidirect
241. C2×Q16×C73C23semidirect
243. C2×SD16×C73C23semidirect
246. C2×M16×C73C23semidirect
572. C2×C73#3586semidirect
589. C22×#137D73semidirect
591. C73C2×#3586semidirect
619. C23×Q8C2×D73semidirect
638. C2×#137C2×D73semidirect
639. C2×#137C2×D73semidirect
640. C2×#137C2×D73semidirect
652. C22×Q16C2×D73semidirect
655. C22×SD16C2×D73semidirect
661. C22×M16C2×D73semidirect
749. C22×Q8C22×D73semidirect
783. #137C22×D73semidirect
784. #137C22×D73semidirect
800. C2×Q16C22×D73semidirect
809. C2×SD16C22×D73semidirect
821. C2×M16C22×D73semidirect
1151. C2#22624714direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179894232
C22×#145566392
#226247142
C2×#179894032
C2×#179894002
C2×#179893962
C2×#179893932
C2×#179893872
C2×#179893862
C2×#179893852
C22×#145566222
C2×#137×D732
C2×#179893532
C22×#137×C732
C2×#358673