Finite Group Databasebeta

← C2×#22625210 #34016037

Subgroups — C2×#22625210 #34016037

Order 18688.

1426 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989557C211yesmaximal, characteristic
2C22×C22⋊#10596833C211yesmaximal, characteristic
3#22625210C218yesmaximal, direct product factor
4C2×#17989433C212yesmaximal, complemented
5C2×#17989432C212yesmaximal, complemented
6C22×#14556568C211yesmaximal, characteristic
7C22×#11924037—21no—
8C23×#10596833—21no—
9#17989557—22no—
10#17989557C2214yes—
11C2×C22⋊#10596833—21no—
12C2×C22⋊#10596833—22no—
13C2×C22⋊#10596833—21no—
14C2×C22⋊#10596833C2212yes—
15C2×C22⋊#10596833C2212yes—
16C2×C22⋊#10596833C2214yes—
17#17989433C2218yescomplemented
18#17989432C2218yescomplemented
19C23×Dic146C411yescharacteristic
20C24×Dic73C2211yescharacteristic
21C2×#14556568—21no—
22C2×#14556568—21no—
23C2×#14556568—21no—
24C2×#14556568—22no—
25C2×#14556568—21no—
26C2×#14556568—22no—
27C2×#14556568C414yes—
28C2×#14556568C2214yes—
29C22×C4⋊Dic73C2211yescharacteristic
30C22×#11924007C411yescharacteristic
31C22×#11924007C2211yescharacteristic
32C22×C22⋊Dic73C411yescharacteristic
33C22×C22⋊C4×C73C411yescharacteristic
34C2×#11924037—24no—
35C2×#11924037—44no—
36C22×#10596833—22no—
37C22×#10596833—24no—
38C22×#10596833—22no—
39C22×#10596833—44no—
40C22⋊#10596833—22no—
41C22⋊#10596833—24no—
42C22⋊#10596833—24no—
43C22⋊#10596833—22no—
44C22⋊#10596833C2314yes—
45C22⋊#10596833C2314yes—
46C22×Dic146—22no—
47C22×Dic146—21no—
48C22×Dic146—21no—
49C22×Dic146—44no—
50C22×Dic146C2×C414yes—
51C23×Dic73—44no—
52C23×Dic73C2×C411yescharacteristic
53C23×Dic73C2×C411yescharacteristic
54C23×Dic73C2×C411yescharacteristic
55C23×Dic73C2×C412yes—
56C23×Dic73D411yescharacteristic
57C23×Dic73D411yescharacteristic
58C23×Dic73D411yescharacteristic
59C23×Dic73D412yes—
60C23×Dic73D411yescharacteristic
61C23×Dic73D412yes—
62C23×Dic73C2311yescharacteristic
63C23×Dic73C2312yes—
64#14556568—24no—
65#14556568—24no—
66#14556568—24no—
67#14556568—24no—
68#14556568—24no—
69#14556568—24no—
70#14556568—24no—
71#14556568—24no—
72C2×C4⋊Dic73—21no—
73C2×C4⋊Dic73—21no—
74C2×C4⋊Dic73—21no—
75C2×C4⋊Dic73—21no—
76C2×C4⋊Dic73C2×C412yes—
77C2×C4⋊Dic73C2312yes—
78C2×#11924007—22no—
79C2×#11924007—21no—
80C2×#11924007—21no—
81C2×#11924007—21no—
82C2×#11924007—21no—
83C2×#11924007—21no—
84C2×#11924007—21no—
85C2×#11924007C2×C414yes—
86C2×#11924007C2×C412yes—
87C2×#11924007C2312yes—
88C2×C22⋊Dic73—21no—
89C2×C22⋊Dic73—22no—
90C2×C22⋊Dic73—21no—
91C2×C22⋊Dic73C2×C414yes—
92C25×C73C2×C411yescharacteristic
93C23×C4×C73C2×C411yescharacteristic
94C23×C4×C73C2×C411yescharacteristic
95C2×C22⋊C4×C73—21no—
96C2×C22⋊C4×C73—22no—
97C2×C22⋊C4×C73—21no—
98C2×C22⋊C4×C73C2×C414yes—
99#11924037—48no—
100C2×#10596833—24no—
101C2×#10596833—24no—
102C2×#10596833—44no—
103C2×#10596833—48no—
104C2×#10596833—44no—
105C2×Dic146—24no—
106C2×Dic146—24no—
107C2×Dic146—44no—
108C2×Dic146—48no—
109C2×Dic146—44no—
110C2×Dic146—48no—
111C22×Dic73—24no—
112C22×Dic73—24no—
113C22×Dic73—24no—
114C22×Dic73—21no—
115C22×Dic73—21no—
116C22×Dic73—21no—
117C22×Dic73—21no—
118C22×Dic73—24no—
119C22×Dic73—44no—
120C22×Dic73—44no—
121C22×Dic73—44no—
122C22×Dic73—44no—
123C22×Dic73—42no—
124C22×Dic73—42no—
125C22×Dic73—42no—
126C22×Dic73—42no—
127C22×Dic73C22⋊C412yes—
128C22×Dic73C22⋊C411yescharacteristic
129C22×Dic73C22⋊C412yes—
130C22×Dic73C22⋊C412yes—
131C22×Dic73C22⋊C412yes—
132C22×Dic73C22⋊C412yes—
133C22×Dic73C22⋊C411yescharacteristic
134C22×Dic73C22×C412yes—
135C22×Dic73C22×C412yes—
136C22×Dic73C22×C412yes—
137C22×Dic73C22×C411yescharacteristic
138C22×Dic73C2×D411yescharacteristic
139C22×Dic73C2×D411yescharacteristic
140C22×Dic73C2×D412yes—
141C22×Dic73C2×D412yes—
142C22×Dic73C2×D411yescharacteristic
143C22×Dic73C2×D411yescharacteristic
144C22×Dic73C2×D412yes—
145C22×Dic73C2×D412yes—
146C22×Dic73C2411yescharacteristic
147C4⋊Dic73—22no—
148C4⋊Dic73—22no—
149C4⋊Dic73—22no—
150C4⋊Dic73—22no—
151#11924007—22no—
152#11924007—22no—
153#11924007—24no—
154#11924007—24no—
155#11924007—22no—
156#11924007—22no—
157C22⋊Dic73—24no—
158C22⋊Dic73—24no—
159C24×C73—24no—
160C24×C73—24no—
161C24×C73—42no—
162C24×C73C22⋊C411yescharacteristic
163C24×C73C22⋊C412yes—
164C24×C73C22⋊C411yescharacteristic
165C24×C73C22×C412yes—
166C24×C73C22×C411yescharacteristic
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—24no—
172C22×C4×C73—42no—
173C22×C4×C73C22×C412yes—
174C22×C4×C73C22×C412yes—
175C22⋊C4×C73—24no—
176C22⋊C4×C73—24no—
177C23×C73—22no—
178C23×C73—22no—
179C23×C73—22no—
180C23×C73—22no—
181C23×C73—24no—
182C23×C73—24no—
183C23×C73—22no—
184C23×C73—22no—
185C23×C73—24no—
186C23×C73—22no—
187C23×C73—24no—
188C23×C73—42no—
189C23×C73—42no—
190C23×C73—416no—
191C23×C73#10114yes—
192C23×C73C2×C22⋊C412yes—
193C23×C73C2×C22⋊C411yescharacteristic
194C23×C73C2×C22⋊C412yes—
195C23×C73C2×C22⋊C411yescharacteristic
196C23×C73#13114yes—
197C23×C73C23×C411yescharacteristic
198C2×C4×C73—22no—
199C2×C4×C73—22no—
200C2×C4×C73—24no—
201C2×C4×C73—42no—
202C2×C4×C73—42no—
203C2×C4×C73—42no—
204C2×C4×C73—42no—
205C2×C4×C73—42no—
206C2×Dic73—22no—
207C2×Dic73—22no—
208C2×Dic73—22no—
209C2×Dic73—24no—
210C2×Dic73—24no—
211C2×Dic73—24no—
212C2×Dic73—24no—
213C2×Dic73—24no—
214C2×Dic73—24no—
215C2×Dic73—22no—
216C2×Dic73—22no—
217C2×Dic73—24no—
218C2×Dic73—42no—
219C2×Dic73—42no—
220C2×Dic73—41no—
221C2×Dic73—42no—
222C2×Dic73—42no—
223C2×Dic73—41no—
224C2×Dic73—41no—
225C2×Dic73—41no—
226C2×Dic73—42no—
227C2×Dic73—42no—
228C2×Dic73—42no—
229C2×Dic73—42no—
230C2×Dic73—42no—
231C2×Dic73#9914yes—
232C2×Dic73C2×C22⋊C411yescharacteristic
233C2×Dic73C2×C22⋊C411yescharacteristic
234C2×Dic73C2×C22⋊C412yes—
235C2×Dic73C2×C22⋊C412yes—
236C2×Dic73C22×D411yescharacteristic
237C2×Dic73C22×D411yescharacteristic
238Dic146—48no—
239Dic146—48no—
240#10596833—44no—
241#10596833—44no—
242C22×C73—22no—
243C22×C73—21no—
244C22×C73—21no—
245C22×C73—22no—
246C22×C73—21no—
247C22×C73—21no—
248C22×C73—28no—
249C22×C73—28no—
250C22×C73—22no—
251C22×C73—22no—
252C22×C73—22no—
253C22×C73—48no—
254C22×C73—48no—
255C22×C73—44no—
256C22×C73#40812yes—
257C22×C73#40812yes—
258C22×C73C2×#9912yes—
259C22×C73C2×#10114yes—
260C22×C73C2×#10112yes—
261C22×C73C22×C22⋊C411yescharacteristic
262C22×C73C2×#13112yes—
263C4×C73—42no—
264C4×C73—42no—
265Dic73—21no—
266Dic73—21no—
267Dic73—22no—
268Dic73—21no—
269Dic73—21no—
270Dic73—42no—
271Dic73—42no—
272Dic73C2×#9914yes—
273C2×#1472—731nomaximal, Sylow
274C2×C73—22no—
275C2×C73—22no—
276C2×C73—24no—
277C2×C73—42no—
278C2×C73#147214yescomplemented
279C2×C73C2×#40811yescharacteristic
280C2×C73C22×#9911yescharacteristic
281C2×C73C22×#10111yescharacteristic
282C22×C22⋊Q8—731no—
283C2×#407—731no—
284C22×C22⋊C8—731no—
285#1472—738no—
286C2×#324—732no—
287C2×#324—732no—
288C73C2×#147211yescharacteristic, complemented, Sylow
289C23×Q8—731no—
290C24×C4—731no—
291C22×M16—1461no—
292C23×C8—1461no—
293C2×C22⋊Q8—734no—
294C2×C22⋊Q8—734no—
295C2×C22⋊Q8—1462no—
296C2×C22⋊Q8—1461no—
297C2×C22⋊Q8—1461no—
298C2×C22⋊Q8—1462no—
299C2×C22⋊Q8—1461no—
300C2×C22⋊Q8—1461no—
301C22×C4⋊C4—731no—
302C22×C4⋊C4—731no—
303C22×C4⋊C4—731no—
304C22×C22⋊C4—731no—
305C22×C22⋊C4#6440811yescharacteristic
306#407—734no—
307#407—1462no—
308C2×C22⋊C8—732no—
309C2×C22⋊C8—734no—
310C2×C22⋊C8—732no—
311C2×C22⋊C8—1462no—
312C2×C22⋊C8—1461no—
313C2×C22⋊C8—1461no—
314#324—738no—
315#324—738no—
316C25C2×#6440811yescharacteristic
317C22×Q8—2924no—
318C22×Q8—734no—
319C22×Q8—1462no—
320C22×Q8—1461no—
321C22×Q8—1461no—
322C23×C4—2924no—
323C23×C4—731no—
324C23×C4—731no—
325C23×C4—732no—
326C23×C4—732no—
327C23×C4—731no—
328C23×C4—732no—
329C23×C4—732no—
330C23×C4—731no—
331C23×C4—731no—
332C23×C4—731no—
333C23×C4—731no—
334C23×C4—731no—
335C23×C4C2×#6440811yescharacteristic
336C23×C4C2×#6440811yescharacteristic
337C2×M16—2924no—
338C2×M16—1464no—
339C22×C8—2924no—
340C22×C8—1464no—
341C22×C8—1462no—
342C22×C8—1462no—
343C22⋊Q8—1464no—
344C22⋊Q8—1464no—
345C22⋊Q8—1464no—
346C22⋊Q8—1464no—
347C22⋊Q8—1464no—
348C22⋊Q8—1464no—
349C22⋊Q8—1464no—
350C22⋊Q8—1464no—
351C2×C4⋊C4—732no—
352C2×C4⋊C4—732no—
353C2×C4⋊C4—732no—
354C2×C4⋊C4—734no—
355C2×C4⋊C4—732no—
356C2×C4⋊C4—1462no—
357C2×C4⋊C4—1461no—
358C2×C4⋊C4—1461no—
359C2×C4⋊C4—1461no—
360C2×C4⋊C4—1461no—
361C2×C4⋊C4—1461no—
362C2×C4⋊C4—1461no—
363C2×C4⋊C4—1461no—
364C2×C4⋊C4—1461no—
365C2×C4⋊C4—1461no—
366C2×C4⋊C4—1461no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—734no—
371C2×C22⋊C4—1462no—
372C2×C22⋊C4—1461no—
373C2×C22⋊C4—1461no—
374C2×C22⋊C4C2×#6440814yes—
375C22⋊C8—734no—
376C22⋊C8—734no—
377C22⋊C8—1462no—
378C22⋊C8—1464no—
379C22⋊C8—1462no—
380C22⋊C8—1464no—
381C24—24no—
382C24—24no—
383C24—42no—
384C24C22⋊#6440811yescharacteristic
385C24C22⋊#6440812yes—
386C24C22⋊#6440811yescharacteristic
387C24C22×#6440812yes—
388C24C22×#6440811yescharacteristic
389C2×Q8—2924no—
390C2×Q8—2928no—
391C2×Q8—2928no—
392C2×Q8—2924no—
393C2×Q8—1464no—
394C2×Q8—1464no—
395C22×C4—24no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—42no—
401C22×C4—2922no—
402C22×C4—2922no—
403C22×C4—2922no—
404C22×C4—2922no—
405C22×C4—2924no—
406C22×C4—2924no—
407C22×C4—2924no—
408C22×C4—2924no—
409C22×C4—731no—
410C22×C4—731no—
411C22×C4—732no—
412C22×C4—732no—
413C22×C4—731no—
414C22×C4—731no—
415C22×C4—732no—
416C22×C4—732no—
417C22×C4—732no—
418C22×C4—731no—
419C22×C4—732no—
420C22×C4—732no—
421C22×C4—732no—
422C22×C4—732no—
423C22×C4—732no—
424C22×C4—732no—
425C22×C4—731no—
426C22×C4—731no—
427C22×C4—731no—
428C22×C4—732no—
429C22×C4—1464no—
430C22×C4—1461no—
431C22×C4—1461no—
432C22×C4—1461no—
433C22×C4—1461no—
434C22×C4—1464no—
435C22×C4—1464no—
436C22×C4—1464no—
437C22×C4C22×#6440812yes—
438C22×C4C22×#6440812yes—
439M16—2928no—
440C2×C8—2928no—
441C2×C8—2924no—
442C2×C8—2924no—
443C2×C8—1464no—
444C2×C8—1464no—
445C4⋊C4—1464no—
446C4⋊C4—1464no—
447C4⋊C4—1462no—
448C4⋊C4—1462no—
449C4⋊C4—1462no—
450C4⋊C4—1462no—
451C4⋊C4—1462no—
452C4⋊C4—1462no—
453C4⋊C4—1462no—
454C4⋊C4—1462no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—1464no—
458C22⋊C4—1464no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—24no—
464C23—24no—
465C23—22no—
466C23—22no—
467C23—24no—
468C23—22no—
469C23—24no—
470C23—42no—
471C23—42no—
472C23—416no—
473C23#1455665214yes—
474C23C2×C22⋊#6440812yes—
475C23C2×C22⋊#6440811yescharacteristic
476C23C2×C22⋊#6440812yes—
477C23C2×C22⋊#6440811yescharacteristic
478C23#1455667814yes—
479C23C23×#6440811yescharacteristic
480Q8—2928no—
481Q8—2928no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—2922no—
491C2×C4—2922no—
492C2×C4—2922no—
493C2×C4—2922no—
494C2×C4—2922no—
495C2×C4—2921no—
496C2×C4—2922no—
497C2×C4—2922no—
498C2×C4—2921no—
499C2×C4—2921no—
500C2×C4—2922no—
501C2×C4—2922no—
502C2×C4—2921no—
503C2×C4—732no—
504C2×C4—734no—
505C2×C4—731no—
506C2×C4—731no—
507C2×C4—731no—
508C2×C4—731no—
509C2×C4—732no—
510C2×C4—1462no—
511C2×C4—1462no—
512C2×C4—1464no—
513C2×C4—1464no—
514C2×C4—1464no—
515C2×C4—1464no—
516C2×C4—1464no—
517C2×C4—1464no—
518C2×C4—1464no—
519C2×C4—1462no—
520C2×C4—1462no—
521C2×C4—1462no—
522C8—2924no—
523C8—2924no—
524C22—28no—
525C22—28no—
526C22—22no—
527C22—21no—
528C22—21no—
529C22—22no—
530C22—21no—
531C22—21no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—48no—
536C22—48no—
537C22—44no—
538C22#1798956012yes—
539C22#1798956012yes—
540C22D73⋊#9912yes—
541C22C2×#1455665214yes—
542C22C2×#1455665212yes—
543C22C22×C22⋊#6440811yescharacteristic
544C22C2×#1455667812yes—
545C4—42no—
546C4—42no—
547C4—2922no—
548C4—2922no—
549C4—734no—
550C4—1461no—
551C4—1461no—
552C4—1462no—
553C4—1461no—
554C4—1461no—
555C2—22no—
556C2—22no—
557C2—24no—
558C2—42no—
559C2#2262521014yesdirect product factor
560C2C2×#1798956011yescharacteristic
561C2C2×D73⋊#9911yescharacteristic
562C2C22×#1455665211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC23×C73C23×C4
FrattiniC23C23×#64408
FittingC22×C22⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC25×C73C2×C4
cosocleC22×Dic73C24
hypercenterC22×C22⋊C4#64408
hypocenterC73C2×#1472
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #22625210C2direct (N × H)
4. C2×#17989433C2semidirect
5. C2×#17989432C2semidirect
17. #17989433C22semidirect
18. #17989432C22semidirect
278. C2×C73#1472semidirect
288. C73C2×#1472semidirect
559. C2#22625210direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179895572
C22×C22⋊#105968332
#226252102
C2×#179894332
C2×#179894322
C22×#145565682
C2×#147273