Finite Group Databasebeta

← #34023909

Subgroups — #34023909

Order 18688.

1130 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989604C211yesmaximal, characteristic, complemented
2C2×#17989590C211yesmaximal, characteristic, complemented
3#22626102C212yesmaximal, complemented
4#22626054C212yesmaximal, complemented
5#22625910C212yesmaximal, complemented
6#22625908C212yesmaximal, complemented
7#22625790C212yesmaximal, complemented
8#22625789C212yesmaximal, complemented
9C2×#17989114C211yesmaximal, characteristic
10C22×#11924037C2212yes—
11#17989604—24no—
12#17989590—24no—
13C2×#14556658C2212yes—
14C2×#14556658C2212yes—
15C2×C4⋊#10596833C2212yes—
16C2×#14556648C2214yes—
17C2×C22⋊#10596833C2212yes—
18C2×C22⋊#10596833C2214yes—
19C2×C4×#10596833C2212yes—
20#17989453C2214yes—
21#17989453C2214yes—
22#17989114—24no—
23#17989114—24no—
24C2×#14556586C411yescharacteristic
25C2×#14556584C411yescharacteristic
26C2×#14556581C411yescharacteristic
27C2×#14556577C411yescharacteristic
28C2×#14556574C411yescharacteristic
29C2×#14556568C411yescharacteristic
30C2×#14556563C411yescharacteristic
31C2×#14556556C2211yescharacteristic
32C2×D4×Dic73C2211yescharacteristic
33C2×#14556551C2211yescharacteristic
34C2×#14556551C2211yescharacteristic
35C2×#14556549C2211yescharacteristic
36C2×#14556547C2211yescharacteristic
37C22×C4×Dic73C2211yescharacteristic
38C2×#123×C73C411yescharacteristic
39C2×#11924037—24no—
40C2×#11924037—44no—
41C22×#10596833C2314yes—
42C22×#10596833C2314yes—
43#14556658—24no—
44#14556658—24no—
45C4⋊#10596833—24no—
46#14556648—44no—
47C22⋊#10596833—24no—
48C22⋊#10596833—44no—
49C4×#10596833—24no—
50C22×Dic146C2×C411yescharacteristic
51C22×C22⋊D73C2×C411yescharacteristic
52C22×C22⋊D73C2×C411yescharacteristic
53C23×Dic73C2×C411yescharacteristic
54C23×Dic73C2311yescharacteristic
55C23×Dic73C2311yescharacteristic
56C22×C4×D73C2311yescharacteristic
57#14556586—24no—
58#14556584—24no—
59#14556581—24no—
60#14556577—24no—
61#14556574—24no—
62#14556568—24no—
63#14556563—24no—
64#14556556—22no—
65#14556556—22no—
66D4×Dic73—22no—
67D4×Dic73—22no—
68#14556551—22no—
69#14556551—22no—
70#14556551—22no—
71#14556551—22no—
72#14556549—22no—
73#14556549—22no—
74#14556547—22no—
75#14556547—22no—
76C2×C4⋊Dic73C2×C411yescharacteristic
77C2×C4⋊Dic73C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×#11924007C2×C411yescharacteristic
84C2×C22⋊Dic73C2×C411yescharacteristic
85C2×C22⋊Dic73C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×#11924005C2×C411yescharacteristic
88C2×#11924005C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×C4×Dic73C2×C411yescharacteristic
92C2×C4×Dic73C2×C411yescharacteristic
93C2×C4×Dic73D414yes—
94C2×C4×Dic73D414yes—
95C2×C4×Dic73C2311yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C22×D4×C73C2×C411yescharacteristic
100C23×C4×C73C2×C411yescharacteristic
101#123×C73—24no—
102C2×C4⋊C4×C73C2×C411yescharacteristic
103C2×C4⋊C4×C73C2×C411yescharacteristic
104C2×C22⋊C4×C73C2×C411yescharacteristic
105C2×C22⋊C4×C73C2×C411yescharacteristic
106C2×C22⋊C4×C73C2×C411yescharacteristic
107#11924037—48no—
108C2×#10596833—24no—
109C2×#10596833—24no—
110C2×#10596833—24no—
111C2×#10596833—24no—
112C2×#10596833—24no—
113C2×#10596833—24no—
114C23×D73C22×C411yescharacteristic
115C2×Dic146—22no—
116C2×Dic146—24no—
117C2×C22⋊D73—22no—
118C2×C22⋊D73—22no—
119C2×C22⋊D73—24no—
120C2×C22⋊D73—42no—
121C22×Dic73—24no—
122C22×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—22no—
127C22×Dic73—22no—
128C22×Dic73C22⋊C414yes—
129C22×Dic73C22×C411yescharacteristic
130C22×Dic73C22×C411yescharacteristic
131C22×Dic73C22×C411yescharacteristic
132C22×Dic73C22×C411yescharacteristic
133C22×Dic73C22×C411yescharacteristic
134C22×Dic73C22×C411yescharacteristic
135C22×Dic73C2×D412yes—
136C22×Dic73C2×D412yes—
137C22×Dic73C2411yescharacteristic
138C2×C4×D73—21no—
139C2×C4×D73—21no—
140C2×C4×D73—22no—
141C2×C4×D73—22no—
142C4⋊Dic73—22no—
143C4⋊Dic73—22no—
144#11924007—22no—
145#11924007—22no—
146#11924007—22no—
147#11924007—22no—
148#11924007—22no—
149#11924007—22no—
150C22⋊Dic73—22no—
151C22⋊Dic73—22no—
152C22⋊Dic73—22no—
153#11924005—22no—
154#11924005—22no—
155#11924005—22no—
156#11924005—22no—
157C4×Dic73—21no—
158C4×Dic73—21no—
159C4×Dic73—21no—
160C4×Dic73—21no—
161C4×Dic73C22⋊C414yes—
162C4×Dic73C22⋊C414yes—
163C4×Dic73C2×D412yes—
164C4×Dic73C2×D412yes—
165C4×Dic73C2×D412yes—
166C4×Dic73C2×D412yes—
167C24×C73C22×C411yescharacteristic
168C24×C73C22×C411yescharacteristic
169C2×D4×C73—22no—
170C2×D4×C73—42no—
171C22×C4×C73—42no—
172C22×C4×C73C22⋊C414yes—
173C22×C4×C73C22×C411yescharacteristic
174C22×C4×C73C22×C411yescharacteristic
175C22×C4×C73C22×C411yescharacteristic
176C22×C4×C73C22×C411yescharacteristic
177C22×C4×C73C22×C411yescharacteristic
178C4⋊C4×C73—22no—
179C4⋊C4×C73—22no—
180C22⋊C4×C73—22no—
181C22⋊C4×C73—22no—
182C22⋊C4×C73—22no—
183C23×C73—22no—
184C23×C73—22no—
185C23×C73—22no—
186C23×C73—21no—
187C23×C73—22no—
188C23×C73—22no—
189C23×C73—22no—
190C23×C73C2×C22⋊C412yes—
191C23×C73C23×C411yescharacteristic
192C22×D73—21no—
193C22×D73—22no—
194C22×D73—22no—
195C22×D73—22no—
196D4×C73—44no—
197C2×C4×C73—22no—
198C2×C4×C73—22no—
199C2×C4×C73—21no—
200C2×C4×C73—21no—
201C2×C4×C73—21no—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—22no—
205C2×C4×C73—44no—
206C2×C4×C73C2×C22⋊C412yes—
207C2×C4×C73C2×C22⋊C412yes—
208C22⋊D73—44no—
209C22⋊D73—44no—
210C2×Dic73—22no—
211C2×Dic73—22no—
212C2×Dic73—22no—
213C2×Dic73—22no—
214C2×Dic73—24no—
215C2×Dic73—28no—
216C2×Dic73—21no—
217C2×Dic73—21no—
218C2×Dic73—21no—
219C2×Dic73—22no—
220C2×Dic73—22no—
221C2×Dic73—22no—
222C2×Dic73—41no—
223C2×Dic73—41no—
224C2×Dic73—42no—
225C2×Dic73C2×C22⋊C412yes—
226C2×Dic73C2×C22⋊C412yes—
227C2×Dic73C2×C22⋊C412yes—
228C2×Dic73#13114yes—
229C2×Dic73C22×D411yescharacteristic
230C2×Dic73C22×D411yescharacteristic
231C2×Dic73H(5,𝔽2)12yes—
232C2×Dic732−1+412yes—
233C4×D73—41no—
234C4×D73—41no—
235C4×D73—42no—
236Dic146—44no—
237#10596833—44no—
238#10596833—44no—
239C22×C73—22no—
240C22×C73—22no—
241C22×C73—22no—
242C22×C73—44no—
243C22×C73—41no—
244C22×C73—41no—
245C22×C73—41no—
246C22×C73—44no—
247C22×C73C22×C22⋊C411yescharacteristic
248C22×C73#52012yes—
249C22×C73C2×#13112yes—
250C22×C73#56812yes—
251C2×D73—41no—
252C2×D73—41no—
253C2×D73—41no—
254C2×D73—44no—
255C4×C73—22no—
256C4×C73—22no—
257C4×C73—41no—
258C4×C73—41no—
259C4×C73—41no—
260Dic73—22no—
261Dic73—22no—
262Dic73—41no—
263Dic73—41no—
264Dic73—41no—
265Dic73#40814yes—
266Dic73#53511yescharacteristic
267Dic73#53611yescharacteristic
268Dic73#53712yes—
269#21850—731nomaximal, Sylow
270C2×C73—42no—
271C2×C73—81no—
272C2×C73#231111yescharacteristic
273C2×C73C2×#40811yescharacteristic
274C2×C73#287911yescharacteristic
275C2×C73#299314yes—
276D73—81no—
277C2×#529—731no—
278C2×#431—731no—
279C2×#423—731no—
280#1984—732no—
281#1954—732no—
282#1870—732no—
283#1870—732no—
284#1798—732no—
285#1798—732no—
286C73#2185011yescharacteristic, complemented, Sylow
287C22×M16—732no—
288#529—1464no—
289#529—1464no—
290C2×#126—731no—
291C2×#126—731no—
292C2×#125—731no—
293C2×#124—731no—
294C2×#123—731no—
295C2×#123#6440811yescharacteristic
296C2×C22⋊Q8—731no—
297C2×#121—731no—
298C2×C4×Q8—731no—
299C2×C4×D4—731no—
300C2×C4×D4—731no—
301C2×C4×D4—731no—
302C2×#117—731no—
303C2×#117—731no—
304C22×C42—731no—
305#431—1464no—
306#423—1464no—
307C2×C4⋊C8—732no—
308C2×C4⋊C8—732no—
309C2×C4⋊C8—732no—
310C2×C22⋊C8—734no—
311C2×C22⋊C8—734no—
312C2×C22⋊C8—732no—
313C2×C4×C8—732no—
314#336—734no—
315#336—734no—
316C22×Q8—731no—
317C22×D4—731no—
318C22×D4—731no—
319C22×D4C2×#6440811yescharacteristic
320C23×C4—731no—
321C23×C4—731no—
322C23×C4—731no—
323C23×C4—731no—
324C23×C4C2×#6440811yescharacteristic
325C2×M16—2924no—
326C2×M16—1464no—
327C22×C8—734no—
328C22×C8—734no—
329#126—1464no—
330#126—1464no—
331#125—1464no—
332#124—1464no—
333#123—24no—
334#123—1464no—
335C22⋊Q8—1464no—
336#121—1464no—
337C4×Q8—1462no—
338C4×Q8—1462no—
339C4×D4—1462no—
340C4×D4—1462no—
341C4×D4—1462no—
342C4×D4—1462no—
343C4×D4—1462no—
344C4×D4—1462no—
345#117—1462no—
346#117—1462no—
347#117—1462no—
348#117—1462no—
349C2×C4⋊C4—731no—
350C2×C4⋊C4—731no—
351C2×C4⋊C4—731no—
352C2×C4⋊C4—731no—
353C2×C4⋊C4—731no—
354C2×C4⋊C4—731no—
355C2×C4⋊C4—731no—
356C2×C4⋊C4—731no—
357C2×C4⋊C4C2×#6440811yescharacteristic
358C2×C4⋊C4C2×#6440811yescharacteristic
359C2×C22⋊C4—731no—
360C2×C22⋊C4—731no—
361C2×C22⋊C4—731no—
362C2×C22⋊C4—731no—
363C2×C22⋊C4—731no—
364C2×C22⋊C4—731no—
365C2×C22⋊C4—731no—
366C2×C22⋊C4C2×#6440811yescharacteristic
367C2×C22⋊C4C2×#6440811yescharacteristic
368C2×C22⋊C4C2×#6440811yescharacteristic
369C2×C42—734no—
370C2×C42—734no—
371C2×C42—731no—
372C2×C42—731no—
373C2×C42—731no—
374C2×C42—731no—
375C2×C42—731no—
376C2×C42—731no—
377C4⋊C8—1464no—
378C4⋊C8—1464no—
379C4⋊C8—1464no—
380C22⋊C8—2924no—
381C22⋊C8—2924no—
382C22⋊C8—1464no—
383C4×C8—1464no—
384C24—731no—
385C24C22×#6440811yescharacteristic
386C24C22×#6440811yescharacteristic
387C2×Q8—1462no—
388C2×Q8—1464no—
389C2×D4—22no—
390C2×D4—42no—
391C2×D4—2922no—
392C2×D4—1462no—
393C2×D4—1464no—
394C2×D4—1462no—
395C22×C4—42no—
396C22×C4—731no—
397C22×C4—731no—
398C22×C4—731no—
399C22×C4—731no—
400C22×C4—734no—
401C22×C4—732no—
402C22×C4—732no—
403C22×C4—731no—
404C22×C4—731no—
405C22×C4—731no—
406C22×C4—1462no—
407C22×C4—1461no—
408C22×C4—1461no—
409C22×C4—1462no—
410C22×C4—1462no—
411C22×C4—1461no—
412C22×C4—1461no—
413C22×C4—1462no—
414C22×C4—1462no—
415C22×C4—1462no—
416C22×C4—1464no—
417C22×C4C22⋊#6440814yes—
418C22×C4C22×#6440811yescharacteristic
419C22×C4C22×#6440811yescharacteristic
420C22×C4C22×#6440811yescharacteristic
421C22×C4C22×#6440811yescharacteristic
422C22×C4C22×#6440811yescharacteristic
423M16—2928no—
424C2×C8—1464no—
425C2×C8—1464no—
426C2×C8—1464no—
427C2×C8—1464no—
428C2×C8—1464no—
429C2×C8—1464no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—1462no—
433C4⋊C4—1462no—
434C4⋊C4—1462no—
435C4⋊C4—1462no—
436C4⋊C4—1462no—
437C4⋊C4—1462no—
438C4⋊C4—1462no—
439C4⋊C4—1462no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—1462no—
444C22⋊C4—1462no—
445C22⋊C4—1462no—
446C22⋊C4—1462no—
447C22⋊C4—1462no—
448C22⋊C4—1462no—
449C22⋊C4—1462no—
450C42—734no—
451C42—734no—
452C42—732no—
453C42—732no—
454C42—732no—
455C42—732no—
456C42—1461no—
457C42—1461no—
458C42—1461no—
459C42—1461no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—21no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—1461no—
468C23—1462no—
469C23—1462no—
470C23—1462no—
471C23C2×C22⋊#6440812yes—
472C23C23×#6440811yescharacteristic
473Q8—2924no—
474D4—44no—
475D4—2924no—
476D4—2924no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—44no—
486C2×C4—2921no—
487C2×C4—2922no—
488C2×C4—2921no—
489C2×C4—2921no—
490C2×C4—2922no—
491C2×C4—2921no—
492C2×C4—731no—
493C2×C4—731no—
494C2×C4—732no—
495C2×C4—732no—
496C2×C4—732no—
497C2×C4—734no—
498C2×C4—732no—
499C2×C4—732no—
500C2×C4—1461no—
501C2×C4—1461no—
502C2×C4—1461no—
503C2×C4—1462no—
504C2×C4—1462no—
505C2×C4—1462no—
506C2×C4—1462no—
507C2×C4—1464no—
508C2×C4—1462no—
509C2×C4—1468no—
510C2×C4—1462no—
511C2×C4—1462no—
512C2×C4C2×C22⋊#6440812yes—
513C2×C4C2×C22⋊#6440812yes—
514C8—2924no—
515C8—2924no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—44no—
520C22—44no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22—2924no—
525C22—2921no—
526C22—2921no—
527C22—2921no—
528C22C22×C22⋊#6440811yescharacteristic
529C22#1798965612yes—
530C22D73⋊#13112yes—
531C22#1798966512yes—
532C4—22no—
533C4—22no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—2921no—
538C4—2921no—
539C4—2921no—
540C4—731no—
541C4—732no—
542C4—731no—
543C4—734no—
544C4—1462no—
545C4—1462no—
546C2—42no—
547C2—81no—
548C2—5841no—
549C2#2262640611yescharacteristic
550C2D73⋊#40811yescharacteristic
551C2#2262651511yescharacteristic
552C2#2262687214yes—
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
FittingC2×#123×C73C4
prime radicalC2×#14556563C4
cosocleC22×Dic73C24
hypercenterC2×#123#64408
hypocenterC73#21850
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#17989604C2semidirect
2. C2×#17989590C2semidirect
3. #22626102C2semidirect
4. #22626054C2semidirect
5. #22625910C2semidirect
6. #22625908C2semidirect
7. #22625790C2semidirect
8. #22625789C2semidirect
286. C73#21850semidirect

Maximal subgroups

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

subgroupindex
C2×#179896042
C2×#179895902
#226261022
#226260542
#226259102
#226259082
#226257902
#226257892
C2×#179891142
#2185073