Finite Group Databasebeta

← #34017539

Subgroups — #34017539

Order 18688.

962 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626607C211yesmaximal, characteristic
2#22626607C211yesmaximal, characteristic
3#22625413C214yesmaximal, complemented
4#22625395C214yesmaximal, complemented
5#22625393C214yesmaximal, complemented
6C22×#14556582C211yesmaximal, characteristic
7#17989608C2212yes—
8#17989608C2212yes—
9#17989607C2212yes—
10#17989607C2212yes—
11#17989604—21no—
12#17989604—21no—
13#17989603—21no—
14#17989603—21no—
15#17989590—21no—
16#17989590—21no—
17#17989557—21no—
18#17989557—21no—
19C4×#11924037C2212yes—
20C4×#11924037C2212yes—
21#17989444C22116yescomplemented
22C2×#14556582—21no—
23C2×#14556582—21no—
24C2×#14556582—21no—
25C2×#14556582—21no—
26C2×#14556582—21no—
27C2×#14556582—21no—
28C2×#14556582C412yes—
29C2×#14556582C412yes—
30C2×#14556582C412yes—
31C2×#14556582C2212yes—
32C2×#14556582C2212yes—
33C2×#14556582C2212yes—
34C22×C4⋊Dic73—21no—
35C22×C4⋊Dic73C411yescharacteristic
36C22×#11924007—21no—
37C22×C4×Dic73C2211yescharacteristic
38C22×C4⋊C4×C73C411yescharacteristic
39C2×#11924037—22no—
40C2×#11924037—22no—
41#14556658—22no—
42#14556658—22no—
43C4⋊#10596833—22no—
44C4⋊#10596833—22no—
45C22⋊#10596833—22no—
46C22⋊#10596833—22no—
47C22⋊#10596833—22no—
48C22⋊#10596833—22no—
49#14556646C2314yes—
50#14556646C2314yes—
51C4×#10596833—22no—
52C4×#10596833—22no—
53C23×Dic73—21no—
54C23×Dic73D411yescharacteristic
55C23×Dic73D411yescharacteristic
56#14556582—22no—
57#14556582—22no—
58#14556582—22no—
59#14556582—22no—
60#14556582—22no—
61#14556582—22no—
62#14556582—22no—
63#14556582—22no—
64#14556582—22no—
65#14556582—22no—
66#14556582—22no—
67#14556582—22no—
68#14556582C2×C414yes—
69#14556582C2×C414yes—
70#14556582C2×C414yes—
71#14556582C2314yes—
72C2×C4⋊Dic73—22no—
73C2×C4⋊Dic73—22no—
74C2×C4⋊Dic73—22no—
75C2×C4⋊Dic73—22no—
76C2×C4⋊Dic73—22no—
77C2×C4⋊Dic73—22no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73—21no—
80C2×C4⋊Dic73—21no—
81C2×C4⋊Dic73C2×C412yes—
82C2×C4⋊Dic73C2×C412yes—
83C2×C4⋊Dic73C2×C412yes—
84C2×#11924007—22no—
85C2×#11924007—22no—
86C2×#11924007—22no—
87C2×#11924007—22no—
88C2×#11924007—22no—
89C2×#11924007—22no—
90C2×C4×Dic73C2×C411yescharacteristic
91C2×C4×Dic73C2×C411yescharacteristic
92C2×C4×Dic73C2×C411yescharacteristic
93C2×C4×Dic73D411yescharacteristic
94C2×C4×Dic73D411yescharacteristic
95C2×C4×Dic73D411yescharacteristic
96C2×C4×Dic73D411yescharacteristic
97C2×C4×Dic73D411yescharacteristic
98C2×C4×Dic73D411yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101C2×C4×Dic73C2311yescharacteristic
102C23×C4×C73—21no—
103C23×C4×C73C2×C411yescharacteristic
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73C2×C412yes—
108C2×C4⋊C4×C73C2×C412yes—
109C2×C4⋊C4×C73C2×C412yes—
110#11924037—44no—
111#11924037—44no—
112C2×#10596833—24no—
113C2×#10596833—24no—
114C22×Dic73—22no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—42no—
118C22×Dic73—42no—
119C22×Dic73—44no—
120C22×Dic73C22⋊C411yescharacteristic
121C22×Dic73C22⋊C411yescharacteristic
122C22×Dic73C22⋊C411yescharacteristic
123C22×Dic73C22⋊C411yescharacteristic
124C22×Dic73C22⋊C411yescharacteristic
125C22×Dic73C22⋊C411yescharacteristic
126C22×Dic73C2×D411yescharacteristic
127C22×Dic73C2×D411yescharacteristic
128C22×Dic73C2×D411yescharacteristic
129C22×Dic73C2×D411yescharacteristic
130C22×Dic73C2×D411yescharacteristic
131C22×Dic73C2×D411yescharacteristic
132C4⋊Dic73—22no—
133C4⋊Dic73—22no—
134C4⋊Dic73—22no—
135C4⋊Dic73—24no—
136C4⋊Dic73—24no—
137C4⋊Dic73—24no—
138C4⋊Dic73—24no—
139C4⋊Dic73C22×C414yes—
140#11924007—24no—
141#11924007—24no—
142#11924007—24no—
143#11924007—24no—
144C4×Dic73C22⋊C411yescharacteristic
145C4×Dic73C22⋊C411yescharacteristic
146C4×Dic73C22⋊C411yescharacteristic
147C4×Dic73C22⋊C411yescharacteristic
148C4×Dic73C22⋊C411yescharacteristic
149C4×Dic73C22⋊C411yescharacteristic
150C4×Dic73C22×C411yescharacteristic
151C4×Dic73C22×C411yescharacteristic
152C4×Dic73C22×C411yescharacteristic
153C4×Dic73C2×D411yescharacteristic
154C4×Dic73C2×D411yescharacteristic
155C4×Dic73C2×D411yescharacteristic
156C4×Dic73C2×D411yescharacteristic
157C4×Dic73C2×D411yescharacteristic
158C4×Dic73C2×D411yescharacteristic
159C4×Dic73C2411yescharacteristic
160C24×C73C22⋊C411yescharacteristic
161C22×C4×C73—24no—
162C22×C4×C73—22no—
163C22×C4×C73—22no—
164C22×C4×C73—22no—
165C22×C4×C73—44no—
166C22×C4×C73C22⋊C411yescharacteristic
167C22×C4×C73C22⋊C411yescharacteristic
168C22×C4×C73C22⋊C411yescharacteristic
169C22×C4×C73C22×C411yescharacteristic
170C22×C4×C73C22×C411yescharacteristic
171C22×C4×C73C22×C411yescharacteristic
172C4⋊C4×C73—22no—
173C4⋊C4×C73—22no—
174C4⋊C4×C73—22no—
175C4⋊C4×C73C22×C414yes—
176C23×C73—22no—
177C23×C73—22no—
178C23×C73—22no—
179C23×C73C2×C22⋊C411yescharacteristic
180C23×C73C2×C22⋊C411yescharacteristic
181C23×C73C2×C22⋊C411yescharacteristic
182C2×C4×C73—22no—
183C2×C4×C73—22no—
184C2×C4×C73—22no—
185C2×C4×C73—22no—
186C2×C4×C73—22no—
187C2×C4×C73—24no—
188C2×C4×C73—44no—
189C2×C4×C73—44no—
190C2×C4×C73—44no—
191C2×C4×C73#10114yes—
192C2×C4×C73C2×C22⋊C411yescharacteristic
193C2×C4×C73C2×C22⋊C411yescharacteristic
194C2×C4×C73C2×C22⋊C411yescharacteristic
195C2×C4×C73C23×C411yescharacteristic
196C2×Dic73—22no—
197C2×Dic73—22no—
198C2×Dic73—22no—
199C2×Dic73—22no—
200C2×Dic73—24no—
201C2×Dic73—41no—
202C2×Dic73—41no—
203C2×Dic73—41no—
204C2×Dic73—41no—
205C2×Dic73—41no—
206C2×Dic73—41no—
207C2×Dic73—41no—
208C2×Dic73—41no—
209C2×Dic73—44no—
210C2×Dic73—44no—
211C2×Dic73—44no—
212C2×Dic73C2×C22⋊C411yescharacteristic
213C2×Dic73C2×C22⋊C411yescharacteristic
214C2×Dic73C2×C22⋊C411yescharacteristic
215C2×Dic73C2×C22⋊C411yescharacteristic
216C2×Dic73C2×C22⋊C411yescharacteristic
217C2×Dic73C2×C22⋊C411yescharacteristic
218C2×Dic73C22×D411yescharacteristic
219C2×Dic73C22×D411yescharacteristic
220#10596833—44no—
221#10596833—44no—
222C22×C73—28no—
223C22×C73—21no—
224C22×C73—21no—
225C22×C73—21no—
226C22×C73—21no—
227C22×C73—21no—
228C22×C73—21no—
229C22×C73C2×#10112yes—
230C22×C73#42112yes—
231C22×C73#42112yes—
232C22×C73C22×C22⋊C411yescharacteristic
233C4×C73—21no—
234C4×C73—21no—
235C4×C73—44no—
236C4×C73C2×#10112yes—
237C4×C73C2×#10112yes—
238Dic73—21no—
239Dic73—21no—
240Dic73—21no—
241Dic73—21no—
242Dic73—21no—
243Dic73—21no—
244Dic73—21no—
245Dic73—21no—
246Dic73—44no—
247#17667—731nomaximal, Sylow
248C2×C73—22no—
249C2×C73—22no—
250C2×C73—22no—
251C2×C73C22×#10111yescharacteristic
252C2×C73C2×#42111yescharacteristic
253C2×C73C2×#42111yescharacteristic
254C22×#125—731no—
255#2920—731no—
256#2920—731no—
257#1534—734no—
258#1528—734no—
259#1528—734no—
260C73#1766711yescharacteristic, complemented, Sylow
261C2×#125—732no—
262C2×#125—732no—
263C2×#125—732no—
264C2×#125—732no—
265C2×#125—732no—
266C2×#125—732no—
267C2×#125—1461no—
268C2×#125—1461no—
269C2×#125—1461no—
270C2×#125—1461no—
271C2×#125—1461no—
272C2×#125—1461no—
273C22×C4⋊C4—731no—
274C22×C4⋊C4—1461no—
275C22×C4⋊C4—1461no—
276C22×C4⋊C4#6440811yescharacteristic
277C22×C42—731no—
278#432—732no—
279#432—732no—
280#432—732no—
281#432—732no—
282#431—1461no—
283#431—1461no—
284#431—1461no—
285#431—1461no—
286#423—1461no—
287#423—1461no—
288#407—1461no—
289#407—1461no—
290C4×M16—732no—
291C4×M16—732no—
292#330—7316no—
293C23×C4—21no—
294C23×C4—731no—
295C23×C4—731no—
296C23×C4—1461no—
297C23×C4C2×#6440811yescharacteristic
298C2×M16—1462no—
299C2×M16—1462no—
300#125—734no—
301#125—734no—
302#125—734no—
303#125—734no—
304#125—1462no—
305#125—1462no—
306#125—1462no—
307#125—1462no—
308#125—1462no—
309#125—1462no—
310#125—1462no—
311#125—1462no—
312#125—1462no—
313#125—1462no—
314#125—1462no—
315#125—1462no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—732no—
320C2×C4⋊C4—732no—
321C2×C4⋊C4—732no—
322C2×C4⋊C4—1462no—
323C2×C4⋊C4—1462no—
324C2×C4⋊C4—1462no—
325C2×C4⋊C4—1462no—
326C2×C4⋊C4—1462no—
327C2×C4⋊C4—1462no—
328C2×C4⋊C4—1462no—
329C2×C4⋊C4—1462no—
330C2×C4⋊C4—1462no—
331C2×C4⋊C4—1462no—
332C2×C4⋊C4—1462no—
333C2×C4⋊C4—1462no—
334C2×C4⋊C4—1461no—
335C2×C4⋊C4—1461no—
336C2×C4⋊C4—1461no—
337C2×C4⋊C4C2×#6440812yes—
338C2×C4⋊C4C2×#6440812yes—
339C2×C4⋊C4C2×#6440812yes—
340C2×C42—731no—
341C2×C42—731no—
342C2×C42—731no—
343C2×C42—731no—
344C2×C42—731no—
345C2×C42—731no—
346C2×C42—731no—
347C2×C42—731no—
348C2×C42—731no—
349C2×C42—731no—
350C2×C42—731no—
351C2×C42—731no—
352C4⋊C8—1462no—
353C4⋊C8—1462no—
354C4⋊C8—1462no—
355C4⋊C8—1462no—
356C22⋊C8—1462no—
357C22⋊C8—1462no—
358C22⋊C8—1462no—
359C22⋊C8—1462no—
360#97—734no—
361#97—734no—
362C4×C8—1462no—
363C4×C8—1462no—
364C24C22⋊#6440811yescharacteristic
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—44no—
370C22×C4—2924no—
371C22×C4—2922no—
372C22×C4—2922no—
373C22×C4—731no—
374C22×C4—731no—
375C22×C4—731no—
376C22×C4—731no—
377C22×C4—731no—
378C22×C4—731no—
379C22×C4—731no—
380C22×C4—731no—
381C22×C4—731no—
382C22×C4—731no—
383C22×C4—731no—
384C22×C4—731no—
385C22×C4—1462no—
386C22×C4—1462no—
387C22×C4—1462no—
388C22×C4C22⋊#6440811yescharacteristic
389C22×C4C22⋊#6440811yescharacteristic
390C22×C4C22⋊#6440811yescharacteristic
391C22×C4C22×#6440811yescharacteristic
392C22×C4C22×#6440811yescharacteristic
393C22×C4C22×#6440811yescharacteristic
394M16—2924no—
395M16—2924no—
396C2×C8—1464no—
397C2×C8—1464no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—734no—
402C4⋊C4—1464no—
403C4⋊C4—1464no—
404C4⋊C4—1464no—
405C4⋊C4—1464no—
406C4⋊C4—1464no—
407C4⋊C4—1464no—
408C4⋊C4—1464no—
409C4⋊C4—1464no—
410C4⋊C4—1462no—
411C4⋊C4—1462no—
412C4⋊C4—1462no—
413C4⋊C4C22×#6440814yes—
414C42—731no—
415C42—731no—
416C42—731no—
417C42—731no—
418C42—731no—
419C42—731no—
420C42—731no—
421C42—731no—
422C42—731no—
423C42—731no—
424C42—731no—
425C42—731no—
426C42—731no—
427C42—731no—
428C42—731no—
429C42—731no—
430C23—22no—
431C23—22no—
432C23—22no—
433C23C2×C22⋊#6440811yescharacteristic
434C23C2×C22⋊#6440811yescharacteristic
435C23C2×C22⋊#6440811yescharacteristic
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—2924no—
446C2×C4—2924no—
447C2×C4—2924no—
448C2×C4—2921no—
449C2×C4—2921no—
450C2×C4—2921no—
451C2×C4—2921no—
452C2×C4—2921no—
453C2×C4—2921no—
454C2×C4—2921no—
455C2×C4—2921no—
456C2×C4—731no—
457C2×C4—731no—
458C2×C4—731no—
459C2×C4—731no—
460C2×C4—731no—
461C2×C4—731no—
462C2×C4—731no—
463C2×C4—731no—
464C2×C4—1464no—
465C2×C4—1462no—
466C2×C4—1462no—
467C2×C4—1462no—
468C2×C4—1462no—
469C2×C4#1455665214yes—
470C2×C4C2×C22⋊#6440811yescharacteristic
471C2×C4C2×C22⋊#6440811yescharacteristic
472C2×C4C2×C22⋊#6440811yescharacteristic
473C2×C4C23×#6440811yescharacteristic
474C8—2924no—
475C8—2924no—
476C22—28no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22C2×#1455665212yes—
484C22#1798958512yes—
485C22#1798958612yes—
486C22C22×C22⋊#6440811yescharacteristic
487C4—21no—
488C4—21no—
489C4—44no—
490C4—2924no—
491C4—1461no—
492C4—1461no—
493C4—1461no—
494C4—1461no—
495C4—1461no—
496C4—1461no—
497C4—1461no—
498C4—1461no—
499C4C2×#1455665212yes—
500C4C2×#1455665212yes—
501C2—22no—
502C2—22no—
503C2—22no—
504C2C22×#1455665211yescharacteristic
505C2C2×#1798958511yescharacteristic
506C2C2×#1798958611yescharacteristic
subgroupG/H
centerC22C22×C22⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC22×C4⋊C4×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC4×Dic73C24
hypercenterC22×C4⋊C4#64408
hypocenterC73#17667
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #22625413C2semidirect
4. #22625395C2semidirect
5. #22625393C2semidirect
21. #17989444C22semidirect
260. C73#17667semidirect

Maximal subgroups

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

subgroupindex
#226266072
#226254132
#226253952
#226253932
C22×#145565822
#1766773