Finite Group Databasebeta

← #34005200

Subgroups — #34005200

Order 18688.

680 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625786C211yesmaximal, characteristic
2C4×#14556648C211yesmaximal, characteristic
3#22624767C212yesmaximal, complemented
4#22624767C212yesmaximal, complemented
5C4×C4⋊C4×D73C211yesmaximal, characteristic
6C2×C4⋊#10596833C2212yes—
7C2×#14556648—21no—
8C2×#14556648—21no—
9C2×C4×#10596833C2212yes—
10#17989453—21no—
11#17989453—21no—
12C2×C4⋊C4×D73C411yescharacteristic
13C2×C4⋊C4×D73C411yescharacteristic
14C2×C42×D73—21no—
15C2×C42×D73C2211yescharacteristic
16C4⋊C4×Dic73C2211yescharacteristic
17C4⋊C4×Dic73C2211yescharacteristic
18C4×#11924007—21no—
19C4×C4⋊Dic73C411yescharacteristic
20#17988438—21no—
21#95×D73—21no—
22C4×C4⋊C4×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25C4⋊#10596833—22no—
26C4⋊#10596833—22no—
27#14556648—24no—
28#14556648—42no—
29C4×#10596833—22no—
30C4×#10596833—22no—
31C22×C4×D73—21no—
32C22×C4×D73—21no—
33C22×C4×D73C2×C411yescharacteristic
34C22×C4×D73D411yescharacteristic
35C22×C4×D73D411yescharacteristic
36C2×C4⋊Dic73C2×C411yescharacteristic
37C2×C4⋊Dic73C2×C411yescharacteristic
38C2×#11924007—21no—
39C2×#11924007—21no—
40C4⋊C4×D73—22no—
41C4⋊C4×D73—22no—
42C4⋊C4×D73—22no—
43C4⋊C4×D73C814yescomplemented
44C2×C4×Dic73—21no—
45C2×C4×Dic73—21no—
46C2×C4×Dic73—21no—
47C2×C4×Dic73D411yescharacteristic
48C2×C4×Dic73D411yescharacteristic
49C2×C4×Dic73C2311yescharacteristic
50C42×D73—22no—
51C42×D73—22no—
52C42×D73—42no—
53C42×D73—42no—
54#14556498—21no—
55#14556498—21no—
56#14556498—21no—
57C2×C4⋊C4×C73C2×C411yescharacteristic
58C2×C4⋊C4×C73C2×C411yescharacteristic
59C2×C42×C73—21no—
60C2×C42×C73C2×C411yescharacteristic
61#95×C73—21no—
62C2×#10596833—24no—
63C2×#10596833—42no—
64C2×#10596833—42no—
65C2×#10596833—42no—
66C2×#10596833—42no—
67C2×#10596833—42no—
68C23×D73C22⋊C411yescharacteristic
69C22×Dic73—21no—
70C22×Dic73—21no—
71C22×Dic73C22⋊C411yescharacteristic
72C22×Dic73C2×D411yescharacteristic
73C22×Dic73C2×D411yescharacteristic
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76C2×C4×D73—21no—
77C2×C4×D73—21no—
78C2×C4×D73—22no—
79C2×C4×D73—22no—
80C2×C4×D73—24no—
81C2×C4×D73—24no—
82C2×C4×D73—22no—
83C2×C4×D73—22no—
84C2×C4×D73—41no—
85C2×C4×D73—42no—
86C2×C4×D73—42no—
87C2×C4×D73—42no—
88C2×C4×D73—42no—
89C2×C4×D73C2×C812yes—
90C2×C4×D73M1612yes—
91C2×C4×D73D812yes—
92C2×C4×D73SD1612yes—
93C4⋊Dic73—21no—
94C4⋊Dic73—21no—
95C4⋊Dic73C2×C812yes—
96C4⋊Dic73M1612yes—
97#11924007—24no—
98#11924007—24no—
99C4×Dic73—22no—
100C4×Dic73—22no—
101C4×Dic73—42no—
102C4×Dic73—41no—
103C4×Dic73—41no—
104C4×Dic73—41no—
105C4×Dic73—41no—
106C4×Dic73#4112yes—
107C4×Dic73#4112yes—
108C22×C4×C73—21no—
109C22×C4×C73—21no—
110C22×C4×C73C22⋊C411yescharacteristic
111C22×C4×C73C22⋊C411yescharacteristic
112C22×C4×C73C22×C411yescharacteristic
113C4⋊C4×C73—21no—
114C4⋊C4×C73—21no—
115C4⋊C4×C73C2×C812yes—
116C4⋊C4×C73M1612yes—
117C42×C73—21no—
118C42×C73—21no—
119C42×C73—42no—
120C23×C73C2×C22⋊C411yescharacteristic
121C22×D73—21no—
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—21no—
125C22×D73C22⋊C812yes—
126C22×D73#10212yes—
127C22×D73#10412yes—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—22no—
132C2×C4×C73—22no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—41no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73#10212yes—
140C2×C4×C73#11711yescharacteristic
141C2×C4×C73#11711yescharacteristic
142C2×C4×C73C22×C811yescharacteristic
143C2×C4×C73C2×M1611yescharacteristic
144C2×C4×C73C2×M1611yescharacteristic
145C2×C4×C73C2×M1611yescharacteristic
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—22no—
151C2×Dic73—22no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—41no—
155C2×Dic73—41no—
156C2×Dic73C22⋊C812yes—
157C2×Dic73#12312yes—
158C2×Dic73#12312yes—
159C2×Dic73C2×D811yescharacteristic
160C2×Dic73C2×SD1611yescharacteristic
161C2×Dic73#13712yes—
162C4×D73—22no—
163C4×D73—22no—
164C4×D73—22no—
165C4×D73—22no—
166C4×D73—24no—
167C4×D73—24no—
168C4×D73—44no—
169C4×D73—48no—
170C4×D73—48no—
171#10596833—44no—
172#10596833—82no—
173C22×C73#38111yescharacteristic
174C22×C73C2×C22⋊C811yescharacteristic
175C22×C73#40711yescharacteristic
176C22×C73C2×#10211yescharacteristic
177C22×C73#41911yescharacteristic
178C22×C73C2×#10411yescharacteristic
179C22×C73#42111yescharacteristic
180C2×D73—22no—
181C2×D73—22no—
182C2×D73—22no—
183C2×D73—22no—
184C2×D73—22no—
185C2×D73—22no—
186C2×D73D4⋊C814yes—
187C4×C73—22no—
188C4×C73—41no—
189C4×C73—42no—
190C4×C73—42no—
191C4×C73#43111yescharacteristic
192C4×C73#43111yescharacteristic
193C4×C73#43211yescharacteristic
194C4×C73#43211yescharacteristic
195Dic73—22no—
196Dic73—22no—
197Dic73—42no—
198Dic73—42no—
199Dic73#48012yes—
200Dic73#48312yes—
201#8706—731nomaximal, Sylow
202C2×C73C2×D4⋊C811yescharacteristic
203C2×C73#147911yescharacteristic
204C2×C73#148611yescharacteristic
205C2×C73#149111yescharacteristic
206C2×C73#181711yescharacteristic
207C2×C73#182311yescharacteristic
208C2×C73#182611yescharacteristic
209D73—24no—
210C2×C4×C4⋊C4—731no—
211#1797—731no—
212C4×C22⋊C8—731no—
213#1279—732no—
214#1279—732no—
215C73#870611yescharacteristic, complemented, Sylow
216C22×C4⋊C4—731no—
217C22×C4⋊C4—731no—
218C22×C42—731no—
219C22×C42—1461no—
220C2×C4⋊C8—732no—
221C2×C22⋊C8—1461no—
222C2×C22⋊C8—1461no—
223C2×C4×C8—732no—
224C4×C4⋊C4—731no—
225C4×C4⋊C4—731no—
226C4×C4⋊C4—731no—
227C4×C4⋊C4—1461no—
228C4×C4⋊C4—1461no—
229C4×C4⋊C4#6440811yescharacteristic
230C2×#95—1461no—
231#336—1461no—
232#336—1461no—
233C23×C4—731no—
234C23×C4—731no—
235C23×C4—731no—
236C23×C4—1461no—
237C23×C4—1461no—
238C22×C8—1462no—
239C22×C8—1462no—
240C2×C4⋊C4—731no—
241C2×C4⋊C4—731no—
242C2×C4⋊C4—734no—
243C2×C4⋊C4—1462no—
244C2×C4⋊C4—1462no—
245C2×C4⋊C4—1461no—
246C2×C4⋊C4—1461no—
247C2×C4⋊C4—1462no—
248C2×C4⋊C4C2×#6440811yescharacteristic
249C2×C4⋊C4C2×#6440811yescharacteristic
250C2×C42—21no—
251C2×C42—2922no—
252C2×C42—2922no—
253C2×C42—731no—
254C2×C42—731no—
255C2×C42—731no—
256C2×C42—1462no—
257C2×C42—1462no—
258C2×C42—1461no—
259C2×C42—1461no—
260C2×C42—1461no—
261C2×C42C2×#6440811yescharacteristic
262C4⋊C8—1462no—
263C4⋊C8—1462no—
264C22⋊C8—2922no—
265C22⋊C8—1464no—
266C4×C8—1462no—
267C4×C8—1462no—
268#95—21no—
269#95—1461no—
270#95—1461no—
271#95—1461no—
272C24—731no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—2921no—
276C22×C4—2922no—
277C22×C4—2922no—
278C22×C4—2922no—
279C22×C4—2922no—
280C22×C4—731no—
281C22×C4—731no—
282C22×C4—731no—
283C22×C4—732no—
284C22×C4—732no—
285C22×C4—732no—
286C22×C4—732no—
287C22×C4—1462no—
288C22×C4—1462no—
289C22×C4—1464no—
290C22×C4—1464no—
291C22×C4—1462no—
292C22×C4—1462no—
293C22×C4—1461no—
294C22×C4—1461no—
295C22×C4—1461no—
296C22×C4—1461no—
297C22×C4—1461no—
298C22×C4—1461no—
299C22×C4C22⋊#6440811yescharacteristic
300C22×C4C22⋊#6440811yescharacteristic
301C22×C4C22×#6440811yescharacteristic
302C2×C8—2922no—
303C2×C8—2922no—
304C2×C8—2922no—
305C2×C8—2922no—
306C2×C8—2922no—
307C2×C8—1464no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—732no—
311C4⋊C4—732no—
312C4⋊C4—1464no—
313C4⋊C4—1464no—
314C4⋊C4—1461no—
315C4⋊C4—1461no—
316C4⋊C4#1192403612yes—
317C4⋊C4#1192403812yes—
318C42—21no—
319C42—21no—
320C42—42no—
321C42—2921no—
322C42—2921no—
323C42—2921no—
324C42—2921no—
325C42—2922no—
326C42—732no—
327C42—732no—
328C42—1462no—
329C42—1462no—
330C23—732no—
331C23—732no—
332C23—732no—
333C23—1461no—
334C23—1461no—
335C23—1461no—
336C23—1461no—
337C23C2×C22⋊#6440811yescharacteristic
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—2928no—
350C2×C4—2928no—
351C2×C4—2924no—
352C2×C4—2921no—
353C2×C4—2921no—
354C2×C4—2921no—
355C2×C4—2921no—
356C2×C4—732no—
357C2×C4—731no—
358C2×C4—731no—
359C2×C4—732no—
360C2×C4—732no—
361C2×C4—732no—
362C2×C4—1464no—
363C2×C4—1464no—
364C2×C4—1462no—
365C2×C4—1462no—
366C2×C4—1461no—
367C2×C4—1461no—
368C2×C4—1461no—
369C2×C4—1461no—
370C2×C4—1462no—
371C2×C4—1462no—
372C2×C4—1462no—
373C2×C4—1462no—
374C2×C4#1455665312yes—
375C2×C4#1455667011yescharacteristic
376C2×C4#1455667011yescharacteristic
377C2×C4C2×#1192403611yescharacteristic
378C2×C4D73⋊M1611yescharacteristic
379C2×C4D73⋊M1611yescharacteristic
380C2×C4C2×#1192403811yescharacteristic
381C8—2924no—
382C8—5842no—
383C22—734no—
384C22—1462no—
385C22—1462no—
386C22—1462no—
387C22—1462no—
388C22—1462no—
389C22—1462no—
390C22#1798953011yescharacteristic
391C22#1798955511yescharacteristic
392C22#1798955811yescharacteristic
393C22C2×#1455665311yescharacteristic
394C22#1798958011yescharacteristic
395C22D73⋊#10411yescharacteristic
396C22#1798958411yescharacteristic
397C4—22no—
398C4—41no—
399C4—42no—
400C4—42no—
401C4—2922no—
402C4—2922no—
403C4—732no—
404C4—732no—
405C4—1462no—
406C4—1462no—
407C4#1798960511yescharacteristic
408C4#1798960611yescharacteristic
409C4#1798960911yescharacteristic
410C4#1798961011yescharacteristic
411C2—1464no—
412C2#2262521711yescharacteristic
413C2#2262523411yescharacteristic
414C2#2262525711yescharacteristic
415C2#2262527411yescharacteristic
416C2#2262582311yescharacteristic
417C2#2262583411yescharacteristic
418C2#2262583911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC4×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC4×C4⋊C4#64408
hypocenterC73#8706
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #22624767C2semidirect
4. #22624767C2semidirect
43. C4⋊C4×D73C8semidirect
215. C73#8706semidirect

Maximal subgroups

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

subgroupindex
#226257862
C4×#145566482
#226247672
C4×C4⋊C4×D732
#870673