Finite Group Databasebeta

← #33001962

Subgroups — #33001962

Order 18688.

512 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988377C212yesmaximal
2#22609923C211yesmaximal, characteristic
3#22609919C211yesmaximal, characteristic
4#22608049C212yesmaximal
5C73×#2322C211yesmaximal, characteristic
6#17988611—21no—
7C2×#14556508C2212yes—
8C2×#14556506C2212yes—
9#17988447—21no—
10#17988377—24no—
11#17988356—21no—
12#17988354—21no—
13C2×#123×C73C2211yescharacteristic
14C2×C4×D4×C73C2211yescharacteristic
15C22×C4⋊C4×C73C411yescharacteristic, complemented
16#389×C73—21no—
17#388×C73—21no—
18#387×C73—21no—
19#386×C73C2211yescharacteristic
20#385×C73—21no—
21#385×C73C411yescharacteristic, complemented
22#381×C73C411yescharacteristic, complemented
23C4×C22⋊C4×C73C411yescharacteristic, complemented
24C2×#11924012—22no—
25C2×C4⋊Dic73—41no—
26C2×C22⋊Dic73—22no—
27C4⋊#10596831—41no—
28C4⋊#10596831—41no—
29#14556508—22no—
30#14556508—22no—
31#14556506—22no—
32#14556506—22no—
33#14556498—41no—
34C22×D4×C73C2311yescharacteristic
35C23×C4×C73C2×C411yescharacteristic
36C23×C4×C73C2×C411yescharacteristic
37C23×C4×C73C2×C411yescharacteristic
38C23×C4×C73D411yescharacteristic
39#123×C73—21no—
40#123×C73—21no—
41#123×C73D412yes—
42#123×C73Q812yes—
43C4×D4×C73—41no—
44C4×D4×C73—41no—
45C2×C4⋊C4×C73—21no—
46C2×C4⋊C4×C73—21no—
47C2×C4⋊C4×C73—21no—
48C2×C4⋊C4×C73—21no—
49C2×C4⋊C4×C73—41no—
50C2×C4⋊C4×C73—41no—
51C2×C4⋊C4×C73D411yescharacteristic
52C2×C22⋊C4×C73—21no—
53C2×C22⋊C4×C73—21no—
54C2×C22⋊C4×C73C2×C411yescharacteristic
55C2×C22⋊C4×C73C2×C411yescharacteristic
56C2×C22⋊C4×C73C2×C411yescharacteristic
57C2×C22⋊C4×C73D411yescharacteristic
58C2×C42×C73—21no—
59C2×C42×C73D411yescharacteristic
60#95×C73—21no—
61#95×C73—21no—
62#95×C73—21no—
63#95×C73—21no—
64#95×C73—21no—
65C22×Dic73—42no—
66#11924012—42no—
67#11924012—42no—
68C2×#10596831—42no—
69C4⋊Dic73—82no—
70C22⋊Dic73—42no—
71C22⋊Dic73—42no—
72C24×C73C22×C411yescharacteristic
73C24×C73C2×D411yescharacteristic
74C2×D4×C73—41no—
75C2×D4×C73—41no—
76C2×D4×C73C2×D411yescharacteristic
77C2×D4×C73C2×Q811yescharacteristic
78C2×D4×C73#4111yescharacteristic
79C2×D4×C73#4111yescharacteristic
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—41no—
90C22×C4×C73—41no—
91C22×C4×C73—41no—
92C22×C4×C73—81no—
93C22×C4×C73—81no—
94C22×C4×C73—81no—
95C22×C4×C73C22⋊C411yescharacteristic
96C22×C4×C73C22⋊C411yescharacteristic
97C22×C4×C73C22⋊C411yescharacteristic
98C22×C4×C73C22⋊C411yescharacteristic
99C22×C4×C73C4⋊C412yescomplemented
100C22×C4×C73C2×D411yescharacteristic
101C4⋊C4×C73—22no—
102C4⋊C4×C73—22no—
103C4⋊C4×C73—41no—
104C4⋊C4×C73—42no—
105C4⋊C4×C73—41no—
106C4⋊C4×C73—41no—
107C4⋊C4×C73—81no—
108C22⋊C4×C73—21no—
109C22⋊C4×C73—22no—
110C22⋊C4×C73—22no—
111C22⋊C4×C73—41no—
112C22⋊C4×C73—41no—
113C22⋊C4×C73—41no—
114C22⋊C4×C73—81no—
115C22⋊C4×C73C4⋊C412yescomplemented
116C42×C73—21no—
117C42×C73—21no—
118C42×C73—81no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—21no—
123C23×C73—41no—
124C23×C73—41no—
125C23×C73—41no—
126C23×C73—41no—
127C23×C73C2×C22⋊C411yescharacteristic
128C23×C73C2×C4⋊C411yescharacteristic
129C23×C73#11711yescharacteristic
130C23×C73#12111yescharacteristic
131C23×C73C22⋊Q811yescharacteristic
132D4×C73—41no—
133D4×C73—41no—
134D4×C73—41no—
135D4×C73—41no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—22no—
139C2×C4×C73—22no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—41no—
144C2×C4×C73—42no—
145C2×C4×C73—41no—
146C2×C4×C73—41no—
147C2×C4×C73—42no—
148C2×C4×C73—41no—
149C2×C4×C73—41no—
150C2×C4×C73—41no—
151C2×C4×C73—41no—
152C2×C4×C73—42no—
153C2×C4×C73—41no—
154C2×C4×C73—41no—
155C2×C4×C73—41no—
156C2×C4×C73—41no—
157C2×C4×C73—41no—
158C2×C4×C73—41no—
159C2×C4×C73—41no—
160C2×C4×C73—81no—
161C2×C4×C73—81no—
162C2×C4×C73—81no—
163C2×C4×C73—82no—
164C2×C4×C73#9911yescharacteristic
165C2×C4×C73#9911yescharacteristic
166C2×C4×C73#12111yescharacteristic
167C2×C4×C73C22⋊Q811yescharacteristic
168C2×Dic73—82no—
169C2×Dic73—82no—
170C2×Dic73—82no—
171#10596831—82no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—21no—
175C22×C73—21no—
176C22×C73—21no—
177C22×C73—21no—
178C22×C73—41no—
179C22×C73—41no—
180C22×C73—41no—
181C22×C73—41no—
182C22×C73—42no—
183C22×C73—41no—
184C22×C73—41no—
185C22×C73—41no—
186C22×C73—41no—
187C22×C73—81no—
188C22×C73#38011yescharacteristic
189C22×C73C2×#9911yescharacteristic
190C22×C73#41011yescharacteristic
191C4×C73—21no—
192C4×C73—21no—
193C4×C73—21no—
194C4×C73—21no—
195C4×C73—42no—
196C4×C73—42no—
197C4×C73—41no—
198C4×C73—41no—
199C4×C73—41no—
200C4×C73—81no—
201C4×C73—81no—
202Dic73—162no—
203#12796—731nomaximal, Sylow
204C2×C73—21no—
205C2×C73—21no—
206C2×C73—41no—
207C2×C73—41no—
208C2×C73—41no—
209C2×C73—41no—
210C2×C73#179911yescharacteristic
211C2×C73#212111yescharacteristic
212C2×C73#212311yescharacteristic
213#2322D7311yescharacteristic
214C2×#352—732no—
215#1800—731no—
216#1799—731no—
217#1390—732no—
218C73#1279611yescharacteristic, complemented, Sylow
219C2×#123C2×D7311yescharacteristic
220C2×C4×D4C2×D7311yescharacteristic
221C22×C4⋊C4Dic7311yescharacteristic, complemented
222#423—1461no—
223C2×#100—732no—
224C2×#99—732no—
225#389—21no—
226#388—21no—
227#387—21no—
228#386C2×D7311yescharacteristic
229#385—21no—
230#385Dic7311yescharacteristic, complemented
231#381Dic7311yescharacteristic, complemented
232#380—1461no—
233C4×C22⋊C4Dic7311yescharacteristic, complemented
234#352—1464no—
235#343—1461no—
236#342—1461no—
237C22×D4C22×D7311yescharacteristic
238C23×C4C2×Dic7311yescharacteristic
239C23×C4C2×Dic7311yescharacteristic
240C23×C4C2×Dic7311yescharacteristic
241C23×C4C22⋊D7311yescharacteristic
242C2×M16—1462no—
243#123—21no—
244#123—21no—
245#123Dic14612yes—
246#123D29212yes—
247C4×D4—41no—
248C4×D4—41no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—41no—
254C2×C4⋊C4—41no—
255C2×C4⋊C4—2921no—
256C2×C4⋊C4C22⋊D7311yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—1462no—
260C2×C22⋊C4C2×Dic7311yescharacteristic
261C2×C22⋊C4C2×Dic7311yescharacteristic
262C2×C22⋊C4C2×Dic7311yescharacteristic
263C2×C22⋊C4C22⋊D7311yescharacteristic
264C2×C42—21no—
265C2×C42C22⋊D7311yescharacteristic
266C4⋊C8—2921no—
267C4⋊C8—2921no—
268#100—1462no—
269#100—1462no—
270#99—1462no—
271#99—1462no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95—21no—
276#95—21no—
277#95—2921no—
278C24C22×Dic7311yescharacteristic
279C24C2×C22⋊D7311yescharacteristic
280C2×D4—41no—
281C2×D4—41no—
282C2×D4C2×D29211yescharacteristic
283C2×D4C2×Dic14611yescharacteristic
284C2×D4#1192402811yescharacteristic
285C2×D4#1192402811yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—81no—
299C22×C4—81no—
300C22×C4—81no—
301C22×C4—2922no—
302C22×C4C22⋊Dic7311yescharacteristic
303C22×C4C22⋊Dic7311yescharacteristic
304C22×C4C22⋊Dic7311yescharacteristic
305C22×C4C22⋊Dic7311yescharacteristic
306C22×C4C4⋊Dic7312yescomplemented
307C22×C4C2×C22⋊D7311yescharacteristic
308M16—2922no—
309M16—2922no—
310C2×C8—2922no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—81no—
318C4⋊C4—5842no—
319C22⋊C4—21no—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—81no—
326C22⋊C4—2922no—
327C22⋊C4—2922no—
328C22⋊C4C4⋊Dic7312yescomplemented
329C42—21no—
330C42—21no—
331C42—81no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23C2×C22⋊Dic7311yescharacteristic
341C23C2×C4⋊Dic7311yescharacteristic
342C23#1455655011yescharacteristic
343C23#1455656511yescharacteristic
344C23#1455657011yescharacteristic
345D4—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4—5842no—
378C2×C4—5842no—
379C2×C4—5842no—
380C2×C4#1455650611yescharacteristic
381C2×C4#1455650611yescharacteristic
382C2×C4#1455656511yescharacteristic
383C2×C4#1455657011yescharacteristic
384C8—5842no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22#1798844711yescharacteristic
402C22C2×#1455650611yescharacteristic
403C22#1798856111yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—42no—
413C4—81no—
414C4—81no—
415C4—11682no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2—41no—
421C2—41no—
422C2#2260991911yescharacteristic
423C2#2261157711yescharacteristic
424C2#2261158511yescharacteristic
subgroupG/H
centerC22C2×#14556506
commutatorC24×C73C22×C4
FrattiniC22×D4C22×D73
FittingC73×#2322C2
socleC22×C73C2×#99
prime radical, cosocleC22×D4×C73C23
hypercenter#2322D73
hypocenterC73#12796
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2322

Complements

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

NH ≅ G/Ntype
15. C22×C4⋊C4×C73C4semidirect
21. #385×C73C4semidirect
22. #381×C73C4semidirect
23. C4×C22⋊C4×C73C4semidirect
99. C22×C4×C73C4⋊C4semidirect
115. C22⋊C4×C73C4⋊C4semidirect
218. C73#12796semidirect
221. C22×C4⋊C4Dic73semidirect
230. #385Dic73semidirect
231. #381Dic73semidirect
233. C4×C22⋊C4Dic73semidirect
306. C22×C4C4⋊Dic73semidirect
328. C22⋊C4C4⋊Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179883772
#226099232
#226099192
#226080492
C73×#23222
#1279673