Finite Group Databasebeta

← #32978887

Subgroups — #32978887

Order 18688.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988658C211yesmaximal, characteristic
2#22609956C211yesmaximal, characteristic, complemented
3#22609916C212yesmaximal
4#22607798C212yesmaximal, complemented
5C73×#1808C211yesmaximal, characteristic, complemented
6C22×#11924011C411yescharacteristic, complemented
7C2×C4×C22⋊D73C2211yescharacteristic
8#17988658—21no—
9#17988658—21no—
10#17988658—21no—
11#17988658—21no—
12C2×#14556523—21no—
13C2×#14556520C411yescharacteristic, complemented
14C2×#14556505—22no—
15C2×C22⋊#10596831C2211yescharacteristic
16C2×#14556503C411yescharacteristic, complemented
17C2×#14556501C411yescharacteristic, complemented
18#17988447C2212yes—
19#17988353—22no—
20#17988350—21no—
21C23×C8×C73C2211yescharacteristic
22C2×#107×C73—21no—
23#380×C73C2212yes—
24#340×C73—21no—
25C22×C22⋊D73D411yescharacteristic
26C22×C4×D73C2×C411yescharacteristic
27C2×#11924011—21no—
28C2×#11924011—21no—
29C2×#11924011—42no—
30C22×#10596831C2×C411yescharacteristic
31C22×#10596831C2×C411yescharacteristic
32C4×C22⋊D73—21no—
33C4×C22⋊D73—21no—
34C4×C22⋊D73—21no—
35C4×C22⋊D73—21no—
36C2×C4⋊Dic73—22no—
37C2×#11924007Q811yescharacteristic
38C2×C22⋊Dic73—22no—
39C2×C22⋊Dic73D411yescharacteristic
40C2×#11924005Q811yescharacteristic
41C2×C4×Dic73C2×C411yescharacteristic
42#14556523—42no—
43#14556520—21no—
44#14556520—21no—
45#14556505—44no—
46C22⋊#10596831—21no—
47C22⋊#10596831—21no—
48#14556503—21no—
49#14556503—21no—
50#14556501—21no—
51#14556501—21no—
52#14556498—22no—
53C23×C4×C73C2311yescharacteristic
54C22×C8×C73—42no—
55C22×C8×C73C2×C411yescharacteristic
56C22×C8×C73C2×C411yescharacteristic
57C22×C8×C73D411yescharacteristic
58C22×C8×C73D411yescharacteristic
59C22×C8×C73D411yescharacteristic
60C22×C8×C73D411yescharacteristic
61C2×C4⋊C4×C73—22no—
62C2×C22⋊C4×C73—22no—
63#107×C73—42no—
64#95×C73—22no—
65C23×D73C4⋊C411yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—22no—
69C2×C22⋊D73—22no—
70C22×Dic73—42no—
71C22×Dic73C4⋊C411yescharacteristic
72C22×Dic73C4⋊C411yescharacteristic
73C22×Dic73C4⋊C411yescharacteristic
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76C2×C4×D73—41no—
77C2×C4×D73—41no—
78#11924011—42no—
79#11924011—42no—
80C2×#10596831—21no—
81C2×#10596831—21no—
82C2×#10596831—41no—
83C2×#10596831—41no—
84C4⋊Dic73—42no—
85C4⋊Dic73—42no—
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—42no—
91C22⋊Dic73—42no—
92#11924005—21no—
93#11924005—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C24×C73C2×D411yescharacteristic
97C22×C4×C73—41no—
98C22×C4×C73—41no—
99C22×C4×C73—42no—
100C22×C4×C73C22×C411yescharacteristic
101C22×C4×C73C2×D411yescharacteristic
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73C2×Q811yescharacteristic
104C22×C4×C73#4111yescharacteristic
105C22×C4×C73#4111yescharacteristic
106C2×C8×C73—22no—
107C2×C8×C73—22no—
108C2×C8×C73—22no—
109C2×C8×C73—41no—
110C2×C8×C73—41no—
111C2×C8×C73—41no—
112C2×C8×C73C22⋊C411yescharacteristic
113C2×C8×C73C22⋊C411yescharacteristic
114C2×C8×C73C22⋊C411yescharacteristic
115C2×C8×C73C22⋊C411yescharacteristic
116C4⋊C4×C73—42no—
117C4⋊C4×C73—42no—
118C22⋊C4×C73—42no—
119C22⋊C4×C73—42no—
120C23×C73—41no—
121C23×C73—41no—
122C23×C73C2×C4⋊C411yescharacteristic
123C23×C73#12111yescharacteristic
124C23×C73#12111yescharacteristic
125C23×C73AGL(1,ℤ/8)12yes—
126C23×C73#13712yes—
127C22×D73—21no—
128C22×D73—22no—
129C22×D73—41no—
130C22×D73—41no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—41no—
140C2×C4×C73—82no—
141C2×C4×C73—82no—
142C2×C4×C73—82no—
143C2×C4×C73C2×C22⋊C411yescharacteristic
144C2×C4×C73#11711yescharacteristic
145C2×C4×C73C22⋊Q811yescharacteristic
146C2×C4×C73C22⋊Q811yescharacteristic
147C22⋊D73—42no—
148C22⋊D73—41no—
149C22⋊D73—41no—
150C2×Dic73—21no—
151C2×Dic73—21no—
152C2×Dic73—21no—
153C2×Dic73—22no—
154C2×Dic73—41no—
155C2×Dic73—41no—
156C2×Dic73—82no—
157C2×Dic73—82no—
158C2×Dic73—82no—
159C4×D73—42no—
160C4×D73—41no—
161C4×D73—41no—
162C8×C73—21no—
163C8×C73—21no—
164C8×C73—21no—
165C8×C73#9912yescomplemented
166#10596831—41no—
167#10596831—41no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—42no—
175C22×C73—42no—
176C22×C73#38011yescharacteristic
177C22×C73#42812yes—
178C22×C73#46812yes—
179C22×C73#46911yescharacteristic
180C22×C73#47011yescharacteristic
181C2×D73—41no—
182C2×D73—41no—
183C2×D73—41no—
184C2×D73—82no—
185C4×C73—21no—
186C4×C73—21no—
187C4×C73—21no—
188C4×C73—162no—
189C4×C73C2×#9911yescharacteristic
190C4×C73#41011yescharacteristic
191Dic73—41no—
192Dic73—41no—
193Dic73—41no—
194Dic73—162no—
195#8610—731nomaximal, Sylow
196C2×C73—22no—
197C2×C73—21no—
198C2×C73—22no—
199C2×C73—21no—
200C2×C73#179911yescharacteristic
201C2×C73#180911yescharacteristic
202C2×C73#181211yescharacteristic
203D73—81no—
204C2×#435—731no—
205#1808D7311yescharacteristic, complemented
206#1807—731no—
207#1799—732no—
208#1289—732no—
209C73#861011yescharacteristic, complemented, Sylow
210C22×M16—731no—
211C23×C8C2×D7311yescharacteristic
212C2×C4×D4—731no—
213#435—1461no—
214#435—1461no—
215#435—1461no—
216#435—1461no—
217C2×#107—21no—
218C2×#106—1461no—
219C2×C4⋊C8—731no—
220C2×#99—1462no—
221C2×C22⋊C8—731no—
222C2×C22⋊C8—731no—
223C2×#97—731no—
224#380—732no—
225#380C2×D7312yes—
226#342—1462no—
227#340—21no—
228#340—1461no—
229C22×D4—731no—
230C23×C4—731no—
231C23×C4C22×D7311yescharacteristic
232C2×M16—2922no—
233C2×M16—1461no—
234C2×M16—1461no—
235C22×C8—42no—
236C22×C8—731no—
237C22×C8—731no—
238C22×C8C4×D7311yescharacteristic
239C22×C8C4×D7311yescharacteristic
240C22×C8D29211yescharacteristic
241C22×C8D29211yescharacteristic
242C22×C8C22⋊D7311yescharacteristic
243C22×C8C22⋊D7311yescharacteristic
244C4×D4—1461no—
245C4×D4—1461no—
246C4×D4—1461no—
247C4×D4—1461no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—731no—
250C2×C4⋊C4—1462no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—731no—
253C2×C22⋊C4—731no—
254C2×C22⋊C4—1462no—
255C2×C42—731no—
256#107—42no—
257#106—2922no—
258C4⋊C8—1461no—
259C4⋊C8—1461no—
260#99—2924no—
261C22⋊C8—1461no—
262C22⋊C8—1461no—
263C22⋊C8—1461no—
264C22⋊C8—1461no—
265#97—1461no—
266#97—1461no—
267#95—22no—
268#95—1462no—
269C24—731no—
270C24D4×D7311yescharacteristic
271C2×D4—1461no—
272C2×D4—1461no—
273C2×D4—1462no—
274C2×D4—1462no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—2921no—
279C22×C4—2921no—
280C22×C4—2922no—
281C22×C4—731no—
282C22×C4—731no—
283C22×C4—731no—
284C22×C4—1461no—
285C22×C4—1461no—
286C22×C4C2×C4×D7311yescharacteristic
287C22×C4C2×C22⋊D7311yescharacteristic
288C22×C4C2×D29211yescharacteristic
289C22×C4Q8×D7311yescharacteristic
290C22×C4#1192402711yescharacteristic
291C22×C4#1192402911yescharacteristic
292M16—2922no—
293M16—2922no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—2921no—
301C2×C8—2921no—
302C2×C8—1461no—
303C2×C8—1461no—
304C2×C8#1192400511yescharacteristic
305C2×C8#1192400511yescharacteristic
306C2×C8#1192400511yescharacteristic
307C2×C8#1192400511yescharacteristic
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—2922no—
311C4⋊C4—2922no—
312C4⋊C4—1461no—
313C4⋊C4—1461no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—2922no—
317C22⋊C4—2922no—
318C22⋊C4—1461no—
319C22⋊C4—1461no—
320C22⋊C4—1461no—
321C22⋊C4—1461no—
322C42—1461no—
323C42—1461no—
324C23—41no—
325C23—41no—
326C23—2921no—
327C23—2921no—
328C23—1461no—
329C23—1462no—
330C23C4⋊C4×D7311yescharacteristic
331C23#1455656211yescharacteristic
332C23#1455656611yescharacteristic
333C23#1455661512yes—
334C23#1455662312yes—
335D4—2922no—
336D4—2921no—
337D4—2921no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—2922no—
351C2×C4—2921no—
352C2×C4—2921no—
353C2×C4—2921no—
354C2×C4—2921no—
355C2×C4—5842no—
356C2×C4—5842no—
357C2×C4—5842no—
358C2×C4—1462no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4C2×#1192400511yescharacteristic
363C2×C4#1455654911yescharacteristic
364C2×C4#1455656711yescharacteristic
365C2×C4#1455657111yescharacteristic
366C8—21no—
367C8—21no—
368C8—21no—
369C8—2921no—
370C8—2921no—
371C8#1455650512yescomplemented
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—42no—
379C22—42no—
380C22—2921no—
381C22—2921no—
382C22—2921no—
383C22—5842no—
384C22#1798844411yescharacteristic
385C22#1798862812yes—
386C22#1798883412yes—
387C22#1798883711yescharacteristic
388C22#1798884211yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—162no—
393C4—2921no—
394C4—2921no—
395C4—2921no—
396C4—11682no—
397C4C2×#1455650511yescharacteristic
398C4#1798856011yescharacteristic
399C2—21no—
400C2—22no—
401C2—22no—
402C2—21no—
403C2—5841no—
404C2#2260991611yescharacteristic
405C2#2260996511yescharacteristic
406C2#2260997411yescharacteristic
subgroupG/H
centerC22#17988444
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1808C2
socleC22×C73#380
prime radicalC22×C22⋊D73D4
cosocleC23×C4×C73C23
hypercenter#1808D73
hypocenterC73#8610
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. #22609956C2semidirect
4. #22607798C2semidirect
5. C73×#1808C2semidirect
6. C22×#11924011C4semidirect
13. C2×#14556520C4semidirect
16. C2×#14556503C4semidirect
17. C2×#14556501C4semidirect
165. C8×C73#99semidirect
205. #1808D73semidirect
209. C73#8610semidirect
371. C8#14556505semidirect

Maximal subgroups

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

subgroupindex
C2×#179886582
#226099562
#226099162
#226077982
C73×#18082
#861073