Finite Group Databasebeta

← D73⋊#2986 #34031868

Subgroups — D73⋊#2986 #34031868

Order 18688.

1794 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626842C214yesmaximal, complemented
2#22626841C214yesmaximal, complemented
3#22626840C218yesmaximal, complemented
4D73⋊#446C214yesmaximal, complemented
5Q8×#11924036C214yesmaximal, complemented
6D73⋊#433C214yesmaximal
7#22626595C212yesmaximal
8#533×D73C211yesmaximal, characteristic
9#17989639C22116yescomplemented
10#17989638C2218yescomplemented
11#17989637C2218yescomplemented
12#17989636C22116yescomplemented
13#17989636C2218yescomplemented
14Q8×#10596833C2218yescomplemented
15#17989612C22116yes—
16#17989611C22116yes—
17#17989606C2214yes—
18#17989605C2214yes—
19#17989604C2214yes—
20#17989603C2214yes—
21#17989588C2212yes—
22#17989588C2212yes—
23#17989588C2218yes—
24#17989555C2214yes—
25#17989546C2214yes—
26C4×#11924036C2214yes—
27C4×#11924036C2214yes—
28#17989144C411yescharacteristic
29#17989143C2212yes—
30#17989142C2212yes—
31#17989141C414yes—
32#17989140C412yes—
33#17989139C2214yes—
34C4⋊Q8×D73C412yes—
35#125×D73C412yes—
36C22⋊Q8×D73C414yes—
37C4×Q8×D73C2214yes—
38#117×D73C2212yes—
39C2×C42×D73C2211yescharacteristic
40#533×C73C411yescharacteristic
41C2×#11924036C2314yes—
42C2×#11924036C2314yes—
43#14556658C2314yes—
44#14556658C23116yes—
45#14556658C2314yes—
46C4⋊#10596833C2314yes—
47C4⋊#10596833C23116yes—
48C4⋊#10596833C2314yes—
49#14556648C2318yes—
50C22⋊#10596833C2318yes—
51#14556646C23116yes—
52C4×#10596833C23116yes—
53C4×#10596833C2318yes—
54C4×#10596833C2318yes—
55C2×Q8×D73C2×C414yes—
56C22×C4×D73C2×C412yes—
57C22×C4×D73C2311yescharacteristic
58#14556591C2×C412yes—
59#14556590C2×C414yes—
60#14556590C2×C414yes—
61#14556589C2×C414yes—
62#14556583C2×C412yes—
63#14556582C2×C414yes—
64#14556581C2×C418yes—
65#14556571C2×C414yes—
66#14556570C2×C414yes—
67#14556569C2×C418yes—
68#14556568C2×C418yes—
69#14556567C2×C414yes—
70Q8×Dic73C2314yes—
71C4×Dic146C2×C418yes—
72C4×Dic146C2×C414yes—
73#14556556C2314yes—
74#14556556C2318yes—
75#14556550C2×C412yes—
76#14556549C2314yes—
77#14556548C2×C414yes—
78#14556547C2314yes—
79C4⋊C4×D73C2×C414yes—
80C4⋊C4×D73C2×C414yes—
81C4⋊C4×D73C2×C418yes—
82C22⋊C4×D73C2×C414yes—
83C2×C4×Dic73C2×C411yescharacteristic
84C2×C4×Dic73C2312yes—
85C42×D73C2×C411yescharacteristic
86C42×D73C2×C412yes—
87C42×D73C2×C411yescharacteristic
88C42×D73C2311yescharacteristic
89C42×D73C2311yescharacteristic
90C42×D73C2312yes—
91C42×D73C2314yes—
92C4⋊Q8×C73C2×C412yes—
93#125×C73C2×C412yes—
94C22⋊Q8×C73C2×C414yes—
95C4×Q8×C73C2×C414yes—
96#117×C73C2×C412yes—
97C2×C42×C73C2×C411yescharacteristic
98#11924036—28no—
99#11924036—28no—
100C2×#10596833C2418yes—
101C2×#10596833C2418yes—
102C23×D73C22×C411yescharacteristic
103C2×Dic146C22×C418yes—
104C2×Dic146C22×C414yes—
105Q8×D73—216no—
106C22×Dic73C22×C412yes—
107C22×Dic73C2411yescharacteristic
108C2×C4×D73—28no—
109C2×C4×D73—24no—
110C2×C4×D73C22×C411yescharacteristic
111C2×C4×D73C22×C411yescharacteristic
112C2×C4×D73C22×C412yes—
113C2×C4×D73C22×C412yes—
114C2×C4×D73C22×C412yes—
115C2×C4×D73C22×C418yes—
116C2×C4×D73C22×C412yes—
117C2×C4×D73C2411yescharacteristic
118C2×C4×D73C2411yescharacteristic
119C4⋊Dic73C22×C414yes—
120C4⋊Dic73C22×C414yes—
121C4⋊Dic73C22×C418yes—
122#11924007C22×C418yes—
123#11924007C22×C418yes—
124#11924007C22×C418yes—
125#11924007C22×C418yes—
126C22⋊Dic73C22×C414yes—
127#11924005C22×C418yes—
128C4×Dic73C22×C412yes—
129C4×Dic73C22×C412yes—
130C4×Dic73C22×C412yes—
131C4×Dic73C22×C411yescharacteristic
132C4×Dic73C22×C411yescharacteristic
133C4×Dic73C22×C414yes—
134C4×Dic73C2412yes—
135C4×Dic73C2412yes—
136C4×Dic73C2418yes—
137C2×Q8×C73C22×C414yes—
138C22×C4×C73C22×C411yescharacteristic
139C22×C4×C73C22×C412yes—
140C4⋊C4×C73C22×C414yes—
141C4⋊C4×C73C22×C418yes—
142C4⋊C4×C73C22×C414yes—
143C22⋊C4×C73C22×C414yes—
144C42×C73C22×C412yes—
145C42×C73C22×C411yescharacteristic
146C42×C73C22×C411yescharacteristic
147C42×C73C22×C414yes—
148C23×C73C23×C411yescharacteristic
149C22×D73—22no—
150C22×D73—24no—
151C22×D73C23×C411yescharacteristic
152C22×D73C23×C411yescharacteristic
153Q8×C73—28no—
154C2×C4×C73—22no—
155C2×C4×C73—24no—
156C2×C4×C73C23×C411yescharacteristic
157C2×C4×C73C23×C412yes—
158C2×C4×C73C23×C418yes—
159C2×C4×C73C23×C412yes—
160C2×C4×C73C23×C411yescharacteristic
161C2×Dic73—24no—
162C2×Dic73—22no—
163C2×Dic73C23×C411yescharacteristic
164C2×Dic73C23×C412yes—
165C2×Dic73C23×C418yes—
166C2×Dic73C23×C412yes—
167C2×Dic73C2511yescharacteristic
168C4×D73—22no—
169C4×D73—24no—
170C4×D73—216no—
171C4×D73—22no—
172C4×D73—24no—
173C4×D73—24no—
174C4×D73—22no—
175C4×D73#13118yes—
176C4×D732−1+414yes—
177Dic146—28no—
178Dic146—216no—
179#10596833—28no—
180#10596833—28no—
181C22×C73—21no—
182C22×C73—22no—
183C22×C73C24×C411yescharacteristic
184C2×D73—21no—
185C2×D73—22no—
186C2×D73—44no—
187C2×D73#51912yes—
188C2×D73C2×#13114yes—
189C4×C73—21no—
190C4×C73—28no—
191C4×C73—22no—
192C4×C73#51912yes—
193C4×C73C2×#13114yes—
194Dic73—21no—
195Dic73—28no—
196Dic73—22no—
197Dic73C2×#13114yes—
198Dic73C2×2−1+412yes—
199C2×#2986—731nomaximal, Sylow
200C2×C73—41no—
201C2×C73C2×#51911yescharacteristic
202C2×C73C22×#13112yes—
203D73—41no—
204D73#298614yescomplemented
205C2×#533—731no—
206#2986—738no—
207#2986—734no—
208#2986—734no—
209C2×#446—734no—
210C2×C8×Q8—734no—
211C2×#433—734no—
212C2×#431—732no—
213C73C2×#298611yescharacteristic, complemented, Sylow
214#533—732no—
215#533—732no—
216#533—734no—
217#533—734no—
218#533—732no—
219#533—731no—
220#533#6440811yescharacteristic
221C2×C4⋊Q8—732no—
222C2×#125—732no—
223C2×C22⋊Q8—734no—
224C2×C4×Q8—734no—
225C2×#117—732no—
226C22×C42—731no—
227#446—738no—
228#446—738no—
229#446—7316no—
230C8×Q8—738no—
231C8×Q8—738no—
232C8×Q8—7316no—
233#433—7316no—
234#433—7316no—
235#431—734no—
236#431—734no—
237#431—734no—
238#431—734no—
239C2×C4⋊C8—732no—
240C2×C4⋊C8—732no—
241C2×C4⋊C8—738no—
242C2×C22⋊C8—734no—
243C2×#97—734no—
244C2×C4×C8—734no—
245C2×C4×C8—734no—
246C22×Q8—734no—
247C23×C4—731no—
248C23×C4—732no—
249C22×C8—734no—
250C22×C8—734no—
251C4⋊Q8—734no—
252C4⋊Q8—734no—
253C4⋊Q8—734no—
254C4⋊Q8—732no—
255C4⋊Q8C2×#6440812yes—
256#125—738no—
257#125—734no—
258#125—732no—
259#125C2×#6440812yes—
260C22⋊Q8—734no—
261C22⋊Q8—734no—
262C22⋊Q8—738no—
263C22⋊Q8—734no—
264C22⋊Q8—738no—
265C22⋊Q8C2×#6440814yes—
266C4×Q8—734no—
267C4×Q8—734no—
268C4×Q8—738no—
269C4×Q8—738no—
270C4×Q8—734no—
271C4×Q8C2×#6440814yes—
272#117—732no—
273#117—734no—
274#117—734no—
275#117—734no—
276#117C2×#6440812yes—
277C2×C4⋊C4—734no—
278C2×C4⋊C4—738no—
279C2×C4⋊C4—734no—
280C2×C22⋊C4—734no—
281C2×C42—731no—
282C2×C42—732no—
283C2×C42—734no—
284C2×C42—732no—
285C2×C42—731no—
286C2×C42—731no—
287C2×C42—732no—
288C2×C42—731no—
289C2×C42—731no—
290C2×C42C2×#6440811yescharacteristic
291C4⋊C8—734no—
292C4⋊C8—734no—
293C4⋊C8—734no—
294C4⋊C8—734no—
295C4⋊C8—7316no—
296C4⋊C8—7316no—
297C22⋊C8—738no—
298C22⋊C8—738no—
299#97—7316no—
300C4×C8—738no—
301C4×C8—738no—
302C4×C8—7316no—
303C24—731no—
304C2×Q8—738no—
305C2×Q8—734no—
306C2×Q8—14616no—
307C2×Q8C22×#6440814yes—
308C22×C4—732no—
309C22×C4—731no—
310C22×C4—732no—
311C22×C4—731no—
312C22×C4—731no—
313C22×C4—732no—
314C22×C4—732no—
315C22×C4—732no—
316C22×C4—738no—
317C22×C4—731no—
318C22×C4—731no—
319C22×C4—1464no—
320C22×C4—1468no—
321C22×C4C22×#6440812yes—
322C22×C4C22×#6440811yescharacteristic
323C2×C8—738no—
324C2×C8—738no—
325C2×C8—1468no—
326C2×C8—1468no—
327C4⋊C4—738no—
328C4⋊C4—738no—
329C4⋊C4—738no—
330C4⋊C4—738no—
331C4⋊C4—734no—
332C4⋊C4—738no—
333C4⋊C4—734no—
334C4⋊C4C22×#6440814yes—
335C4⋊C4C22×#6440818yes—
336C4⋊C4C22×#6440814yes—
337C22⋊C4—734no—
338C22⋊C4—738no—
339C22⋊C4C22×#6440814yes—
340C42—732no—
341C42—731no—
342C42—731no—
343C42—732no—
344C42—732no—
345C42—732no—
346C42—738no—
347C42—732no—
348C42—734no—
349C42C22×#6440811yescharacteristic
350C42C22×#6440811yescharacteristic
351C42C22×#6440812yes—
352C42C22×#6440814yes—
353C23—731no—
354C23—731no—
355C23—1462no—
356C23—1464no—
357C23C23×#6440811yescharacteristic
358Q8—28no—
359Q8—14616no—
360Q8—1468no—
361C2×C4—22no—
362C2×C4—24no—
363C2×C4—731no—
364C2×C4—732no—
365C2×C4—734no—
366C2×C4—738no—
367C2×C4—731no—
368C2×C4—732no—
369C2×C4—738no—
370C2×C4—1462no—
371C2×C4—1464no—
372C2×C4—1462no—
373C2×C4—1464no—
374C2×C4—14616no—
375C2×C4—1462no—
376C2×C4—1464no—
377C2×C4—1462no—
378C2×C4—1464no—
379C2×C4C23×#6440811yescharacteristic
380C2×C4C23×#6440812yes—
381C2×C4C23×#6440818yes—
382C2×C4C23×#6440812yes—
383C2×C4C23×#6440811yescharacteristic
384C8—1468no—
385C8—1468no—
386C22—21no—
387C22—22no—
388C22—2924no—
389C22—732no—
390C22—734no—
391C22—1461no—
392C22—1462no—
393C22C24×#6440811yescharacteristic
394C4—21no—
395C4—22no—
396C4—28no—
397C4—732no—
398C4—734no—
399C4—1461no—
400C4—1462no—
401C4—1468no—
402C4#1798965512yes—
403C4D73⋊#13114yes—
404C2—41no—
405C2—2921no—
406C2—734no—
407C2C2×#1798965511yescharacteristic
408C2C2×D73⋊#13112yes—
subgroupG/H
centerC2×C4C23×#64408
commutator, socleC22×C73C24×C4
FrattiniC22C24×#64408
Fitting#533×C73C4
prime radicalC23×D73C22×C4
cosocleC2×Dic73C25
hypercenter#533#64408
hypocenterC73C2×#2986
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. #22626842C2semidirect
2. #22626841C2semidirect
3. #22626840C2semidirect
4. D73⋊#446C2semidirect
5. Q8×#11924036C2semidirect
9. #17989639C22semidirect
10. #17989638C22semidirect
11. #17989637C22semidirect
12. #17989636C22semidirect
13. #17989636C22semidirect
14. Q8×#10596833C22semidirect
204. D73#2986semidirect
213. C73C2×#2986semidirect

Maximal subgroups

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

subgroupindex
#226268422
#226268412
#226268402
D73⋊#4462
Q8×#119240362
D73⋊#4332
#226265952
#533×D732
C2×#298673