Finite Group Databasebeta

← D73⋊#2987 #34031872

Subgroups — D73⋊#2987 #34031872

Order 18688.

1706 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626845C214yesmaximal, complemented
2#22626844C214yesmaximal, complemented
3#22626843C218yesmaximal, complemented
4D73⋊#446C218yesmaximal, complemented
5D73⋊#433C214yesmaximal
6D73⋊#432C212yesmaximal
7#533×D73C211yesmaximal, characteristic
8#17989639C22116yescomplemented
9#17989639C22116yescomplemented
10#17989638C22116yescomplemented
11#17989637C22116yescomplemented
12#17989612C22116yes—
13#17989611C22116yes—
14#17989610C2214yes—
15#17989609C2214yes—
16#17989608C2214yes—
17#17989607C2214yes—
18#17989588C2214yes—
19#17989588C2218yes—
20#17989555C2214yes—
21#17989546C2214yes—
22#17989546C2214yes—
23C4×#11924036C2214yes—
24#17989144C411yescharacteristic
25#17989143C2212yes—
26#17989142C2212yes—
27#17989141C414yes—
28#17989140C412yes—
29#17989139C2214yes—
30C4⋊Q8×D73C412yes—
31#125×D73C412yes—
32C22⋊Q8×D73C414yes—
33C4×Q8×D73C2214yes—
34#117×D73C2212yes—
35C2×C42×D73C2211yescharacteristic
36#533×C73C411yescharacteristic
37C2×#11924036C2318yes—
38#14556658C2318yes—
39#14556658C23116yes—
40C4⋊#10596833C23116yes—
41C4⋊#10596833C2318yes—
42#14556648C2318yes—
43C22⋊#10596833C2318yes—
44#14556646C2318yes—
45#14556646C23116yes—
46#14556646C2318yes—
47C4×#10596833C23116yes—
48C2×Q8×D73C2×C414yes—
49C22×C4×D73C2×C412yes—
50C22×C4×D73C2311yescharacteristic
51#14556591C2×C412yes—
52#14556590C2×C414yes—
53#14556590C2×C414yes—
54#14556589C2×C414yes—
55#14556583C2×C412yes—
56#14556582C2×C414yes—
57#14556581C2×C418yes—
58#14556571C2×C414yes—
59#14556570C2×C414yes—
60#14556569C2×C418yes—
61#14556568C2×C418yes—
62#14556567C2×C414yes—
63Q8×Dic73C2314yes—
64C4×Dic146C2×C418yes—
65C4×Dic146C2×C414yes—
66#14556556C2318yes—
67#14556556C2314yes—
68#14556550C2×C412yes—
69#14556549C2314yes—
70#14556548C2×C414yes—
71#14556547C2314yes—
72C4⋊C4×D73C2×C414yes—
73C4⋊C4×D73C2×C414yes—
74C4⋊C4×D73C2×C418yes—
75C22⋊C4×D73C2×C414yes—
76C2×C4×Dic73C2×C411yescharacteristic
77C2×C4×Dic73C2312yes—
78C42×D73C2×C411yescharacteristic
79C42×D73C2×C412yes—
80C42×D73C2×C411yescharacteristic
81C42×D73C2311yescharacteristic
82C42×D73C2311yescharacteristic
83C42×D73C2312yes—
84C42×D73C2314yes—
85C4⋊Q8×C73C2×C412yes—
86#125×C73C2×C412yes—
87C22⋊Q8×C73C2×C414yes—
88C4×Q8×C73C2×C414yes—
89#117×C73C2×C412yes—
90C2×C42×C73C2×C411yescharacteristic
91#11924036—216no—
92C2×#10596833C24116yes—
93C23×D73C22×C411yescharacteristic
94C2×Dic146C22×C418yes—
95C2×Dic146C22×C414yes—
96Q8×D73—48no—
97C22×Dic73C22×C412yes—
98C22×Dic73C2411yescharacteristic
99C2×C4×D73—24no—
100C2×C4×D73—44no—
101C2×C4×D73C22×C411yescharacteristic
102C2×C4×D73C22×C411yescharacteristic
103C2×C4×D73C22×C412yes—
104C2×C4×D73C22×C412yes—
105C2×C4×D73C22×C418yes—
106C2×C4×D73C22×C412yes—
107C2×C4×D73C22×C412yes—
108C2×C4×D73C2411yescharacteristic
109C2×C4×D73C2411yescharacteristic
110C4⋊Dic73C22×C414yes—
111C4⋊Dic73C22×C414yes—
112C4⋊Dic73C22×C418yes—
113#11924007C22×C418yes—
114#11924007C22×C418yes—
115#11924007C22×C418yes—
116#11924007C22×C418yes—
117C22⋊Dic73C22×C414yes—
118#11924005C22×C418yes—
119C4×Dic73C22×C412yes—
120C4×Dic73C22×C412yes—
121C4×Dic73C22×C412yes—
122C4×Dic73C22×C411yescharacteristic
123C4×Dic73C22×C411yescharacteristic
124C4×Dic73C22×C414yes—
125C4×Dic73C2412yes—
126C4×Dic73C2412yes—
127C4×Dic73C2418yes—
128C2×Q8×C73C22×C414yes—
129C22×C4×C73C22×C411yescharacteristic
130C22×C4×C73C22×C412yes—
131C4⋊C4×C73C22×C414yes—
132C4⋊C4×C73C22×C418yes—
133C4⋊C4×C73C22×C414yes—
134C22⋊C4×C73C22×C414yes—
135C42×C73C22×C412yes—
136C42×C73C22×C411yescharacteristic
137C42×C73C22×C411yescharacteristic
138C42×C73C22×C414yes—
139C23×C73C23×C411yescharacteristic
140C22×D73—22no—
141C22×D73—24no—
142C22×D73C23×C411yescharacteristic
143C22×D73C23×C411yescharacteristic
144Q8×C73—44no—
145C2×C4×C73—22no—
146C2×C4×C73—42no—
147C2×C4×C73C23×C411yescharacteristic
148C2×C4×C73C23×C412yes—
149C2×C4×C73C23×C412yes—
150C2×C4×C73C23×C418yes—
151C2×C4×C73C23×C411yescharacteristic
152C2×Dic73—22no—
153C2×Dic73—42no—
154C2×Dic73C23×C411yescharacteristic
155C2×Dic73C23×C412yes—
156C2×Dic73C23×C412yes—
157C2×Dic73C23×C418yes—
158C2×Dic73C2511yescharacteristic
159C4×D73—22no—
160C4×D73—24no—
161C4×D73—24no—
162C4×D73—216no—
163C4×D73—22no—
164C4×D73—22no—
165C4×D73—42no—
166C4×D73—42no—
167C4×D732−1+414yes—
168Dic146—48no—
169Dic146—44no—
170#10596833—216no—
171C22×C73—21no—
172C22×C73—22no—
173C22×C73C24×C411yescharacteristic
174C2×D73—21no—
175C2×D73—22no—
176C2×D73—44no—
177C2×D73#51912yes—
178C2×D73#56814yes—
179C4×C73—21no—
180C4×C73—22no—
181C4×C73—28no—
182C4×C73—22no—
183C4×C73#51912yes—
184Dic73—21no—
185Dic73—22no—
186Dic73—28no—
187Dic73—22no—
188Dic73C2×2−1+412yes—
189C2×#2987—731nomaximal, Sylow
190C2×C73—41no—
191C2×C73C2×#51911yescharacteristic
192C2×C73C2×#56812yes—
193D73—41no—
194D73#298714yescomplemented
195C2×#533—731no—
196#2987—738no—
197#2987—734no—
198#2987—734no—
199C2×#446—738no—
200C2×#433—734no—
201C2×#432—732no—
202C73C2×#298711yescharacteristic, complemented, Sylow
203#533—732no—
204#533—732no—
205#533—734no—
206#533—734no—
207#533—732no—
208#533—731no—
209#533#6440811yescharacteristic
210C2×C4⋊Q8—732no—
211C2×#125—732no—
212C2×C22⋊Q8—734no—
213C2×C4×Q8—734no—
214C2×#117—732no—
215C22×C42—731no—
216#446—7316no—
217#446—7316no—
218#446—7316no—
219#446—7316no—
220#433—7316no—
221#433—7316no—
222#432—734no—
223#432—734no—
224#432—734no—
225#432—734no—
226C2×C4⋊C8—734no—
227C2×C4⋊C8—738no—
228C2×C22⋊C8—734no—
229C2×#97—734no—
230C2×#97—734no—
231C2×C4×C8—734no—
232C22×Q8—734no—
233C23×C4—732no—
234C23×C4—731no—
235C22×C8—738no—
236C4⋊Q8—734no—
237C4⋊Q8—734no—
238C4⋊Q8—734no—
239C4⋊Q8—732no—
240C4⋊Q8C2×#6440812yes—
241#125—738no—
242#125—734no—
243#125—732no—
244#125C2×#6440812yes—
245C22⋊Q8—734no—
246C22⋊Q8—734no—
247C22⋊Q8—738no—
248C22⋊Q8—734no—
249C22⋊Q8—738no—
250C22⋊Q8C2×#6440814yes—
251C4×Q8—734no—
252C4×Q8—734no—
253C4×Q8—738no—
254C4×Q8—738no—
255C4×Q8—734no—
256C4×Q8C2×#6440814yes—
257#117—732no—
258#117—734no—
259#117—734no—
260#117—734no—
261#117C2×#6440812yes—
262C2×C4⋊C4—734no—
263C2×C4⋊C4—738no—
264C2×C4⋊C4—734no—
265C2×C22⋊C4—734no—
266C2×C42—731no—
267C2×C42—732no—
268C2×C42—734no—
269C2×C42—732no—
270C2×C42—731no—
271C2×C42—731no—
272C2×C42—732no—
273C2×C42—731no—
274C2×C42—731no—
275C2×C42C2×#6440811yescharacteristic
276C4⋊C8—738no—
277C4⋊C8—738no—
278C4⋊C8—7316no—
279C4⋊C8—7316no—
280C22⋊C8—738no—
281C22⋊C8—738no—
282#97—738no—
283#97—738no—
284#97—7316no—
285C4×C8—7316no—
286C24—731no—
287C2×Q8—2928no—
288C2×Q8—738no—
289C2×Q8—734no—
290C2×Q8C22×#6440814yes—
291C22×C4—2924no—
292C22×C4—732no—
293C22×C4—732no—
294C22×C4—732no—
295C22×C4—731no—
296C22×C4—731no—
297C22×C4—732no—
298C22×C4—731no—
299C22×C4—732no—
300C22×C4—738no—
301C22×C4—731no—
302C22×C4—731no—
303C22×C4—1464no—
304C22×C4C22×#6440811yescharacteristic
305C22×C4C22×#6440812yes—
306C2×C8—7316no—
307C2×C8—14616no—
308C4⋊C4—738no—
309C4⋊C4—738no—
310C4⋊C4—738no—
311C4⋊C4—738no—
312C4⋊C4—734no—
313C4⋊C4—738no—
314C4⋊C4—734no—
315C4⋊C4C22×#6440814yes—
316C4⋊C4C22×#6440818yes—
317C4⋊C4C22×#6440814yes—
318C22⋊C4—734no—
319C22⋊C4—738no—
320C22⋊C4C22×#6440814yes—
321C42—732no—
322C42—731no—
323C42—732no—
324C42—731no—
325C42—738no—
326C42—732no—
327C42—732no—
328C42—732no—
329C42—734no—
330C42C22×#6440811yescharacteristic
331C42C22×#6440811yescharacteristic
332C42C22×#6440812yes—
333C42C22×#6440814yes—
334C23—731no—
335C23—731no—
336C23—1464no—
337C23—1462no—
338C23C23×#6440811yescharacteristic
339Q8—44no—
340Q8—2924no—
341Q8—2928no—
342C2×C4—22no—
343C2×C4—42no—
344C2×C4—2922no—
345C2×C4—2922no—
346C2×C4—2922no—
347C2×C4—731no—
348C2×C4—734no—
349C2×C4—731no—
350C2×C4—732no—
351C2×C4—732no—
352C2×C4—738no—
353C2×C4—1462no—
354C2×C4—1464no—
355C2×C4—1464no—
356C2×C4—1462no—
357C2×C4—14616no—
358C2×C4—1462no—
359C2×C4—1462no—
360C2×C4C23×#6440811yescharacteristic
361C2×C4C23×#6440812yes—
362C2×C4C23×#6440812yes—
363C2×C4C23×#6440818yes—
364C2×C4C23×#6440811yescharacteristic
365C8—14616no—
366C22—21no—
367C22—22no—
368C22—2924no—
369C22—732no—
370C22—734no—
371C22—1461no—
372C22—1462no—
373C22C24×#6440811yescharacteristic
374C4—21no—
375C4—22no—
376C4—22no—
377C4—28no—
378C4—732no—
379C4—1461no—
380C4—1462no—
381C4—1462no—
382C4—1468no—
383C4#1798965512yes—
384C2—41no—
385C2—2921no—
386C2—734no—
387C2C2×#1798965511yescharacteristic
388C2D73⋊#56812yes—
subgroupG/H
centerC2×C4C23×#64408
commutator, socleC22×C73C24×C4
FrattiniC22C24×#64408
Fitting#533×C73C4
prime radicalC23×D73C22×C4
cosocleC2×Dic73C25
hypercenter#533#64408
hypocenterC73C2×#2987
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. #22626845C2semidirect
2. #22626844C2semidirect
3. #22626843C2semidirect
4. D73⋊#446C2semidirect
8. #17989639C22semidirect
9. #17989639C22semidirect
10. #17989638C22semidirect
11. #17989637C22semidirect
194. D73#2987semidirect
202. C73C2×#2987semidirect

Maximal subgroups

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

subgroupindex
#226268452
#226268442
#226268432
D73⋊#4462
D73⋊#4332
D73⋊#4322
#533×D732
C2×#298773