Finite Group Databasebeta

← #32989150

Subgroups — #32989150

Order 18688.

422 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610916C211yesmaximal, characteristic
2#22608502C211yesmaximal, characteristic
3C2×#17988323C211yesmaximal, characteristic
4#22607810C211yesmaximal, characteristic
5#22607798C211yesmaximal, characteristic
6#22607779C211yesmaximal, characteristic
7C73×#2569C211yesmaximal, characteristic
8C2×#14556570C2211yescharacteristic
9C2×C22⋊#10596831C2211yescharacteristic
10C2×C22⋊#10596831C2211yescharacteristic
11#17988447C2211yescharacteristic
12#17988353—21no—
13#17988353—21no—
14#17988323—21no—
15#17988323—21no—
16#17988323—21no—
17#17988323—21no—
18#400×C73—21no—
19#398×C73—21no—
20#387×C73—21no—
21#387×C73—21no—
22#385×C73—21no—
23#380×C73—21no—
24#380×C73C2211yescharacteristic
25C4×C22⋊C4×C73C2211yescharacteristic
26C2×#95×C73C2211yescharacteristic
27C22×Dic146Q811yescharacteristic
28C22×#10596831—21no—
29C22×#10596831—21no—
30#14556570—21no—
31#14556570—21no—
32#14556570—21no—
33#14556570—21no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73Q811yescharacteristic
36C2×#11924007—21no—
37C2×C22⋊Dic73—21no—
38C2×C22⋊Dic73—21no—
39C22⋊#10596831—21no—
40C22⋊#10596831—21no—
41C22⋊#10596831—21no—
42C22⋊#10596831—21no—
43#14556498—21no—
44C23×C4×C73—21no—
45C23×C4×C73C2311yescharacteristic
46C2×C4⋊C4×C73—21no—
47C2×C4⋊C4×C73—21no—
48C2×C4⋊C4×C73—21no—
49C2×C4⋊C4×C73—21no—
50C2×C4⋊C4×C73—21no—
51C2×C22⋊C4×C73—21no—
52C2×C22⋊C4×C73D411yescharacteristic
53C2×C22⋊C4×C73D411yescharacteristic
54C2×C42×C73—21no—
55#95×C73—21no—
56#95×C73—21no—
57#95×C73—21no—
58#95×C73—21no—
59#95×C73—21no—
60#95×C73—21no—
61#95×C73D411yescharacteristic
62#95×C73D411yescharacteristic
63#95×C73D411yescharacteristic
64#95×C73D411yescharacteristic
65C2×Dic146—21no—
66C2×Dic146—21no—
67C2×Dic146—81no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C22×Dic73—41no—
71C2×#10596831—41no—
72C2×#10596831—41no—
73C2×#10596831—81no—
74C2×#10596831—81no—
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73—81no—
78#11924007—41no—
79#11924007—41no—
80C22⋊Dic73—41no—
81C22⋊Dic73—41no—
82C22⋊Dic73—41no—
83C22⋊Dic73—41no—
84C24×C73C2×D411yescharacteristic
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73—42no—
92C22×C4×C73—41no—
93C22×C4×C73—41no—
94C22×C4×C73—81no—
95C22×C4×C73—81no—
96C22×C4×C73C2×D411yescharacteristic
97C22×C4×C73C2×D411yescharacteristic
98C22×C4×C73C2×Q811yescharacteristic
99C22×C4×C73#4111yescharacteristic
100C22×C4×C73#4111yescharacteristic
101C22×C4×C73#4111yescharacteristic
102C4⋊C4×C73—42no—
103C4⋊C4×C73—42no—
104C4⋊C4×C73—81no—
105C4⋊C4×C73—81no—
106C4⋊C4×C73—81no—
107C22⋊C4×C73—21no—
108C22⋊C4×C73—21no—
109C22⋊C4×C73—21no—
110C22⋊C4×C73—21no—
111C22⋊C4×C73—41no—
112C22⋊C4×C73—41no—
113C42×C73—81no—
114C23×C73—41no—
115C23×C73—41no—
116C23×C73#12011yescharacteristic
117C23×C73C22⋊Q811yescharacteristic
118C23×C73#12411yescharacteristic
119C23×C73#13511yescharacteristic
120C23×C73#13511yescharacteristic
121C23×C73#13711yescharacteristic
122C23×C73#13711yescharacteristic
123C2×C4×C73—22no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73—41no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—41no—
140C2×C4×C73—41no—
141C2×C4×C73—41no—
142C2×C4×C73—41no—
143C2×C4×C73—41no—
144C2×C4×C73—41no—
145C2×C4×C73—41no—
146C2×C4×C73—41no—
147C2×C4×C73—82no—
148C2×C4×C73—82no—
149C2×C4×C73C22⋊Q811yescharacteristic
150C2×C4×C73C22⋊Q811yescharacteristic
151C2×C4×C73#12411yescharacteristic
152C2×C4×C73#12411yescharacteristic
153C2×Dic73—41no—
154C2×Dic73—41no—
155C2×Dic73—81no—
156C2×Dic73—81no—
157C2×Dic73—81no—
158C2×Dic73—81no—
159C2×Dic73—81no—
160Dic146—81no—
161Dic146—81no—
162#10596831—81no—
163#10596831—81no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—41no—
171C22×C73—41no—
172C22×C73—41no—
173C22×C73—41no—
174C22×C73#39311yescharacteristic
175C22×C73#45211yescharacteristic
176C22×C73#45211yescharacteristic
177C22×C73#47911yescharacteristic
178C22×C73#47911yescharacteristic
179C22×C73#48811yescharacteristic
180C22×C73#49111yescharacteristic
181C4×C73—21no—
182C4×C73—21no—
183C4×C73—21no—
184C4×C73—21no—
185C4×C73—42no—
186C4×C73—81no—
187C4×C73—81no—
188C4×C73—81no—
189C4×C73—81no—
190C4×C73—81no—
191Dic73—81no—
192Dic73—81no—
193Dic73—161no—
194#10377—731nomaximal, Sylow
195C2×C73—21no—
196C2×C73—21no—
197C2×C73—21no—
198C2×C73—21no—
199C2×C73—21no—
200C2×C73—21no—
201C2×C73#202611yescharacteristic
202C2×C73#203111yescharacteristic
203C2×C73#203211yescharacteristic
204#2569D7311yescharacteristic
205#1996—731no—
206#1520—731no—
207C2×#328—731no—
208#1294—731no—
209#1289—731no—
210#1282—731no—
211C73#1037711yescharacteristic, complemented, Sylow
212C2×C22⋊Q8—731no—
213C2×C22⋊C8—731no—
214C2×C22⋊C8—731no—
215#400—21no—
216#398—21no—
217#387—21no—
218#387—21no—
219#385—21no—
220#380—21no—
221#380—731no—
222#380C2×D7311yescharacteristic
223C4×C22⋊C4C2×D7311yescharacteristic
224C2×#95C2×D7311yescharacteristic
225#342—1461no—
226#342—1461no—
227#328—1461no—
228#328—1461no—
229#328—1461no—
230#328—1461no—
231C22×Q8—731no—
232C23×C4—21no—
233C23×C4C22×D7311yescharacteristic
234C22×C8—1461no—
235C22×C8—1461no—
236C22⋊Q8—1461no—
237C22⋊Q8—1461no—
238C22⋊Q8—1461no—
239C22⋊Q8—1461no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—731no—
246C2×C4⋊C4—1461no—
247C2×C4⋊C4—1461no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—1461no—
250C2×C22⋊C4—1461no—
251C2×C22⋊C4C22⋊D7311yescharacteristic
252C2×C22⋊C4C22⋊D7311yescharacteristic
253C2×C42—21no—
254C22⋊C8—1461no—
255C22⋊C8—1461no—
256C22⋊C8—1461no—
257C22⋊C8—1461no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—1461no—
265#95C22⋊D7311yescharacteristic
266#95C22⋊D7311yescharacteristic
267#95C22⋊D7311yescharacteristic
268#95C22⋊D7311yescharacteristic
269C24C2×C22⋊D7311yescharacteristic
270C2×Q8—5841no—
271C2×Q8—1461no—
272C2×Q8—1461no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—81no—
283C22×C4—81no—
284C22×C4—2921no—
285C22×C4—1461no—
286C22×C4—1461no—
287C22×C4C2×C22⋊D7311yescharacteristic
288C22×C4C2×C22⋊D7311yescharacteristic
289C22×C4Q8×D7311yescharacteristic
290C22×C4#1192402911yescharacteristic
291C22×C4#1192402911yescharacteristic
292C22×C4#1192402911yescharacteristic
293C2×C8—2921no—
294C2×C8—2921no—
295C2×C8—5841no—
296C2×C8—5841no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—81no—
300C4⋊C4—81no—
301C4⋊C4—81no—
302C4⋊C4—2921no—
303C4⋊C4—2921no—
304C4⋊C4—5841no—
305C4⋊C4—1461no—
306C4⋊C4—1461no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—2921no—
314C22⋊C4—2921no—
315C22⋊C4—2921no—
316C22⋊C4—2921no—
317C42—81no—
318C23—41no—
319C23—41no—
320C23#1455656011yescharacteristic
321C23#1455656711yescharacteristic
322C23#1455658011yescharacteristic
323C23#1455661111yescharacteristic
324C23#1455661111yescharacteristic
325C23#1455662111yescharacteristic
326C23#1455662111yescharacteristic
327Q8—5841no—
328Q8—5841no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—2921no—
356C2×C4—2921no—
357C2×C4—5841no—
358C2×C4—5841no—
359C2×C4—5841no—
360C2×C4—5841no—
361C2×C4—5841no—
362C2×C4#1455656711yescharacteristic
363C2×C4#1455656711yescharacteristic
364C2×C4#1455658011yescharacteristic
365C2×C4#1455658011yescharacteristic
366C8—5841no—
367C8—5841no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1798849811yescharacteristic
379C22#1798874911yescharacteristic
380C22#1798874911yescharacteristic
381C22#1798889111yescharacteristic
382C22#1798889111yescharacteristic
383C22#1798894411yescharacteristic
384C22#1798895711yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—81no—
395C4—5841no—
396C4—5841no—
397C4—11681no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#2261107911yescharacteristic
405C2#2261110011yescharacteristic
406C2#2261110711yescharacteristic
subgroupG/H
centerC22#17988498
commutator, cosocleC23×C4×C73C23
FrattiniC23×C4C22×D73
FittingC73×#2569C2
socleC22×C73#393
prime radicalC24×C73C2×D4
hypercenter#2569D73
hypocenterC73#10377
LCSG ▷ C23×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2569

Complements

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

NH ≅ G/Ntype
211. C73#10377semidirect

Maximal subgroups

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

subgroupindex
#226109162
#226085022
C2×#179883232
#226078102
#226077982
#226077792
C73×#25692
#1037773