Finite Group Databasebeta

← #32989192

Subgroups — #32989192

Order 18688.

404 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 77 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#22610915C211yesmaximal, characteristic
2#22608463C211yesmaximal, characteristic
3#22608450C211yesmaximal, characteristic
4#22607837C211yesmaximal, characteristic
5#22607817C211yesmaximal, characteristic
6#22607783C211yesmaximal, characteristic
7C73×#2665C211yesmaximal, characteristic
8C2×#14556570C2211yescharacteristic
9#17988551C2211yescharacteristic
10#17988551C2211yescharacteristic
11C4×C22⋊Dic73C2211yescharacteristic
12#17988353—21no—
13#17988353—21no—
14#17988323—21no—
15#17988323—21no—
16#17988323—21no—
17#17988323—21no—
18#400×C73—21no—
19#396×C73—21no—
20#395×C73—21no—
21#393×C73—21no—
22#391×C73—21no—
23#387×C73—21no—
24#381×C73C2211yescharacteristic
25#380×C73C2211yescharacteristic
26C4×C22⋊C4×C73C2211yescharacteristic
27C22×Dic146Q811yescharacteristic, complemented
28C2×#11924012—21no—
29C2×#11924012—21no—
30#14556570—21no—
31#14556570—21no—
32#14556570—21no—
33#14556570—21no—
34C2×C4⋊Dic73Q811yescharacteristic, complemented
35C2×#11924007—21no—
36C2×C22⋊Dic73—21no—
37C2×C22⋊Dic73—21no—
38C2×C4×Dic73—21no—
39C22⋊#10596831—21no—
40C22⋊#10596831—21no—
41C22⋊#10596831—21no—
42C22⋊#10596831—21no—
43#14556498—21no—
44C22×Q8×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×C22⋊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—
71#11924012—81no—
72#11924012—81no—
73C2×#10596831—41no—
74C2×#10596831—41no—
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77#11924007—41no—
78#11924007—41no—
79C22⋊Dic73—22no—
80C22⋊Dic73—41no—
81C22⋊Dic73—41no—
82C22⋊Dic73—41no—
83C4×Dic73—81no—
84C24×C73C2×D411yescharacteristic
85C2×Q8×C73—42no—
86C2×Q8×C73—81no—
87C2×Q8×C73—81no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73—21no—
92C22×C4×C73—21no—
93C22×C4×C73—21no—
94C22×C4×C73—81no—
95C22×C4×C73C2×D411yescharacteristic
96C22×C4×C73C2×D411yescharacteristic
97C22×C4×C73C2×Q811yescharacteristic
98C22×C4×C73#4111yescharacteristic
99C22×C4×C73#4111yescharacteristic
100C22×C4×C73#4111yescharacteristic
101C4⋊C4×C73—42no—
102C4⋊C4×C73—81no—
103C4⋊C4×C73—81no—
104C4⋊C4×C73—81no—
105C22⋊C4×C73—42no—
106C22⋊C4×C73—41no—
107C22⋊C4×C73—41no—
108C22⋊C4×C73—81no—
109C42×C73—81no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73—41no—
113C23×C73—41no—
114C23×C73#12011yescharacteristic
115C23×C73C22⋊Q811yescharacteristic
116C23×C73#12411yescharacteristic
117Q8×C73—84no—
118C2×C4×C73—22no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
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×C73C22⋊Q811yescharacteristic
143C2×C4×C73C22⋊Q811yescharacteristic
144C2×C4×C73#12411yescharacteristic
145C2×C4×C73#12411yescharacteristic
146C2×Dic73—42no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—81no—
150C2×Dic73—81no—
151C2×Dic73—81no—
152C2×Dic73—81no—
153Dic146—81no—
154Dic146—81no—
155#10596831—81no—
156#10596831—81no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—81no—
166C22×C73—81no—
167C22×C73#39311yescharacteristic
168C22×C73#45511yescharacteristic
169C22×C73#45611yescharacteristic
170C4×C73—21no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—21no—
174C4×C73—42no—
175C4×C73—81no—
176C4×C73—81no—
177C4×C73—81no—
178C4×C73—81no—
179C4×C73—81no—
180Dic73—82no—
181Dic73—81no—
182Dic73—81no—
183#10383—731nomaximal, Sylow
184C2×C73—21no—
185C2×C73—21no—
186C2×C73—41no—
187C2×C73—41no—
188C2×C73#202811yescharacteristic
189C2×C73#203111yescharacteristic
190C2×C73#203211yescharacteristic
191#2665D7311yescharacteristic
192#1996—731no—
193#1511—731no—
194#1508—731no—
195#1305—731no—
196#1297—731no—
197#1284—731no—
198C73#1038311yescharacteristic, complemented, Sylow
199C2×C22⋊Q8—731no—
200#407—731no—
201#407—731no—
202#400—21no—
203#396—21no—
204#395—21no—
205#393—21no—
206#391—21no—
207#387—21no—
208#381C2×D7311yescharacteristic
209#380C2×D7311yescharacteristic
210C4×C22⋊C4—731no—
211C4×C22⋊C4C2×D7311yescharacteristic
212#342—1461no—
213#342—1461no—
214#328—1461no—
215#328—1461no—
216#328—1461no—
217#328—1461no—
218C22×Q8—21no—
219C22×Q8—731no—
220C23×C4C22×D7311yescharacteristic
221C2×M16—1461no—
222C2×M16—1461no—
223C22⋊Q8—1461no—
224C22⋊Q8—1461no—
225C22⋊Q8—1461no—
226C22⋊Q8—1461no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—731no—
232C2×C4⋊C4—1461no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—1461no—
236C2×C22⋊C4—1461no—
237C2×C22⋊C4C22⋊D7311yescharacteristic
238C2×C22⋊C4C22⋊D7311yescharacteristic
239C2×C42—21no—
240C2×C42—1461no—
241C22⋊C8—1461no—
242C22⋊C8—1461no—
243C22⋊C8—1461no—
244C22⋊C8—1461no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—1461no—
252#95C22⋊D7311yescharacteristic
253#95C22⋊D7311yescharacteristic
254#95C22⋊D7311yescharacteristic
255#95C22⋊D7311yescharacteristic
256C24C2×C22⋊D7311yescharacteristic
257C2×Q8—42no—
258C2×Q8—81no—
259C2×Q8—81no—
260C2×Q8—5841no—
261C2×Q8—1461no—
262C2×Q8—1461no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—81no—
270C22×C4—2921no—
271C22×C4—1461no—
272C22×C4—1461no—
273C22×C4C2×C22⋊D7311yescharacteristic
274C22×C4C2×C22⋊D7311yescharacteristic
275C22×C4Q8×D7311yescharacteristic
276C22×C4#1192402911yescharacteristic
277C22×C4#1192402911yescharacteristic
278C22×C4#1192402911yescharacteristic
279M16—5841no—
280M16—5841no—
281C2×C8—2921no—
282C2×C8—2921no—
283C4⋊C4—42no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C4⋊C4—2921no—
288C4⋊C4—2921no—
289C4⋊C4—1461no—
290C4⋊C4—1461no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—81no—
295C22⋊C4—2921no—
296C22⋊C4—2921no—
297C22⋊C4—2921no—
298C22⋊C4—1462no—
299C42—81no—
300C42—5841no—
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23#1455656011yescharacteristic
306C23#1455656711yescharacteristic
307C23#1455658011yescharacteristic
308Q8—84no—
309Q8—5841no—
310Q8—5841no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—2922no—
336C2×C4—2921no—
337C2×C4—2921no—
338C2×C4—5841no—
339C2×C4—5841no—
340C2×C4—5841no—
341C2×C4—5841no—
342C2×C4#1455656711yescharacteristic
343C2×C4#1455656711yescharacteristic
344C2×C4#1455658011yescharacteristic
345C2×C4#1455658011yescharacteristic
346C8—5841no—
347C8—5841no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—81no—
357C22—81no—
358C22#1798849811yescharacteristic
359C22#1798876511yescharacteristic
360C22#1798877011yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4—81no—
371C4—5842no—
372C4—5841no—
373C4—5841no—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#2261108911yescharacteristic
379C2#2261110011yescharacteristic
380C2#2261110711yescharacteristic
subgroupG/H
centerC22#17988498
commutator, cosocleC23×C4×C73C23
FrattiniC23×C4C22×D73
FittingC73×#2665C2
socleC22×C73#393
prime radicalC24×C73C2×D4
hypercenter#2665D73
hypocenterC73#10383
LCSG ▷ C23×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2665

Complements

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

NH ≅ G/Ntype
27. C22×Dic146Q8semidirect
34. C2×C4⋊Dic73Q8semidirect
198. C73#10383semidirect

Maximal subgroups

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

subgroupindex
#226109152
#226084632
#226084502
#226078372
#226078172
#226077832
C73×#26652
#1038373