Finite Group Databasebeta

← #34001348

Subgroups — #34001348

Order 18688.

604 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 126 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#22625788C211yesmaximal, characteristic
2C4×#14556648C211yesmaximal, characteristic
3#22624750C212yesmaximal, complemented
4#22624749C212yesmaximal, complemented
5#389×D73C211yesmaximal, characteristic
6C2×#14556658—21no—
7C2×#14556648—21no—
8C2×#14556648—21no—
9C2×C4×#10596833—21no—
10#17989453C2212yes—
11#17989453C2212yes—
12C2×C4⋊C4×D73—21no—
13C2×C4⋊C4×D73C411yescharacteristic
14C2×C4⋊C4×D73C411yescharacteristic
15C2×C42×D73C2211yescharacteristic
16#17988486C2211yescharacteristic
17#17988485C411yescharacteristic
18#17988484—21no—
19#17988483C2211yescharacteristic
20#17988482—21no—
21#95×D73—21no—
22#389×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556658—42no—
26#14556648—24no—
27#14556648—42no—
28C4×#10596833—42no—
29C22×C4×D73—21no—
30C22×C4×D73—21no—
31C22×C4×D73C2×C411yescharacteristic
32C22×C4×D73D411yescharacteristic
33C22×C4×D73D411yescharacteristic
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×C4⋊Dic73C2×C411yescharacteristic
37C2×#11924007—21no—
38C2×#11924007—21no—
39C2×#11924007—21no—
40C2×#11924007—21no—
41C4⋊C4×D73—22no—
42C4⋊C4×D73—42no—
43C4⋊C4×D73—42no—
44C4⋊C4×D73—42no—
45C4⋊C4×D73C814yescomplemented
46C2×C4×Dic73D411yescharacteristic
47C2×C4×Dic73D411yescharacteristic
48C2×C4×Dic73C2311yescharacteristic
49C42×D73—42no—
50#14556498—21no—
51#14556498—21no—
52#14556498—21no—
53C2×C4⋊C4×C73—21no—
54C2×C4⋊C4×C73C2×C411yescharacteristic
55C2×C4⋊C4×C73C2×C411yescharacteristic
56C2×C42×C73C2×C411yescharacteristic
57#95×C73—21no—
58C2×#10596833—24no—
59C2×#10596833—42no—
60C2×#10596833—42no—
61C2×#10596833—42no—
62C2×#10596833—42no—
63C2×#10596833—42no—
64C23×D73C22⋊C411yescharacteristic
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73C22⋊C411yescharacteristic
68C22×Dic73C2×D411yescharacteristic
69C22×Dic73C2×D411yescharacteristic
70C2×C4×D73—22no—
71C2×C4×D73—22no—
72C2×C4×D73—24no—
73C2×C4×D73—22no—
74C2×C4×D73—22no—
75C2×C4×D73—41no—
76C2×C4×D73—41no—
77C2×C4×D73—41no—
78C2×C4×D73—42no—
79C2×C4×D73—42no—
80C2×C4×D73—42no—
81C2×C4×D73—42no—
82C2×C4×D73—42no—
83C2×C4×D73C2×C812yes—
84C2×C4×D73M1612yes—
85C2×C4×D73D812yes—
86C2×C4×D73SD1612yes—
87C4⋊Dic73—21no—
88C4⋊Dic73—41no—
89C4⋊Dic73—41no—
90C4⋊Dic73—41no—
91C4⋊Dic73C2×C812yes—
92#11924007—24no—
93#11924007—42no—
94#11924007—42no—
95#11924007—41no—
96#11924007—41no—
97C4×Dic73—22no—
98C4×Dic73—22no—
99C4×Dic73—41no—
100C22×C4×C73—21no—
101C22×C4×C73—21no—
102C22×C4×C73C22⋊C411yescharacteristic
103C22×C4×C73C22⋊C411yescharacteristic
104C22×C4×C73C22×C411yescharacteristic
105C4⋊C4×C73—21no—
106C4⋊C4×C73—41no—
107C4⋊C4×C73—42no—
108C4⋊C4×C73C2×C812yes—
109C42×C73—41no—
110C23×C73C2×C22⋊C411yescharacteristic
111C22×D73—21no—
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—21no—
115C22×D73C22⋊C812yes—
116C22×D73#10212yes—
117C22×D73#10412yes—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—22no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73#10212yes—
132C2×C4×C73C22×C811yescharacteristic
133C2×C4×C73C2×M1611yescharacteristic
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—22no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73C22⋊C812yes—
145C2×Dic73#9912yes—
146C2×Dic73#10112yes—
147C2×Dic73C2×D811yescharacteristic
148C2×Dic73C2×SD1611yescharacteristic
149C2×Dic73#13712yes—
150C4×D73—24no—
151C4×D73—24no—
152C4×D73—42no—
153C4×D73—42no—
154C4×D73—44no—
155C4×D73—48no—
156C4×D73—84no—
157#10596833—44no—
158#10596833—82no—
159C22×C73C2×C22⋊C811yescharacteristic
160C22×C73C2×#9911yescharacteristic
161C22×C73C2×#10111yescharacteristic
162C22×C73C2×#10211yescharacteristic
163C22×C73#41911yescharacteristic
164C22×C73C2×#10411yescharacteristic
165C22×C73#42111yescharacteristic
166C2×D73—22no—
167C2×D73—22no—
168C2×D73—22no—
169C2×D73—22no—
170C2×D73—22no—
171C2×D73—22no—
172C2×D73D4⋊C814yes—
173C4×C73—21no—
174C4×C73—21no—
175C4×C73—22no—
176C4×C73—42no—
177C4×C73—41no—
178C4×C73—81no—
179Dic73—22no—
180Dic73—21no—
181Dic73—21no—
182Dic73—42no—
183Dic73—81no—
184Dic73#32414yes—
185#7573—731nomaximal, Sylow
186C2×C73C2×#32411yescharacteristic
187C2×C73C2×D4⋊C811yescharacteristic
188C2×C73#147911yescharacteristic
189C2×C73#150811yescharacteristic
190C2×C73#151911yescharacteristic
191C2×C73#152811yescharacteristic
192C2×C73#154611yescharacteristic
193D73—24no—
194C2×#389—731no—
195#1797—731no—
196C4×C22⋊C8—731no—
197#1271—732no—
198#1271—732no—
199C73#757311yescharacteristic, complemented, Sylow
200C22×C4⋊C4—731no—
201C22×C4⋊C4—731no—
202C22×C4⋊C4—1461no—
203C22×C42—731no—
204C2×C4⋊C8—1461no—
205C2×C22⋊C8—1461no—
206C2×C22⋊C8—1461no—
207C2×C4×C8—1461no—
208#389—731no—
209#389—731no—
210#389—731no—
211#389—1461no—
212#389—1461no—
213#389#6440811yescharacteristic
214C2×#95—1461no—
215#336—732no—
216#336—732no—
217C23×C4—731no—
218C23×C4—731no—
219C23×C4—731no—
220C23×C4—1461no—
221C23×C4—1461no—
222C22×C8—1462no—
223C22×C8—1462no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—2922no—
226C2×C4⋊C4—2922no—
227C2×C4⋊C4—2922no—
228C2×C4⋊C4—731no—
229C2×C4⋊C4—731no—
230C2×C4⋊C4—734no—
231C2×C4⋊C4—1462no—
232C2×C4⋊C4—1461no—
233C2×C4⋊C4—1461no—
234C2×C4⋊C4—1461no—
235C2×C4⋊C4—1461no—
236C2×C4⋊C4—1461no—
237C2×C4⋊C4C2×#6440811yescharacteristic
238C2×C4⋊C4C2×#6440811yescharacteristic
239C2×C42—2922no—
240C2×C42—731no—
241C2×C42—731no—
242C2×C42—731no—
243C2×C42C2×#6440811yescharacteristic
244C4⋊C8—2922no—
245C22⋊C8—2922no—
246C22⋊C8—1464no—
247C4×C8—2922no—
248#95—21no—
249#95—1461no—
250#95—1461no—
251#95—1461no—
252C24—731no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2921no—
256C22×C4—2921no—
257C22×C4—2921no—
258C22×C4—2922no—
259C22×C4—2922no—
260C22×C4—2922no—
261C22×C4—2922no—
262C22×C4—2922no—
263C22×C4—732no—
264C22×C4—732no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4—732no—
269C22×C4—732no—
270C22×C4—1462no—
271C22×C4—1462no—
272C22×C4—1464no—
273C22×C4—1462no—
274C22×C4—1462no—
275C22×C4—1461no—
276C22×C4—1461no—
277C22×C4C22⋊#6440811yescharacteristic
278C22×C4C22⋊#6440811yescharacteristic
279C22×C4C22×#6440811yescharacteristic
280C2×C8—2922no—
281C2×C8—2922no—
282C2×C8—2922no—
283C2×C8—2922no—
284C2×C8—2922no—
285C2×C8—1464no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—2921no—
290C4⋊C4—2921no—
291C4⋊C4—2921no—
292C4⋊C4—2922no—
293C4⋊C4—2921no—
294C4⋊C4—2921no—
295C4⋊C4—2922no—
296C4⋊C4—732no—
297C4⋊C4—1464no—
298C4⋊C4—1461no—
299C4⋊C4#1192403612yes—
300C42—41no—
301C42—2921no—
302C42—1462no—
303C42—1462no—
304C23—732no—
305C23—732no—
306C23—732no—
307C23—1461no—
308C23—1461no—
309C23—1461no—
310C23—1461no—
311C23C2×C22⋊#6440811yescharacteristic
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—2922no—
326C2×C4—2922no—
327C2×C4—2928no—
328C2×C4—2924no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—2921no—
332C2×C4—2921no—
333C2×C4—2921no—
334C2×C4—5844no—
335C2×C4—732no—
336C2×C4—732no—
337C2×C4—732no—
338C2×C4—731no—
339C2×C4—731no—
340C2×C4—732no—
341C2×C4—1464no—
342C2×C4—1464no—
343C2×C4—1462no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4#1455665312yes—
349C2×C4C2×#1192403611yescharacteristic
350C2×C4D73⋊M1611yescharacteristic
351C8—2924no—
352C8—5842no—
353C22—734no—
354C22—1462no—
355C22—1462no—
356C22—1462no—
357C22—1462no—
358C22—1462no—
359C22—1462no—
360C22#1798955511yescharacteristic
361C22D73⋊#9911yescharacteristic
362C22D73⋊#10111yescharacteristic
363C22C2×#1455665311yescharacteristic
364C22#1798958011yescharacteristic
365C22D73⋊#10411yescharacteristic
366C22#1798958411yescharacteristic
367C4—22no—
368C4—21no—
369C4—21no—
370C4—41no—
371C4—42no—
372C4—81no—
373C4—2922no—
374C4—5841no—
375C4—734no—
376C4—1462no—
377C4—1461no—
378C4—1461no—
379C2—1464no—
380C2#2262516011yescharacteristic
381C2#2262521711yescharacteristic
382C2#2262523411yescharacteristic
383C2#2262532911yescharacteristic
384C2#2262536611yescharacteristic
385C2#2262539411yescharacteristic
386C2#2262544111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
Fitting#389×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#389#64408
hypocenterC73#7573
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #22624750C2semidirect
4. #22624749C2semidirect
45. C4⋊C4×D73C8semidirect
199. C73#7573semidirect

Maximal subgroups

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

subgroupindex
#226257882
C4×#145566482
#226247502
#226247492
#389×D732
#757373