Finite Group Databasebeta

← #33004648

Subgroups — #33004648

Order 18688.

488 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 99 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#22615274C211yesmaximal, characteristic
2C4×#14556506C211yesmaximal, characteristic
3#22608050C212yesmaximal
4#22608050C212yesmaximal
5C73×#1800C211yesmaximal, characteristic
6C22×#11924007C411yescharacteristic, complemented
7C2×#14556506C2212yes—
8#17988520—21no—
9#17988510—21no—
10#17988471—21no—
11#17988467C2211yescharacteristic
12#17988467C2211yescharacteristic
13#17988460—21no—
14#17988459C411yescharacteristic, complemented
15#17988459C411yescharacteristic, complemented
16#17988447C411yescharacteristic, complemented
17C4×C22⋊Dic73—21no—
18#17988354—21no—
19C2×C4×D4×C73C2211yescharacteristic
20#423×C73—21no—
21C2×#100×C73C2212yes—
22#343×C73—21no—
23C23×Dic73C2×C411yescharacteristic
24C23×Dic73C2×C411yescharacteristic
25C2×C4⋊Dic73—21no—
26C2×#11924007—21no—
27C2×#11924007—21no—
28C2×#11924007—21no—
29C2×#11924007—21no—
30C2×#11924007—41no—
31C2×#11924007—41no—
32C2×C22⋊Dic73—22no—
33C2×C22⋊Dic73—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73C2×C411yescharacteristic
36C2×C22⋊Dic73C2×C411yescharacteristic
37C2×C4×Dic73—41no—
38#14556506—22no—
39#14556506Q814yes—
40#14556498—21no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—41no—
46C22×D4×C73C2311yescharacteristic
47C23×C4×C73C2×C411yescharacteristic
48C23×C4×C73D411yescharacteristic
49C2×M16×C73—22no—
50C4×D4×C73—41no—
51C4×D4×C73—41no—
52C2×C4⋊C4×C73D411yescharacteristic
53C2×C22⋊C4×C73C2×C411yescharacteristic
54C2×C22⋊C4×C73D411yescharacteristic
55C2×C42×C73D411yescharacteristic
56C4⋊C8×C73—41no—
57C4⋊C8×C73—41no—
58#100×C73—24no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73—42no—
64C22×Dic73—41no—
65C22×Dic73—42no—
66C22×Dic73—41no—
67C22×Dic73—81no—
68C4⋊Dic73—81no—
69#11924007—42no—
70#11924007—42no—
71#11924007—41no—
72#11924007—41no—
73#11924007—81no—
74C22⋊Dic73—24no—
75C22⋊Dic73—42no—
76C22⋊Dic73—42no—
77C22⋊Dic73—41no—
78C22⋊Dic73—41no—
79C22⋊Dic73—81no—
80C4×Dic73—82no—
81C24×C73C22×C411yescharacteristic
82C24×C73C2×D411yescharacteristic
83C2×D4×C73—41no—
84C2×D4×C73—41no—
85C2×D4×C73C2×Q812yes—
86C2×D4×C73#4112yes—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73—81no—
92C22×C4×C73—81no—
93C22×C4×C73C22⋊C411yescharacteristic
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C22⋊C411yescharacteristic
96C22×C4×C73C22⋊C411yescharacteristic
97C22×C4×C73C2×D411yescharacteristic
98M16×C73—42no—
99M16×C73—42no—
100C2×C8×C73—42no—
101C4⋊C4×C73—41no—
102C22⋊C4×C73—41no—
103C22⋊C4×C73—41no—
104C42×C73—21no—
105C42×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—41no—
111C23×C73—41no—
112C23×C73—41no—
113C23×C73—41no—
114C23×C73C2×C22⋊C411yescharacteristic
115C23×C73C4×Q812yes—
116C23×C73C22⋊Q812yes—
117D4×C73—42no—
118D4×C73—42no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—41no—
125C2×C4×C73—42no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—81no—
130C2×C4×C73—81no—
131C2×C4×C73—81no—
132C2×C4×C73#9911yescharacteristic
133C2×C4×C73#9911yescharacteristic
134C2×C4×C73#12411yescharacteristic
135C2×C4×C73C4⋊Q811yescharacteristic
136C2×Dic73—22no—
137C2×Dic73—41no—
138C2×Dic73—42no—
139C2×Dic73—41no—
140C2×Dic73—42no—
141C2×Dic73—44no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145C2×Dic73—41no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151C2×Dic73—82no—
152C2×Dic73—82no—
153C2×Dic73—82no—
154C8×C73—82no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—22no—
158C22×C73—22no—
159C22×C73—42no—
160C22×C73—42no—
161C22×C73—42no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—81no—
167C22×C73#39111yescharacteristic
168C22×C73C2×#9911yescharacteristic
169C22×C73#41011yescharacteristic
170C4×C73—21no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—21no—
174C4×C73—41no—
175C4×C73—41no—
176C4×C73—41no—
177Dic73—42no—
178Dic73—81no—
179Dic73—81no—
180Dic73—84no—
181Dic73—81no—
182#13297—731nomaximal, Sylow
183C2×C73—21no—
184C2×C73—21no—
185C2×C73—42no—
186C2×C73—42no—
187C2×C73#199611yescharacteristic
188C2×C73#212011yescharacteristic
189C2×C73#212111yescharacteristic
190#2579—731no—
191#1800D7311yescharacteristic
192C4×#99—731no—
193#1390—732no—
194#1390—732no—
195C73#1329711yescharacteristic, complemented, Sylow
196C2×C4×D4C2×D7311yescharacteristic
197C22×C4⋊C4—731no—
198#423—21no—
199C2×#100C2×D7312yes—
200C2×#99—732no—
201#398—1461no—
202#396—1461no—
203#387—1461no—
204#386—731no—
205#386—731no—
206#385—731no—
207#385—731no—
208#385—1461no—
209#380—731no—
210C4×C22⋊C4—1461no—
211#343—21no—
212#342—1461no—
213C22×D4C22×D7311yescharacteristic
214C23×C4—731no—
215C23×C4—731no—
216C23×C4C4×D7311yescharacteristic
217C23×C4D29211yescharacteristic
218C2×M16—22no—
219C4×D4—41no—
220C4×D4—41no—
221C2×C4⋊C4—2921no—
222C2×C4⋊C4—2921no—
223C2×C4⋊C4—1461no—
224C2×C4⋊C4—1461no—
225C2×C4⋊C4—1461no—
226C2×C4⋊C4—1461no—
227C2×C4⋊C4—1461no—
228C2×C4⋊C4C22⋊D7311yescharacteristic
229C2×C22⋊C4—731no—
230C2×C22⋊C4—731no—
231C2×C22⋊C4—1461no—
232C2×C22⋊C4—1462no—
233C2×C22⋊C4—1461no—
234C2×C22⋊C4C4×D7311yescharacteristic
235C2×C22⋊C4D29211yescharacteristic
236C2×C42—2921no—
237C2×C42C22⋊D7311yescharacteristic
238C4⋊C8—41no—
239C4⋊C8—41no—
240#100—24no—
241#99—734no—
242#99—1462no—
243#95—2921no—
244#95—1461no—
245#95—1461no—
246#95—1461no—
247#95—1461no—
248#95—1461no—
249C24C2×C4×D7311yescharacteristic
250C24C2×D29211yescharacteristic
251C2×D4—41no—
252C2×D4—41no—
253C2×D4Q8×D7312yes—
254C2×D4#1192402712yes—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—81no—
260C22×C4—81no—
261C22×C4—2921no—
262C22×C4—2922no—
263C22×C4—2922no—
264C22×C4—2921no—
265C22×C4—5841no—
266C22×C4—1461no—
267C22×C4—1461no—
268C22×C4—1461no—
269C22×C4—1461no—
270C22×C4#1192400511yescharacteristic
271C22×C4#1192400511yescharacteristic
272C22×C4#1192400511yescharacteristic
273C22×C4#1192400511yescharacteristic
274C22×C4C2×C22⋊D7311yescharacteristic
275M16—42no—
276M16—42no—
277C2×C8—42no—
278C4⋊C4—41no—
279C4⋊C4—2922no—
280C4⋊C4—2922no—
281C4⋊C4—2921no—
282C4⋊C4—2921no—
283C4⋊C4—5841no—
284C4⋊C4—5841no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—2922no—
288C22⋊C4—2922no—
289C22⋊C4—2921no—
290C22⋊C4—2921no—
291C22⋊C4—5841no—
292C22⋊C4—1464no—
293C42—21no—
294C42—21no—
295C42—5842no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23C2×#1192400511yescharacteristic
305C23#1455655612yes—
306C23#1455657112yes—
307D4—42no—
308D4—42no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—2921no—
323C2×C4—2922no—
324C2×C4—2921no—
325C2×C4—2922no—
326C2×C4—2921no—
327C2×C4—2924no—
328C2×C4—2921no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—2921no—
332C2×C4—2921no—
333C2×C4—2921no—
334C2×C4—2921no—
335C2×C4—2921no—
336C2×C4—5842no—
337C2×C4—5842no—
338C2×C4—5842no—
339C2×C4—1462no—
340C2×C4#1455650511yescharacteristic
341C2×C4#1455650511yescharacteristic
342C2×C4#1455657811yescharacteristic
343C2×C4#1455658911yescharacteristic
344C8—82no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—81no—
357C22#1798849211yescharacteristic
358C22C2×#1455650511yescharacteristic
359C22#1798856011yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—2922no—
368C4—5841no—
369C4—5841no—
370C4—5844no—
371C4—5841no—
372C2—21no—
373C2—21no—
374C2—42no—
375C2—42no—
376C2#2261091511yescharacteristic
377C2#2261157311yescharacteristic
378C2#2261157811yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC24×C73C22×C4
FrattiniC22×D4C22×D73
FittingC73×#1800C2
socleC22×C73C2×#99
prime radical, cosocleC22×D4×C73C23
hypercenter#1800D73
hypocenterC73#13297
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
6. C22×#11924007C4semidirect
14. #17988459C4semidirect
15. #17988459C4semidirect
16. #17988447C4semidirect
195. C73#13297semidirect

Maximal subgroups

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

subgroupindex
#226152742
C4×#145565062
#226080502
C73×#18002
#1329773