Finite Group Databasebeta

← #34013937

Subgroups — #34013937

Order 18688.

466 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 112 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#22626265C211yesmaximal, characteristic, complemented
2C2×#17989484C212yesmaximal, complemented
3C2×#17989483C212yesmaximal, complemented
4#22626137C211yesmaximal, characteristic, complemented
5C2×#17988662C211yesmaximal, characteristic
6C2×#14556665C2212yes—
7C2×#14556665C2212yes—
8#17989508—21no—
9#17989508—21no—
10#17989484—24no—
11#17989483—24no—
12#17989476—21no—
13#17989473—21no—
14C22×#11924012C2211yescharacteristic
15C22×#11924011C2211yescharacteristic
16C2×C4×C22⋊D73C411yescharacteristic
17#17988662—21no—
18#17988662—21no—
19#17988662—21no—
20#17988662—21no—
21C2×#14556520C411yescharacteristic
22C2×#14556503C411yescharacteristic
23C2×C8×Dic73C2211yescharacteristic
24C2×C22⋊C8×C73C411yescharacteristic
25#14556665—22no—
26#14556665—22no—
27#14556665—22no—
28#14556665D414yescomplemented
29C2×#11924031—22no—
30C2×#11924031—22no—
31C22×C22⋊D73C811yescharacteristic
32C22×C4×D73C2×C411yescharacteristic
33C2×#11924012—21no—
34C2×#11924012—21no—
35C2×#11924012—22no—
36C2×#11924012—22no—
37C2×#11924011—21no—
38C2×#11924011—21no—
39C2×#11924011—22no—
40C2×#11924011—22no—
41C22×#10596831C2×C411yescharacteristic
42C22×#10596831C2311yescharacteristic
43C4×C22⋊D73—21no—
44C4×C22⋊D73—21no—
45C4×C22⋊D73—21no—
46C4×C22⋊D73—21no—
47C2×#11924007C811yescharacteristic
48C2×C22⋊Dic73C811yescharacteristic
49C2×#11924005C811yescharacteristic
50C2×C4×Dic73C2×C411yescharacteristic
51#14556520—21no—
52#14556520—21no—
53#14556503—21no—
54#14556503—21no—
55C8×Dic73D411yescharacteristic
56C8×Dic73D411yescharacteristic
57C8×Dic73D411yescharacteristic
58C8×Dic73D411yescharacteristic
59C23×C4×C73C2×C411yescharacteristic
60C22×C8×C73C2×C411yescharacteristic
61C22×C8×C73C2×C411yescharacteristic
62C22⋊C8×C73—21no—
63C22⋊C8×C73—21no—
64#11924031—24no—
65#11924031—42no—
66C23×D73C2×C811yescharacteristic
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—42no—
70C22×Dic73C2×C811yescharacteristic
71C22×Dic73C2×C811yescharacteristic
72C22×Dic73C2×C811yescharacteristic
73C2×C4×D73—21no—
74C2×C4×D73—22no—
75C2×C4×D73—21no—
76C2×C4×D73—22no—
77#11924012—42no—
78#11924012—41no—
79#11924012—41no—
80#11924011—42no—
81#11924011—41no—
82#11924011—41no—
83C2×#10596831—21no—
84C2×#10596831—22no—
85C2×#10596831C2×D411yescharacteristic
86C2×#10596831C2×D412yes—
87C2×#10596831C2×D411yescharacteristic
88C2×#10596831#4112yes—
89#11924007—21no—
90#11924007—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93#11924005—21no—
94#11924005—21no—
95C4×Dic73C22⋊C411yescharacteristic
96C4×Dic73C22⋊C411yescharacteristic
97C4×Dic73M1611yescharacteristic
98C4×Dic73M1611yescharacteristic
99C24×C73C2×C811yescharacteristic
100C22×C4×C73—21no—
101C22×C4×C73—22no—
102C22×C4×C73—21no—
103C22×C4×C73—22no—
104C22×C4×C73C2×C811yescharacteristic
105C22×C4×C73C22×C411yescharacteristic
106C2×C8×C73—22no—
107C2×C8×C73—21no—
108C2×C8×C73—22no—
109C2×C8×C73C22⋊C411yescharacteristic
110C2×C8×C73C22⋊C411yescharacteristic
111C23×C73—21no—
112C23×C73—22no—
113C23×C73—41no—
114C23×C73—41no—
115C23×C73C22×C811yescharacteristic
116C22×D73—21no—
117C22×D73—22no—
118C22×D73—41no—
119C22×D73—41no—
120C2×C4×C73—21no—
121C2×C4×C73—22no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73—42no—
125C2×C4×C73C2×C22⋊C411yescharacteristic
126C2×C4×C73C4×D412yes—
127C2×C4×C73C2×M1611yescharacteristic
128C2×C4×C73#13112yes—
129C22⋊D73—42no—
130C22⋊D73—42no—
131C2×Dic73—22no—
132C2×Dic73—21no—
133C2×Dic73—22no—
134C2×Dic73—41no—
135C2×Dic73C22⋊C811yescharacteristic
136C2×Dic73C22⋊C811yescharacteristic
137C2×Dic73C22⋊C811yescharacteristic
138C2×Dic73C22⋊C811yescharacteristic
139C4×D73—41no—
140C4×D73—41no—
141C4×D73—42no—
142C8×C73—21no—
143C8×C73—21no—
144C8×C73—41no—
145#10596831—41no—
146#10596831#12112yes—
147#10596831#12411yescharacteristic
148#10596831#12711yescharacteristic
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—82no—
155C22×C73C2×C22⋊C811yescharacteristic
156C22×C73C8×D412yes—
157C2×D73—41no—
158C2×D73—41no—
159C2×D73—41no—
160C2×D73—82no—
161C4×C73—41no—
162C4×C73#39011yescharacteristic
163C4×C73#40811yescharacteristic
164C4×C73#43612yes—
165Dic73—21no—
166Dic73—21no—
167Dic73—21no—
168Dic73—41no—
169Dic73#34912yescomplemented
170#13194—731nomaximal, Sylow
171C2×C73—22no—
172C2×C73—81no—
173C2×C73#195411yescharacteristic
174C2×C73C2×#34911yescharacteristic
175C2×C73#211511yescharacteristic
176D73—81no—
177C2×#436—731no—
178#2150—731no—
179C2×#349—732no—
180C2×#349—732no—
181C4×M32—731no—
182C73#1319411yescharacteristic, complemented, Sylow
183C22×M16—731no—
184C22×M16—731no—
185C2×C4×D4—731no—
186C2×M32—732no—
187C2×M32—732no—
188#436—1461no—
189#436—1461no—
190#436—1461no—
191#436—1461no—
192C2×C4⋊C8—731no—
193C2×C22⋊C8—731no—
194C2×C22⋊C8#6440811yescharacteristic
195C2×C4×C8—731no—
196C4⋊C16—1461no—
197C4⋊C16—1461no—
198#349—1464no—
199#349—1464no—
200#346—1461no—
201C4×C16—1461no—
202C22×D4—731no—
203C23×C4—731no—
204C23×C4C2×#6440811yescharacteristic
205C2×M16—1462no—
206C2×M16—1462no—
207C2×M16—1461no—
208C2×M16—1461no—
209C2×M16—1462no—
210C2×M16—1461no—
211C2×M16—1461no—
212C2×M16—1462no—
213C22×C8—731no—
214C22×C8—731no—
215C22×C8C2×#6440811yescharacteristic
216C22×C8C2×#6440811yescharacteristic
217C4×D4—1461no—
218C4×D4—1461no—
219C4×D4—1461no—
220C4×D4—1461no—
221C2×C4⋊C4—731no—
222C2×C22⋊C4—731no—
223C2×C22⋊C4—731no—
224C2×C42—731no—
225M32—734no—
226M32—1462no—
227M32—1462no—
228M32—1462no—
229C2×C16—1462no—
230C2×C16—1462no—
231C4⋊C8—1461no—
232C4⋊C8—1461no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235C22⋊C8—1461no—
236C22⋊C8—1461no—
237C4×C8—731no—
238C4×C8—731no—
239C4×C8—731no—
240C4×C8—731no—
241C24—731no—
242C24#1192403611yescharacteristic
243C2×D4—2922no—
244C2×D4—1461no—
245C2×D4—1461no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—731no—
251C22×C4—731no—
252C22×C4—731no—
253C22×C4—1461no—
254C22×C4—1462no—
255C22×C4—1461no—
256C22×C4—1462no—
257C22×C4#1192403611yescharacteristic
258C22×C4C22×#6440811yescharacteristic
259M16—2921no—
260M16—2922no—
261M16—2921no—
262M16—2921no—
263M16—2922no—
264M16—2921no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—22no—
268C2×C8—731no—
269C2×C8—731no—
270C2×C8—732no—
271C2×C8—732no—
272C2×C8—1461no—
273C2×C8—1462no—
274C2×C8C22⋊#6440811yescharacteristic
275C2×C8C22⋊#6440811yescharacteristic
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C42—731no—
283C42—731no—
284C42—731no—
285C42—731no—
286C16—2922no—
287C16—1464no—
288C23—21no—
289C23—22no—
290C23—41no—
291C23—41no—
292C23—2921no—
293C23—2921no—
294C23—1461no—
295C23—1462no—
296C23C2×#1192403611yescharacteristic
297D4—2922no—
298D4—2922no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—2921no—
305C2×C4—2921no—
306C2×C4—2922no—
307C2×C4—2921no—
308C2×C4—731no—
309C2×C4—731no—
310C2×C4—731no—
311C2×C4—731no—
312C2×C4—1461no—
313C2×C4—1462no—
314C2×C4—1462no—
315C2×C4C2×C22⋊#6440811yescharacteristic
316C2×C4D4×#6440812yes—
317C2×C4D73⋊M1611yescharacteristic
318C2×C4#1455667812yes—
319C8—21no—
320C8—21no—
321C8—41no—
322C8—2921no—
323C8—731no—
324C8—732no—
325C8—731no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—82no—
332C22—2921no—
333C22—2921no—
334C22—2921no—
335C22—5842no—
336C22#1798955511yescharacteristic
337C22#1798961412yes—
338C4—41no—
339C4—2921no—
340C4—732no—
341C4—1461no—
342C4—1461no—
343C4—1461no—
344C4#1798953911yescharacteristic
345C4#1798956011yescharacteristic
346C4#1798962012yes—
347C2—22no—
348C2—81no—
349C2—5841no—
350C2#2262605411yescharacteristic
351C2#2262616511yescharacteristic
352C2#2262616811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#64408
commutatorC23×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC2×C22⋊C8×C73C4
socleC22×C73C2×C22⋊C8
prime radicalC22×C22⋊D73C8
cosocleC22×#10596831C23
hypercenterC2×C22⋊C8#64408
hypocenterC73#13194
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #22626265C2semidirect
2. C2×#17989484C2semidirect
3. C2×#17989483C2semidirect
4. #22626137C2semidirect
28. #14556665D4semidirect
169. Dic73#349semidirect
182. C73#13194semidirect

Maximal subgroups

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

subgroupindex
#226262652
C2×#179894842
C2×#179894832
#226261372
C2×#179886622
#1319473