Finite Group Databasebeta

← #32980684

Subgroups — #32980684

Order 18688.

600 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C4×#14556572C211yesmaximal, characteristic
2#22609997C212yesmaximal, complemented
3#22608249C211yesmaximal, characteristic
4#22607778C212yesmaximal, complemented
5C73×#2973C211yesmaximal, characteristic
6C2×#14556572C411yescharacteristic
7C22×C4×Dic73C2211yescharacteristic
8C2×C22⋊#10596831C2212yes—
9#17988475—21no—
10#17988468—21no—
11#17988467C411yescharacteristic
12#17988459C411yescharacteristic
13#17988448C411yescharacteristic
14C4×#11924007—21no—
15C4×C22⋊Dic73—21no—
16C4×C22⋊Dic73C2211yescharacteristic
17#17988341—24no—
18#17988313—21no—
19#17988311—21no—
20C2×C4×D4×C73C2211yescharacteristic
21#435×C73—24no—
22#432×C73—21no—
23#407×C73—21no—
24C2×C22⋊C8×C73C2212yes—
25C23×Dic73C2×C411yescharacteristic
26C23×Dic73C2×C411yescharacteristic
27C22×#10596831—22no—
28#14556572—22no—
29#14556572—22no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×C22⋊Dic73—21no—
33C2×C22⋊Dic73—21no—
34C2×C22⋊Dic73C2×C411yescharacteristic
35C2×C22⋊Dic73C2×C411yescharacteristic
36C2×C4×Dic73—21no—
37C2×C4×Dic73—21no—
38C2×C4×Dic73—21no—
39C2×C4×Dic73—22no—
40C2×C4×Dic73—22no—
41C22⋊#10596831—22no—
42C22⋊#10596831—22no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48C22×D4×C73C2×C411yescharacteristic
49C23×C4×C73D411yescharacteristic
50C23×C4×C73C2311yescharacteristic
51C2×M16×C73—22no—
52C22×C8×C73D414yes—
53C4×D4×C73—22no—
54C4×D4×C73—22no—
55C2×C4⋊C4×C73D411yescharacteristic
56C2×C22⋊C4×C73C2×C411yescharacteristic
57C2×C22⋊C4×C73D411yescharacteristic
58C2×C42×C73D411yescharacteristic
59C4⋊C8×C73—22no—
60C22⋊C8×C73—22no—
61C22⋊C8×C73—22no—
62C22⋊C8×C73—22no—
63#97×C73—22no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—22no—
68C22×Dic73—22no—
69C22×Dic73—21no—
70C22×Dic73—22no—
71C22×Dic73—21no—
72C22×Dic73—42no—
73C22×Dic73M1612yescomplemented
74C2×#10596831—44no—
75C2×#10596831—42no—
76#11924007—24no—
77#11924007—42no—
78C22⋊Dic73—24no—
79C22⋊Dic73—21no—
80C22⋊Dic73—22no—
81C22⋊Dic73—42no—
82C22⋊Dic73M1612yescomplemented
83C4×Dic73—42no—
84C4×Dic73—41no—
85C4×Dic73—42no—
86C4×Dic73—41no—
87C24×C73C22⋊C411yescharacteristic
88C24×C73C22×C411yescharacteristic
89C2×D4×C73—22no—
90C2×D4×C73—21no—
91C2×D4×C73—21no—
92C2×D4×C73—22no—
93C22×C4×C73—21no—
94C22×C4×C73—21no—
95C22×C4×C73—42no—
96C22×C4×C73—42no—
97C22×C4×C73C22⋊C411yescharacteristic
98C22×C4×C73C22⋊C411yescharacteristic
99C22×C4×C73C22⋊C411yescharacteristic
100C22×C4×C73C2×D412yes—
101C22×C4×C73C2×D411yescharacteristic
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73#4112yes—
104M16×C73—82no—
105C2×C8×C73—24no—
106C2×C8×C73—44no—
107C4⋊C4×C73—22no—
108C22⋊C4×C73—22no—
109C22⋊C4×C73—22no—
110C42×C73—21no—
111C42×C73—21no—
112C23×C73—21no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—41no—
116C23×C73—41no—
117C23×C73—41no—
118C23×C73—41no—
119C23×C73C2×C22⋊C411yescharacteristic
120C23×C73C4×D412yes—
121C23×C73C2×M1611yescharacteristic
122C23×C73C2×M1611yescharacteristic
123C23×C73#13112yes—
124D4×C73—42no—
125D4×C73—42no—
126C2×C4×C73—24no—
127C2×C4×C73—22no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—41no—
134C2×C4×C73—42no—
135C2×C4×C73—42no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—81no—
139C2×C4×C73#12011yescharacteristic
140C2×C4×C73#12112yes—
141C2×C4×C73#12311yescharacteristic
142C2×Dic73—22no—
143C2×Dic73—24no—
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—24no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—42no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—42no—
155C2×Dic73—41no—
156C2×Dic73—41no—
157C2×Dic73—41no—
158C8×C73—44no—
159#10596831—82no—
160C22×C73—21no—
161C22×C73—22no—
162C22×C73—21no—
163C22×C73—22no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—42no—
167C22×C73—42no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73—41no—
171C22×C73—81no—
172C22×C73#38611yescharacteristic
173C22×C73#40711yescharacteristic
174C22×C73#40811yescharacteristic
175C22×C73#43512yes—
176C22×C73#43612yes—
177C4×C73—22no—
178C4×C73—21no—
179C4×C73—41no—
180C4×C73—41no—
181C4×C73—41no—
182C4×C73#45812yes—
183Dic73—42no—
184Dic73—42no—
185Dic73—42no—
186Dic73—81no—
187#8968—731nomaximal, Sylow
188C2×C73—21no—
189C2×C73—21no—
190C2×C73—22no—
191C2×C73—22no—
192C2×C73—81no—
193C2×C73#187011yescharacteristic
194C2×C73#189011yescharacteristic
195C2×C73#189111yescharacteristic
196#2973D7311yescharacteristic
197C4×#123—731no—
198#1817—732no—
199#1459—731no—
200#1282—732no—
201C73#896811yescharacteristic, complemented, Sylow
202C2×#123—731no—
203C2×C4×D4C2×D7311yescharacteristic
204C22×C42—731no—
205#435—24no—
206#432—21no—
207#407—21no—
208C2×C22⋊C8—732no—
209C2×C22⋊C8C2×D7312yes—
210#388—1461no—
211#387—1461no—
212#386—731no—
213#385—731no—
214#381—731no—
215C4×C4⋊C4—1461no—
216C4×C22⋊C4—731no—
217C4×C22⋊C4—1461no—
218#336—1464no—
219#324—1461no—
220#323—1461no—
221C22×D4C4×D7311yescharacteristic
222C23×C4—731no—
223C23×C4—731no—
224C23×C4C22⋊D7311yescharacteristic
225C23×C4C22×D7311yescharacteristic
226C2×M16—22no—
227C22×C8—1462no—
228C22×C8C22⋊D7314yes—
229#123—1462no—
230#123—1462no—
231C4×D4—22no—
232C4×D4—22no—
233C2×C4⋊C4—1461no—
234C2×C4⋊C4—1461no—
235C2×C4⋊C4D29211yescharacteristic
236C2×C22⋊C4—731no—
237C2×C22⋊C4—731no—
238C2×C22⋊C4—1461no—
239C2×C22⋊C4—1461no—
240C2×C22⋊C4C4×D7311yescharacteristic
241C2×C22⋊C4D29211yescharacteristic
242C2×C42—1462no—
243C2×C42—1461no—
244C2×C42—1461no—
245C2×C42—1461no—
246C2×C42—1462no—
247C2×C42C22⋊D7311yescharacteristic
248C4⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—22no—
252C22⋊C8—1462no—
253C22⋊C8—1462no—
254#97—22no—
255#95—1461no—
256#95—1461no—
257#95—1461no—
258#95—1461no—
259#95—1461no—
260C24#1192400511yescharacteristic
261C24C2×C4×D7311yescharacteristic
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—2922no—
271C22×C4—732no—
272C22×C4—1461no—
273C22×C4—1461no—
274C22×C4—1461no—
275C22×C4—1461no—
276C22×C4—1462no—
277C22×C4—1462no—
278C22×C4—1461no—
279C22×C4—1462no—
280C22×C4#1192400511yescharacteristic
281C22×C4#1192400511yescharacteristic
282C22×C4#1192400511yescharacteristic
283C22×C4C2×C22⋊D7312yes—
284C22×C4C2×C22⋊D7311yescharacteristic
285C22×C4C2×D29211yescharacteristic
286C22×C4#1192402812yes—
287M16—82no—
288C2×C8—24no—
289C2×C8—44no—
290C2×C8—2924no—
291C2×C8—2922no—
292C4⋊C4—22no—
293C4⋊C4—2922no—
294C4⋊C4—1464no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—2922no—
298C22⋊C4—732no—
299C22⋊C4—1462no—
300C22⋊C4—1464no—
301C22⋊C4—1461no—
302C42—21no—
303C42—21no—
304C42—2922no—
305C42—2921no—
306C42—2922no—
307C42—2921no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23C2×#1192400511yescharacteristic
316C23C4×C22⋊D7312yes—
317C23M16×D7311yescharacteristic
318C23M16×D7311yescharacteristic
319C23#1455659912yes—
320D4—42no—
321D4—42no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—2921no—
336C2×C4—2921no—
337C2×C4—2921no—
338C2×C4—2922no—
339C2×C4—2922no—
340C2×C4—2921no—
341C2×C4—2921no—
342C2×C4—2921no—
343C2×C4—2921no—
344C2×C4—2921no—
345C2×C4—2921no—
346C2×C4—1462no—
347C2×C4—1464no—
348C2×C4—1464no—
349C2×C4—1462no—
350C2×C4—1462no—
351C2×C4#1455656011yescharacteristic
352C2×C4#1455656512yes—
353C2×C4#1455657411yescharacteristic
354C8—44no—
355C8—5842no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—42no—
363C22—42no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—81no—
368C22#1798846611yescharacteristic
369C22#1798855011yescharacteristic
370C22#1798855511yescharacteristic
371C22#1798865612yes—
372C22#1798866312yes—
373C4—22no—
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—2922no—
379C4—2922no—
380C4—2922no—
381C4—5841no—
382C4#1798877712yes—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—22no—
387C2—81no—
388C2#2261022811yescharacteristic
389C2#2261034411yescharacteristic
390C2#2261034911yescharacteristic
subgroupG/H
centerC2×C4#14556560
commutatorC24×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#2973C2
socleC22×C73#386
prime radicalC22×D4×C73C2×C4
cosocleC23×C4×C73C23
hypercenter#2973D73
hypocenterC73#8968
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #22609997C2semidirect
4. #22607778C2semidirect
73. C22×Dic73M16semidirect
82. C22⋊Dic73M16semidirect
201. C73#8968semidirect

Maximal subgroups

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

subgroupindex
C4×#145565722
#226099972
#226082492
#226077782
C73×#29732
#896873