Finite Group Databasebeta

← #33002292

Subgroups — #33002292

Order 18688.

442 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D73C211yesmaximal, characteristic
2#22611541C211yesmaximal, characteristic
3#22609966C211yesmaximal, characteristic
4#22608041C211yesmaximal, characteristic, complemented
5#22608040C211yesmaximal, characteristic, complemented
6#22608039C211yesmaximal, characteristic, complemented
7C73×#1387C211yesmaximal, characteristic, complemented
8C22×C8×D73C2211yescharacteristic
9C2×C4⋊C4×D73—21no—
10C2×#14556531C2211yescharacteristic
11C2×#14556527C2211yescharacteristic
12C2×#14556525C2211yescharacteristic
13C2×#14556524—21no—
14#107×D73—21no—
15#107×D73—21no—
16#107×D73C412yes—
17#107×D73C412yes—
18#17988550—21no—
19#17988366—21no—
20#17988366—21no—
21#17988351—21no—
22C2×M32×C73C2211yescharacteristic
23C2×#108×C73C2211yescharacteristic
24C2×#107×C73C2211yescharacteristic
25C22×C4×D73—41no—
26C22×C4×D73D411yescharacteristic
27C2×#11924012—21no—
28C22×#10596831D411yescharacteristic
29C2×C8×D73—21no—
30C2×C8×D73—21no—
31C2×C8×D73—21no—
32C2×C8×D73—21no—
33C2×C8×D73C2×C411yescharacteristic
34C2×C8×D73C2×C411yescharacteristic
35C2×C8×D73D411yescharacteristic
36C2×C8×D73D411yescharacteristic
37C2×C4⋊Dic73—21no—
38C2×#11924007—41no—
39C4⋊C4×D73—22no—
40C4⋊C4×D73—22no—
41C4⋊C4×D73—41no—
42C4⋊C4×D73—41no—
43#14556531—21no—
44#14556531—21no—
45C2×#11924003—21no—
46#14556527—21no—
47#14556527—21no—
48#14556525—21no—
49#14556525C2×C412yes—
50#14556524—22no—
51#14556524—22no—
52#14556503—41no—
53#14556503—41no—
54C2×M16×C73—21no—
55C22×C8×C73C2311yescharacteristic
56C2×C4⋊C4×C73—21no—
57M32×C73—21no—
58M32×C73—21no—
59C2×C16×C73—21no—
60#108×C73—21no—
61#108×C73—21no—
62#107×C73—21no—
63#107×C73C2×C412yes—
64C23×D73SD1611yescharacteristic
65C22×Dic73—41no—
66C22×Dic73SD1611yescharacteristic
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—42no—
72C2×C4×D73—42no—
73C2×C4×D73—84no—
74C2×C4×D73C22⋊C411yescharacteristic
75C2×C4×D73C22⋊C411yescharacteristic
76C2×C4×D73D811yescharacteristic
77C2×C4×D73D811yescharacteristic
78#11924012—41no—
79#11924012—41no—
80C2×#10596831—21no—
81C2×#10596831—21no—
82C2×#10596831—41no—
83C2×#10596831C22⋊C411yescharacteristic
84C2×#10596831C22⋊C411yescharacteristic
85C8×D73—21no—
86C8×D73—21no—
87C8×D73—21no—
88C8×D73—21no—
89C8×D73—21no—
90C8×D73—21no—
91C8×D73—21no—
92C8×D73—21no—
93C4⋊Dic73—22no—
94C4⋊Dic73—41no—
95#11924007—42no—
96#11924007—42no—
97#11924003—41no—
98C22×C4×C73—41no—
99C22×C4×C73C2×D411yescharacteristic
100M16×C73—41no—
101M16×C73—41no—
102C2×C8×C73—41no—
103C2×C8×C73C22×C411yescharacteristic
104C2×C8×C73C2×D411yescharacteristic
105C2×C8×C73#4111yescharacteristic
106C2×C8×C73#4111yescharacteristic
107C2×C8×C73#4111yescharacteristic
108C2×C8×C73#4111yescharacteristic
109C4⋊C4×C73—22no—
110C4⋊C4×C73—41no—
111C16×C73—41no—
112C23×C73C2×SD1611yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—22no—
116C22×D73—22no—
117C22×D73#10211yescharacteristic
118C22×D73#10211yescharacteristic
119C2×C4×C73—42no—
120C2×C4×C73—82no—
121C2×C4×C73C2×C22⋊C411yescharacteristic
122C2×C4×C73#12311yescharacteristic
123C2×C4×C73#12311yescharacteristic
124C2×C4×C73C2×D811yescharacteristic
125C2×C4×C73#13711yescharacteristic
126C2×C4×C73#13711yescharacteristic
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—42no—
130C2×Dic73—82no—
131C2×Dic73#10211yescharacteristic
132C2×Dic73#10211yescharacteristic
133C4×D73—21no—
134C4×D73—21no—
135C4×D73—21no—
136C4×D73—21no—
137C4×D73—21no—
138C4×D73—21no—
139C4×D73—21no—
140C4×D73—21no—
141C4×D73—84no—
142C4×D73—84no—
143C8×C73—81no—
144C8×C73#11711yescharacteristic
145C8×C73#11711yescharacteristic
146C8×C73#12311yescharacteristic
147C8×C73#12311yescharacteristic
148#10596831—21no—
149#10596831—21no—
150#10596831—81no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73C2×#10211yescharacteristic
154C22×C73#48311yescharacteristic
155C22×C73#48311yescharacteristic
156C2×D73—24no—
157C2×D73—24no—
158C2×D73—21no—
159C2×D73—21no—
160C2×D73—21no—
161C2×D73—21no—
162C2×D73#36112yes—
163C2×D73#36212yes—
164C4×C73—82no—
165C4×C73#38111yescharacteristic
166C4×C73#41911yescharacteristic
167C4×C73#48011yescharacteristic
168C4×C73#48011yescharacteristic
169Dic73—21no—
170Dic73—21no—
171Dic73—82no—
172#12871—731nomaximal, Sylow
173C2×C73—21no—
174C2×C73—21no—
175C2×C73#182311yescharacteristic
176C2×C73C2×#36111yescharacteristic
177C2×C73C2×#36211yescharacteristic
178D73—22no—
179D73—22no—
180C22×#107—731no—
181#2112—731no—
182#1810—731no—
183#1387—731no—
184#1387—731no—
185#1387—731no—
186#1387D7311yescharacteristic, complemented
187C73#1287111yescharacteristic, complemented, Sylow
188C23×C8—731no—
189C22×C4⋊C4—1461no—
190C2×M32—731no—
191C2×M32C2×D7311yescharacteristic
192C2×#108—731no—
193C2×#108C2×D7311yescharacteristic
194C2×#107—731no—
195C2×#107—732no—
196C2×#107—732no—
197C2×#107—1461no—
198C2×#107—1461no—
199C2×#107—1461no—
200C2×#107C2×D7311yescharacteristic
201#407—1461no—
202C22⋊C16—1461no—
203C22⋊C16—1461no—
204#341—1461no—
205C23×C4—2921no—
206C23×C4—731no—
207C2×M16—21no—
208C2×M16—1461no—
209C22×C8—731no—
210C22×C8—731no—
211C22×C8—731no—
212C22×C8—731no—
213C22×C8—731no—
214C22×C8—1461no—
215C22×C8—1461no—
216C22×C8—1461no—
217C22×C8—1461no—
218C22×C8C22×D7311yescharacteristic
219C2×C4⋊C4—21no—
220C2×C4⋊C4—2921no—
221C2×C4⋊C4—2921no—
222C2×C4⋊C4—2921no—
223C2×C4⋊C4—1462no—
224C2×C4⋊C4—1462no—
225C2×C4⋊C4—1461no—
226M32—21no—
227M32—21no—
228M32—1461no—
229M32—1461no—
230C2×C16—21no—
231C2×C16—1461no—
232#108—21no—
233#108—21no—
234#108—1461no—
235#108—1461no—
236#107—21no—
237#107—732no—
238#107—1462no—
239#107—1462no—
240#107—1461no—
241#107C4×D7312yes—
242C22⋊C8—2921no—
243C22⋊C8—2921no—
244C24—731no—
245C22×C4—41no—
246C22×C4—2922no—
247C22×C4—2922no—
248C22×C4—2921no—
249C22×C4—5844no—
250C22×C4—731no—
251C22×C4—731no—
252C22×C4—731no—
253C22×C4—731no—
254C22×C4—731no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4—1461no—
259C22×C4D4×D7311yescharacteristic
260M16—41no—
261M16—41no—
262M16—2921no—
263M16—2921no—
264C2×C8—41no—
265C2×C8—2921no—
266C2×C8—731no—
267C2×C8—731no—
268C2×C8—1461no—
269C2×C8—1461no—
270C2×C8—1461no—
271C2×C8—1461no—
272C2×C8—1461no—
273C2×C8—1461no—
274C2×C8—1461no—
275C2×C8—1461no—
276C2×C8—1461no—
277C2×C8—1461no—
278C2×C8C2×C4×D7311yescharacteristic
279C2×C8D4×D7311yescharacteristic
280C2×C8#1192402711yescharacteristic
281C2×C8#1192402811yescharacteristic
282C2×C8#1192402811yescharacteristic
283C2×C8#1192402911yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—2922no—
287C4⋊C4—2922no—
288C4⋊C4—2921no—
289C4⋊C4—1462no—
290C16—41no—
291C16—2921no—
292C23—731no—
293C23—731no—
294C23—1462no—
295C23—1462no—
296C23—1461no—
297C23—1461no—
298C23SD16×D7311yescharacteristic
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—2922no—
302C2×C4—5844no—
303C2×C4—5844no—
304C2×C4—5842no—
305C2×C4—731no—
306C2×C4—731no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4C22⋊C4×D7311yescharacteristic
318C2×C4#1455657311yescharacteristic
319C2×C4#1455657611yescharacteristic
320C2×C4D8×D7311yescharacteristic
321C2×C4#1455662011yescharacteristic
322C2×C4#1455662311yescharacteristic
323C8—81no—
324C8—5841no—
325C8—1461no—
326C8—1461no—
327C8#1455654811yescharacteristic
328C8#1455654911yescharacteristic
329C8#1455657311yescharacteristic
330C8#1455657611yescharacteristic
331C22—21no—
332C22—21no—
333C22—732no—
334C22—732no—
335C22—1464no—
336C22—1464no—
337C22—1461no—
338C22—1461no—
339C22—1461no—
340C22—1461no—
341C22#102×D7311yescharacteristic
342C22#1798891611yescharacteristic
343C22#1798891911yescharacteristic
344C4—82no—
345C4—5842no—
346C4—1461no—
347C4—1461no—
348C4#1798844911yescharacteristic
349C4#1798859411yescharacteristic
350C4#1798889911yescharacteristic
351C4#1798890211yescharacteristic
352C2—21no—
353C2—21no—
354C2—1462no—
355C2—1462no—
356C2#2261001611yescharacteristic
357C2#361×D7311yescharacteristic
358C2#362×D7311yescharacteristic
subgroupG/H
centerC22#102×D73
commutatorC2×C8×C73C22×C4
FrattiniC22×C8C22×D73
FittingC73×#1387C2
socleC22×C73C2×#102
prime radicalC23×D73SD16
cosocleC22×C8×C73C23
hypercenter#1387D73
hypocenterC73#12871
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
4. #22608041C2semidirect
5. #22608040C2semidirect
6. #22608039C2semidirect
7. C73×#1387C2semidirect
186. #1387D73semidirect
187. C73#12871semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D732
#226115412
#226099662
#226080412
#226080402
#226080392
C73×#13872
#1287173