Finite Group Databasebeta

← #32980099

Subgroups — #32980099

Order 18688.

380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 93 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#22619072C211yesmaximal, characteristic
2#22610084C211yesmaximal, characteristic, complemented
3#22608418C211yesmaximal, characteristic
4#22608342C211yesmaximal, characteristic
5#22607823C211yesmaximal, characteristic, complemented
6#22607780C211yesmaximal, characteristic, complemented
7C73×#1573C211yesmaximal, characteristic, complemented
8#17989121C2211yescharacteristic
9#17988715—21no—
10#17988660—21no—
11#17988655—21no—
12#17988650—21no—
13#17988647—21no—
14#17988612—21no—
15C2×C4⋊#10596831C2211yescharacteristic
16C2×#14556520—21no—
17C2×#14556520—21no—
18C4×#11924012C2211yescharacteristic
19#17988433C2211yescharacteristic
20#17988325C411yescharacteristic
21#17988325C411yescharacteristic
22#17988322C411yescharacteristic
23#17988322C411yescharacteristic
24#17988317—21no—
25#17988314—21no—
26#432×C73C2211yescharacteristic
27#431×C73C2211yescharacteristic
28C2×C4⋊C8×C73C2211yescharacteristic
29#335×C73—21no—
30#334×C73—21no—
31C2×#11924012—21no—
32C2×#11924011—21no—
33C22×#10596831D411yescharacteristic
34C22×#10596831D411yescharacteristic
35C2×C8×D73—21no—
36#14556585—21no—
37#14556583Q811yescharacteristic
38#14556579Q811yescharacteristic
39#14556574—21no—
40#14556570C2×C411yescharacteristic
41#14556565C2×C411yescharacteristic
42C4×Dic146D411yescharacteristic
43C4×D292D411yescharacteristic
44C4×C22⋊D73—21no—
45#14556548—21no—
46C2×C4×Dic73—21no—
47C4⋊#10596831—21no—
48C4⋊#10596831—21no—
49#14556520—21no—
50#14556520—21no—
51#14556520—42no—
52#14556520—42no—
53#14556503—21no—
54#14556503—21no—
55#14556502—21no—
56#14556501—21no—
57C4×#10596831—21no—
58C8×Dic73—21no—
59#14556498—21no—
60#14556498C2×C411yescharacteristic
61#14556498C2×C411yescharacteristic
62C22×C8×C73—21no—
63C2×C42×C73C2311yescharacteristic
64C4⋊C8×C73—21no—
65C4⋊C8×C73—21no—
66C4⋊C8×C73—21no—
67C4⋊C8×C73D411yescharacteristic
68C4⋊C8×C73D411yescharacteristic
69C22⋊C8×C73—21no—
70C22⋊C8×C73C2×C411yescharacteristic
71C22⋊C8×C73C2×C411yescharacteristic
72#97×C73—21no—
73C4×C8×C73—21no—
74C2×Dic146C4⋊C411yescharacteristic
75C2×D292C4⋊C411yescharacteristic
76C2×C22⋊D73—21no—
77C22×Dic73—21no—
78C22×Dic73—21no—
79C2×C4×D73—21no—
80#11924012—22no—
81#11924012—41no—
82#11924011—81no—
83C2×#10596831—21no—
84C2×#10596831—21no—
85C2×#10596831—41no—
86C2×#10596831—41no—
87C2×#10596831—41no—
88C8×D73—81no—
89C4⋊Dic73C4⋊C411yescharacteristic
90C4⋊Dic73C4⋊C411yescharacteristic
91#11924007—21no—
92#11924007—21no—
93#11924007—21no—
94#11924007—21no—
95C22⋊Dic73—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005—21no—
99#11924005—21no—
100C4×Dic73—22no—
101C4×Dic73—22no—
102C4×Dic73—21no—
103C22×C4×C73C22×C411yescharacteristic
104C22×C4×C73C2×D411yescharacteristic
105C22×C4×C73#4111yescharacteristic
106C2×C8×C73—21no—
107C2×C8×C73—21no—
108C2×C8×C73—21no—
109C2×C8×C73—21no—
110C2×C8×C73—41no—
111C2×C8×C73—41no—
112C2×C8×C73—41no—
113C42×C73C2×D411yescharacteristic
114C42×C73C2×D411yescharacteristic
115C42×C73C2×Q811yescharacteristic
116C42×C73#4111yescharacteristic
117C23×C73C4×D411yescharacteristic
118C22×D73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—41no—
124C2×C4×C73C2×C4⋊C411yescharacteristic
125C2×C4×C73C4×D411yescharacteristic
126C2×C4×C73#12011yescharacteristic
127C2×C4×C73C22⋊Q811yescharacteristic
128C2×C4×C73C22⋊Q811yescharacteristic
129C2×C4×C73#12311yescharacteristic
130C22⋊D73—41no—
131C22⋊D73—41no—
132C2×Dic73—22no—
133C2×Dic73—22no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141D292—41no—
142C4×D73—41no—
143C4×D73—41no—
144Dic146—41no—
145C8×C73—41no—
146C8×C73—41no—
147C8×C73—41no—
148C8×C73—41no—
149C8×C73—81no—
150#10596831—42no—
151#10596831—41no—
152#10596831—41no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73#38511yescharacteristic
156C22×C73#44311yescharacteristic
157C22×C73#44411yescharacteristic
158C2×D73—41no—
159C2×D73—41no—
160C2×D73—41no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—21no—
165C4×C73—21no—
166C4×C73#45311yescharacteristic
167C4×C73#45611yescharacteristic
168Dic73—42no—
169Dic73—42no—
170Dic73—41no—
171Dic73—41no—
172Dic73—41no—
173#8876—731nomaximal, Sylow
174C2×C73—21no—
175C2×C73—21no—
176C2×C73#185911yescharacteristic
177C2×C73#186611yescharacteristic
178C2×C73#186811yescharacteristic
179D73—81no—
180#2992—731no—
181#1843—731no—
182#1573D7311yescharacteristic, complemented
183#1500—731no—
184#1483—731no—
185#1300—731no—
186#1283—731no—
187C73#887611yescharacteristic, complemented, Sylow
188#529—731no—
189#446—1461no—
190#435—1461no—
191#435—1461no—
192C8×D4—1461no—
193#433—1461no—
194#432C2×D7311yescharacteristic
195#431C2×D7311yescharacteristic
196#424—1461no—
197C2×C4⋊C8—731no—
198C2×C4⋊C8—1461no—
199C2×C4⋊C8—1461no—
200C2×C4⋊C8C2×D7311yescharacteristic
201C4×M16—731no—
202#376—731no—
203#335—21no—
204#334—21no—
205#328—731no—
206#328—731no—
207#327—731no—
208#327—731no—
209Q8⋊C8—1461no—
210D4⋊C8—1461no—
211C2×M16—1461no—
212C2×M16—1461no—
213C22×C8—21no—
214C22×C8—731no—
215C22×C8—731no—
216C22×C8—1461no—
217#126—1461no—
218#125—731no—
219#124—731no—
220#123—1461no—
221C22⋊Q8—731no—
222#121—731no—
223C4×Q8—731no—
224C4×D4—731no—
225C4×D4—1461no—
226#117—1461no—
227C2×C42—1461no—
228C2×C42C22×D7311yescharacteristic
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—2922no—
233C4⋊C8—2922no—
234C4⋊C8—1461no—
235C4⋊C8—1461no—
236C4⋊C8—1461no—
237C4⋊C8—1461no—
238C4⋊C8C22⋊D7311yescharacteristic
239C4⋊C8C22⋊D7311yescharacteristic
240C22⋊C8—21no—
241C22⋊C8—1461no—
242C22⋊C8—1461no—
243C22⋊C8C4×D7311yescharacteristic
244C22⋊C8C4×D7311yescharacteristic
245#97—21no—
246#97—1461no—
247#97—1461no—
248C4×C8—21no—
249C4×C8—1461no—
250C4×C8—1461no—
251#95—731no—
252#95—731no—
253#95—1461no—
254C2×Q8—731no—
255C2×D4—731no—
256C2×D4—1461no—
257C22×C4—1461no—
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4C2×C4×D7311yescharacteristic
261C22×C4D4×D7311yescharacteristic
262C22×C4#1192402911yescharacteristic
263M16—2921no—
264M16—5841no—
265M16—1462no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—2921no—
274C2×C8—2921no—
275C2×C8—2921no—
276C2×C8—5841no—
277C2×C8—1461no—
278C2×C8—1461no—
279C4⋊C4—731no—
280C4⋊C4—731no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4—1461no—
284C4⋊C4—1461no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C42—1462no—
291C42—1462no—
292C42—1461no—
293C42D4×D7311yescharacteristic
294C42C2×C22⋊D7311yescharacteristic
295C42Q8×D7311yescharacteristic
296C42#1192402811yescharacteristic
297C23—1461no—
298C23#1455655311yescharacteristic
299Q8—2921no—
300D4—2921no—
301D4—2921no—
302D4—2921no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—2921no—
309C2×C4—2921no—
310C2×C4—2921no—
311C2×C4—2921no—
312C2×C4—2921no—
313C2×C4—2921no—
314C2×C4—1462no—
315C2×C4—1462no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4C4⋊C4×D7311yescharacteristic
320C2×C4C4×C22⋊D7311yescharacteristic
321C2×C4#1455655911yescharacteristic
322C2×C4#1455656711yescharacteristic
323C2×C4#1455656911yescharacteristic
324C2×C4#1455657611yescharacteristic
325C8—41no—
326C8—41no—
327C8—41no—
328C8—41no—
329C8—81no—
330C8—2922no—
331C8—2921no—
332C8—2921no—
333C22—21no—
334C22—21no—
335C22—2921no—
336C22—2921no—
337C22—2921no—
338C22#1798845811yescharacteristic
339C22#1798870311yescharacteristic
340C22#1798870811yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—2922no—
347C4—2922no—
348C4—2921no—
349C4—2921no—
350C4—2921no—
351C4#1798875311yescharacteristic
352C4#1798876811yescharacteristic
353C2—21no—
354C2—21no—
355C2—5841no—
356C2#2261015411yescharacteristic
357C2#2261020311yescharacteristic
358C2#2261021511yescharacteristic
subgroupG/H
centerC2×C4#14556559
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1573C2
socleC22×C73#385
prime radical#14556565C2×C4
cosocleC2×C42×C73C23
hypercenter#1573D73
hypocenterC73#8876
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #22610084C2semidirect
5. #22607823C2semidirect
6. #22607780C2semidirect
7. C73×#1573C2semidirect
182. #1573D73semidirect
187. C73#8876semidirect

Maximal subgroups

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

subgroupindex
#226190722
#226100842
#226084182
#226083422
#226078232
#226077802
C73×#15732
#887673