Finite Group Databasebeta

← #33004387

Subgroups — #33004387

Order 18688.

426 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989017C211yesmaximal, characteristic
2C2×#17988416C211yesmaximal, characteristic, complemented
3C2×#17988394C211yesmaximal, characteristic, complemented
4C2×#17988393C211yesmaximal, characteristic, complemented
5C2×C4×#11924003C211yesmaximal, characteristic, complemented
6#22610819C211yesmaximal, characteristic, complemented
7C73×#1974C211yesmaximal, characteristic, complemented
8C2×#14556613C2211yescharacteristic
9#17989017—22no—
10#17989017—22no—
11C2×#14556537C411yescharacteristic, complemented
12C2×#14556535C411yescharacteristic, complemented
13C2×#14556534C411yescharacteristic, complemented
14C2×#14556532C411yescharacteristic, complemented
15C22×#11924003C2211yescharacteristic
16C22×#11924003C2211yescharacteristic
17C2×#14556527C2211yescharacteristic
18C2×#14556519—21no—
19#17988553—21no—
20#17988416—22no—
21#17988394—22no—
22#17988393—22no—
23C4×#11924003—22no—
24C2×#135×C73C2211yescharacteristic
25C2×#108×C73C2211yescharacteristic
26C2×#104×C73—21no—
27#408×C73—21no—
28C2×C4×C8×C73C2211yescharacteristic
29C2×#11924028—21no—
30#14556613—21no—
31#14556613—21no—
32#14556613—21no—
33#14556613—21no—
34C2×Dic292C2×C411yescharacteristic
35C2×#11924017—21no—
36C2×D584C2×C411yescharacteristic
37C2×#11924012—21no—
38#14556537—22no—
39#14556535—22no—
40#14556534—22no—
41#14556532—22no—
42C2×#11924003—21no—
43C2×#11924003—21no—
44C2×#11924003C2×C411yescharacteristic
45C2×#11924003C2×C411yescharacteristic
46C2×#11924003D412yes—
47C2×#11924003D412yes—
48C2×#11924003D412yes—
49#14556527—21no—
50#14556527—21no—
51#14556519—42no—
52#14556503—42no—
53C2×#41×C73—21no—
54#135×C73—21no—
55#135×C73—21no—
56#135×C73—21no—
57#135×C73—21no—
58C2×Q16×C73C2×C411yescharacteristic
59C2×SD16×C73—21no—
60C2×D8×C73C2×C411yescharacteristic
61C2×M16×C73—21no—
62C22×C8×C73D411yescharacteristic
63C22×C8×C73C2311yescharacteristic
64C2×C42×C73D411yescharacteristic
65#108×C73—21no—
66#108×C73—21no—
67#104×C73—42no—
68C22⋊C8×C73—42no—
69C4×C8×C73—21no—
70C4×C8×C73—21no—
71#11924028—41no—
72#11924028—41no—
73#11924028—41no—
74#11924028—41no—
75C2×Dic146—21no—
76C2×D292—21no—
77C2×C22⋊D73—41no—
78C2×C4×D73—41no—
79Dic292—21no—
80Dic292—21no—
81#11924017—41no—
82#11924017—41no—
83D584—21no—
84D584—21no—
85#11924012—41no—
86#11924012—41no—
87C2×#10596831—41no—
88#11924003—22no—
89#11924003C22⋊C412yes—
90#11924003C22⋊C412yes—
91#41×C73—41no—
92#41×C73—41no—
93#41×C73—41no—
94#41×C73—41no—
95C2×Q8×C73—21no—
96C2×D4×C73—21no—
97C2×D4×C73—41no—
98C22×C4×C73—21no—
99C22×C4×C73—41no—
100C22×C4×C73C2×D411yescharacteristic
101Q16×C73—21no—
102Q16×C73—21no—
103SD16×C73—41no—
104SD16×C73—41no—
105D8×C73—21no—
106D8×C73—21no—
107M16×C73—41no—
108M16×C73—41no—
109C2×C8×C73—21no—
110C2×C8×C73—21no—
111C2×C8×C73—41no—
112C2×C8×C73D812yes—
113C2×C8×C73C22×C411yescharacteristic
114C2×C8×C73C2×D411yescharacteristic
115C2×C8×C73C2×D411yescharacteristic
116C2×C8×C73C2×D411yescharacteristic
117C2×C8×C73#4111yescharacteristic
118C2×C8×C73#4111yescharacteristic
119C42×C73—21no—
120C42×C73D812yes—
121C23×C73—41no—
122C23×C73#13511yescharacteristic
123C22×D73—41no—
124Q8×C73—41no—
125Q8×C73—41no—
126D4×C73—41no—
127D4×C73—41no—
128D4×C73—81no—
129D4×C73—81no—
130C2×C4×C73—24no—
131C2×C4×C73—22no—
132C2×C4×C73—41no—
133C2×C4×C73—81no—
134C2×C4×C73—81no—
135C2×C4×C73C4×D411yescharacteristic
136C2×C4×C73#12111yescharacteristic
137C2×C4×C73#12711yescharacteristic
138C2×C4×C73C2×D811yescharacteristic
139C2×C4×C73C2×D811yescharacteristic
140C2×C4×C73#13511yescharacteristic
141C22⋊D73—81no—
142C22⋊D73—81no—
143C2×Dic73—41no—
144D292—41no—
145D292—41no—
146C4×D73—81no—
147C4×D73—81no—
148Dic146—41no—
149Dic146—41no—
150C8×C73—22no—
151C8×C73—81no—
152C8×C73C2×C22⋊C411yescharacteristic
153C8×C73C4×D411yescharacteristic
154C8×C73#12111yescharacteristic
155C8×C73#12411yescharacteristic
156#10596831—81no—
157C22×C73—22no—
158C22×C73—82no—
159C22×C73—81no—
160C22×C73C4×D811yescharacteristic
161C22×C73#46611yescharacteristic
162C22×C73#49511yescharacteristic
163C2×D73—82no—
164C2×D73—81no—
165C4×C73—24no—
166C4×C73—81no—
167C4×C73#39011yescharacteristic
168C4×C73C4×D811yescharacteristic
169C4×C73#46611yescharacteristic
170C4×C73#49311yescharacteristic
171Dic73—81no—
172#13241—731nomaximal, Sylow
173C2×C73—21no—
174C2×C73—21no—
175C2×C73—161no—
176C2×C73#197011yescharacteristic
177C2×C73#217812yes—
178D73—161no—
179C2×#508—731no—
180C2×#368—731no—
181C2×#359—731no—
182C2×#359—731no—
183C2×C4×C16—731no—
184#1974—731no—
185#1974D7311yescharacteristic, complemented
186C73#1324111yescharacteristic, complemented, Sylow
187C2×#135—731no—
188C2×#135C2×D7311yescharacteristic
189#508—1462no—
190#508—1462no—
191C2×Q32—731no—
192C2×SD32—731no—
193C2×SD32—731no—
194C2×D16—731no—
195C22×C16—731no—
196C22×C16—731no—
197C2×#108—731no—
198C2×#108C2×D7311yescharacteristic
199C2×#104—21no—
200C2×#104—1461no—
201#408—21no—
202#408—1461no—
203C2×C4×C8C2×D7311yescharacteristic
204#368—1462no—
205#359—1462no—
206#359—1462no—
207C4×C16—1462no—
208C2×#41—21no—
209C2×#41—1461no—
210#135—21no—
211#135—21no—
212#135—21no—
213#135—21no—
214#135—1461no—
215#135—1461no—
216#135—1461no—
217#135—1461no—
218C2×Q16—731no—
219C2×Q16C4×D7311yescharacteristic
220C2×SD16—21no—
221C2×SD16—1461no—
222C2×D8—731no—
223C2×D8C4×D7311yescharacteristic
224C2×M16—21no—
225C2×M16—1461no—
226C22×C8C22⋊D7311yescharacteristic
227C22×C8C22×D7311yescharacteristic
228C2×C42C22⋊D7311yescharacteristic
229Q32—1462no—
230SD32—1462no—
231SD32—1462no—
232D16—1462no—
233C2×C16—731no—
234C2×C16—731no—
235C2×C16—732no—
236C2×C16—732no—
237C2×C16—732no—
238C2×C16—1461no—
239C2×C16—1461no—
240#108—21no—
241#108—21no—
242#108—1461no—
243#108—1461no—
244#104—42no—
245#104—2922no—
246C22⋊C8—42no—
247C22⋊C8—2922no—
248C4×C8—21no—
249C4×C8—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—2921no—
255#41—2921no—
256#41—2921no—
257#41—2921no—
258C2×Q8—21no—
259C2×Q8—1461no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—2921no—
263C2×D4—1461no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—2921no—
267C22×C4C2×C22⋊D7311yescharacteristic
268Q16—21no—
269Q16—21no—
270Q16—1461no—
271Q16—1461no—
272SD16—41no—
273SD16—41no—
274SD16—2921no—
275SD16—2921no—
276D8—21no—
277D8—21no—
278D8—1461no—
279D8—1461no—
280M16—41no—
281M16—41no—
282M16—2921no—
283M16—2921no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—2921no—
288C2×C8#1192401312yes—
289C2×C8C2×C4×D7311yescharacteristic
290C2×C8D4×D7311yescharacteristic
291C2×C8D4×D7311yescharacteristic
292C2×C8D4×D7311yescharacteristic
293C2×C8#1192402711yescharacteristic
294C2×C8#1192402811yescharacteristic
295C42—21no—
296C42#1192401312yes—
297C16—732no—
298C16—732no—
299C16—1462no—
300C23—41no—
301C23—2921no—
302C23#1455661111yescharacteristic
303Q8—41no—
304Q8—41no—
305Q8—2921no—
306Q8—2921no—
307D4—41no—
308D4—41no—
309D4—81no—
310D4—81no—
311D4—2921no—
312D4—2921no—
313D4—5841no—
314D4—5841no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—2921no—
321C2×C4—5841no—
322C2×C4—5841no—
323C2×C4C4×C22⋊D7311yescharacteristic
324C2×C4#1455656311yescharacteristic
325C2×C4#1455658711yescharacteristic
326C2×C4C2×#1192401311yescharacteristic
327C2×C4C2×#1192401311yescharacteristic
328C2×C4#1455661111yescharacteristic
329C8—22no—
330C8—81no—
331C8—5841no—
332C8C22⋊C4×D7311yescharacteristic
333C8#1455655111yescharacteristic
334C8#1455656411yescharacteristic
335C8#1455657711yescharacteristic
336C22—22no—
337C22—82no—
338C22—81no—
339C22—5842no—
340C22—5841no—
341C22C4×#1192401311yescharacteristic
342C22#1798882111yescharacteristic
343C22#1798896911yescharacteristic
344C4—24no—
345C4—81no—
346C4—5841no—
347C4#1798848711yescharacteristic
348C4C4×#1192401311yescharacteristic
349C4#1798882111yescharacteristic
350C4#1798896311yescharacteristic
351C2—21no—
352C2—21no—
353C2—161no—
354C2—11681no—
355C2#2261079611yescharacteristic
356C2#2261181012yes—
subgroupG/H
centerC2×C4C2×#11924013
commutatorC2×C8×C73C22×C4
FrattiniC22×C8C22×D73
FittingC73×#1974C2
socleC22×C73C4×D8
prime radicalC2×#17989017C2
cosocleC22×C8×C73C23
hypercenter#1974D73
hypocenterC73#13241
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. C2×#17988416C2semidirect
3. C2×#17988394C2semidirect
4. C2×#17988393C2semidirect
5. C2×C4×#11924003C2semidirect
6. #22610819C2semidirect
7. C73×#1974C2semidirect
11. C2×#14556537C4semidirect
12. C2×#14556535C4semidirect
13. C2×#14556534C4semidirect
14. C2×#14556532C4semidirect
185. #1974D73semidirect
186. C73#13241semidirect

Maximal subgroups

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

subgroupindex
C2×#179890172
C2×#179884162
C2×#179883942
C2×#179883932
C2×C4×#119240032
#226108192
C73×#19742
#1324173