Finite Group Databasebeta

← #33004168

Subgroups — #33004168

Order 18688.

430 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×#17988702C211yesmaximal, characteristic
2C2×#17988407C211yesmaximal, characteristic, complemented
3C2×#17988370C211yesmaximal, characteristic, complemented
4#22611546C211yesmaximal, characteristic, complemented
5#22611545C211yesmaximal, characteristic, complemented
6C2×#17988362C211yesmaximal, characteristic, complemented
7C2×#350×C73C211yesmaximal, characteristic, complemented
8C2×#14556611C411yescharacteristic
9C2×#14556597C2211yescharacteristic
10C2×#14556531C2211yescharacteristic
11C22×#11924003C2211yescharacteristic
12#17988702—22no—
13#17988702—22no—
14C2×#14556526C411yescharacteristic
15C2×#14556518C411yescharacteristic
16C2×#14556517C411yescharacteristic
17C2×C8×Dic73C2211yescharacteristic
18#17988407—22no—
19#17988370—22no—
20C22⋊#11924003—22no—
21#17988366—22no—
22#17988362—22no—
23C2×#131×C73C2211yescharacteristic
24C2×M32×C73C2211yescharacteristic
25C22×C16×C73C2211yescharacteristic
26#350×C73—22no—
27C2×#11924028C2×C411yescharacteristic
28#14556611—22no—
29#14556611—22no—
30C2×#11924018C811yescharacteristic
31C2×#11924016C811yescharacteristic
32C2×#11924015C811yescharacteristic
33C2×#11924013C811yescharacteristic
34#14556597—21no—
35#14556597—21no—
36#14556597—21no—
37#14556597—21no—
38C2×#11924012C2×C411yescharacteristic
39C2×#11924011—21no—
40C22×#10596831C2×C411yescharacteristic
41C2×C8×D73—21no—
42C2×C4×Dic73C2×C411yescharacteristic
43#14556531—21no—
44#14556531—21no—
45C2×#11924003—21no—
46C2×#11924003—21no—
47C2×#11924003—21no—
48C2×#11924003D412yes—
49#14556526—22no—
50#14556518—22no—
51#14556517—22no—
52C8×Dic73D412yes—
53C8×Dic73D412yes—
54C2×#41×C73C2×C411yescharacteristic
55#131×C73—21no—
56#131×C73—21no—
57#131×C73—21no—
58#131×C73—21no—
59C2×M16×C73—21no—
60C2×M16×C73C2×C411yescharacteristic
61C22×C8×C73—21no—
62C22×C8×C73C2311yescharacteristic
63M32×C73—21no—
64M32×C73—21no—
65C2×C16×C73—21no—
66C2×C16×C73—21no—
67C2×C16×C73—21no—
68C2×C16×C73D412yes—
69#11924028—21no—
70#11924028—21no—
71#11924028—21no—
72#11924028—21no—
73C2×Dic146C2×C811yescharacteristic
74C2×D292C2×C811yescharacteristic
75C2×C22⋊D73—21no—
76C22×Dic73—21no—
77C2×C4×D73—21no—
78#11924018—22no—
79#11924016—22no—
80#11924015—22no—
81#11924013—22no—
82#11924012—21no—
83#11924012—21no—
84#11924011—41no—
85#11924011—41no—
86C2×#10596831—21no—
87C2×#10596831C22⋊C412yes—
88C2×#10596831C2×C811yescharacteristic
89C2×#10596831C2×C811yescharacteristic
90C2×#10596831M1612yes—
91C8×D73—41no—
92C8×D73—41no—
93C4×Dic73—21no—
94C4×Dic73C22⋊C412yes—
95#11924003—22no—
96#11924003—41no—
97#41×C73—21no—
98#41×C73—21no—
99#41×C73—21no—
100#41×C73—21no—
101C2×Q8×C73C2×C811yescharacteristic
102C2×D4×C73—21no—
103C2×D4×C73C2×C811yescharacteristic
104C22×C4×C73—21no—
105C22×C4×C73C22×C411yescharacteristic
106M16×C73—21no—
107M16×C73—21no—
108M16×C73—41no—
109M16×C73—41no—
110C2×C8×C73—21no—
111C2×C8×C73—41no—
112C2×C8×C73—41no—
113C2×C8×C73C2×D411yescharacteristic
114C2×C8×C73C2×D411yescharacteristic
115C2×C8×C73C2×D411yescharacteristic
116C2×C8×C73C2×D411yescharacteristic
117C2×C8×C73#4111yescharacteristic
118C2×C8×C73#4111yescharacteristic
119C16×C73—22no—
120C16×C73—41no—
121C23×C73—21no—
122C23×C73#13111yescharacteristic
123C22×D73—21no—
124Q8×C73—21no—
125Q8×C73—21no—
126D4×C73—21no—
127D4×C73—21no—
128D4×C73—41no—
129D4×C73—41no—
130C2×C4×C73—21no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73C2×C22⋊C411yescharacteristic
134C2×C4×C73C4×D411yescharacteristic
135C2×C4×C73C4×D411yescharacteristic
136C2×C4×C73C22×C811yescharacteristic
137C2×C4×C73C2×M1611yescharacteristic
138C2×C4×C73#13111yescharacteristic
139C22⋊D73—41no—
140C22⋊D73—41no—
141C2×Dic73—22no—
142C2×Dic73—21no—
143C2×Dic73—42no—
144D292—21no—
145D292—21no—
146C4×D73—41no—
147C4×D73—41no—
148Dic146—21no—
149Dic146—21no—
150C8×C73—41no—
151C8×C73#12111yescharacteristic
152C8×C73#12111yescharacteristic
153C8×C73#12411yescharacteristic
154C8×C73#12711yescharacteristic
155#10596831—41no—
156#10596831C22⋊C812yes—
157#10596831C22⋊C812yes—
158C22×C73—22no—
159C22×C73—42no—
160C22×C73—41no—
161C22×C73#40811yescharacteristic
162C22×C73C8×D411yescharacteristic
163C22×C73#43611yescharacteristic
164C2×D73—42no—
165C2×D73—41no—
166C4×C73—41no—
167C4×C73#39011yescharacteristic
168C4×C73C2×C22⋊C811yescharacteristic
169C4×C73C8×D411yescharacteristic
170C4×C73#43611yescharacteristic
171Dic73—42no—
172Dic73—41no—
173#13196—731nomaximal, Sylow
174C2×C73—21no—
175C2×C73—21no—
176C2×C73—81no—
177C2×C73#195411yescharacteristic
178C2×C73#217112yes—
179D73—81no—
180C2×#443—731no—
181C2×#364—731no—
182C2×#350—731no—
183C2×#350D7311yescharacteristic, complemented
184#2113—731no—
185#2113—731no—
186C2×#346—731no—
187C73#1319611yescharacteristic, complemented, Sylow
188C2×#135—731no—
189C2×#131—731no—
190C2×#131C2×D7311yescharacteristic
191C2×M32—731no—
192C2×M32C2×D7311yescharacteristic
193C22×C16—731no—
194C22×C16C2×D7311yescharacteristic
195#443—1462no—
196#443—1462no—
197C2×#108—731no—
198C2×#104—731no—
199C2×#104—731no—
200C2×C4×C8—731no—
201#364—1462no—
202#350—22no—
203#350—1462no—
204C22⋊C16—1462no—
205C22⋊C16—1462no—
206#346—1462no—
207C2×#41—731no—
208C2×#41C4×D7311yescharacteristic
209#135—1462no—
210#135—1462no—
211C2×Q16—731no—
212C2×SD16—731no—
213C2×SD16—731no—
214C2×D8—731no—
215#131—21no—
216#131—21no—
217#131—21no—
218#131—21no—
219#131—1461no—
220#131—1461no—
221#131—1461no—
222#131—1461no—
223C2×M16—21no—
224C2×M16—731no—
225C2×M16—1461no—
226C2×M16C4×D7311yescharacteristic
227C22×C8—21no—
228C22×C8—731no—
229C22×C8—1461no—
230C22×C8C22×D7311yescharacteristic
231C2×C42—731no—
232M32—21no—
233M32—21no—
234M32—1461no—
235M32—1461no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—732no—
240C2×C16—1461no—
241C2×C16—1461no—
242C2×C16—1461no—
243C2×C16C22⋊D7312yes—
244#108—1462no—
245#104—1462no—
246#104—1462no—
247C4×C8—732no—
248C4×C8—732no—
249#41—21no—
250#41—21no—
251#41—21no—
252#41—21no—
253#41—1461no—
254#41—1461no—
255#41—1461no—
256#41—1461no—
257C2×Q8—731no—
258C2×Q8C8×D7311yescharacteristic
259C2×D4—21no—
260C2×D4—731no—
261C2×D4—1461no—
262C2×D4C8×D7311yescharacteristic
263C22×C4—21no—
264C22×C4—1461no—
265C22×C4—1461no—
266C22×C4C2×C4×D7311yescharacteristic
267Q16—1462no—
268SD16—1462no—
269SD16—1462no—
270D8—1462no—
271M16—21no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—2921no—
276M16—2921no—
277M16—1461no—
278M16—1461no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—2921no—
283C2×C8—2921no—
284C2×C8—732no—
285C2×C8—731no—
286C2×C8—731no—
287C2×C8—732no—
288C2×C8—1461no—
289C2×C8D4×D7311yescharacteristic
290C2×C8D4×D7311yescharacteristic
291C2×C8D4×D7311yescharacteristic
292C2×C8C2×C22⋊D7311yescharacteristic
293C2×C8#1192402711yescharacteristic
294C2×C8#1192402811yescharacteristic
295C42—732no—
296C42—1461no—
297C16—22no—
298C16—41no—
299C16—2921no—
300C16—1462no—
301C23—21no—
302C23—1461no—
303C23#1455659911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1461no—
307Q8—1461no—
308D4—21no—
309D4—21no—
310D4—41no—
311D4—41no—
312D4—2921no—
313D4—2921no—
314D4—1461no—
315D4—1461no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—2922no—
320C2×C4—2921no—
321C2×C4—2921no—
322C2×C4—1461no—
323C2×C4—1462no—
324C2×C4C22⋊C4×D7311yescharacteristic
325C2×C4#1455655111yescharacteristic
326C2×C4C4×C22⋊D7311yescharacteristic
327C2×C4C2×C8×D7311yescharacteristic
328C2×C4M16×D7311yescharacteristic
329C2×C4#1455659711yescharacteristic
330C8—41no—
331C8—2921no—
332C8—732no—
333C8—732no—
334C8#1455656311yescharacteristic
335C8#1455656411yescharacteristic
336C8#1455657711yescharacteristic
337C8#1455658711yescharacteristic
338C22—22no—
339C22—41no—
340C22—42no—
341C22—2921no—
342C22—2922no—
343C22#1798855211yescharacteristic
344C22#1798865011yescharacteristic
345C22#1798866311yescharacteristic
346C4—41no—
347C4—2922no—
348C4—2921no—
349C4#1798848711yescharacteristic
350C4C22⋊C8×D7311yescharacteristic
351C4C8×C22⋊D7311yescharacteristic
352C4#1798866211yescharacteristic
353C2—21no—
354C2—21no—
355C2—81no—
356C2—5841no—
357C2#2261072311yescharacteristic
358C2#2261177012yes—
subgroupG/H
centerC2×C8D4×D73
commutatorC2×C4×C73C22×C8
FrattiniC22×C8C22×D73
FittingC2×#350×C73C2
socleC22×C73C8×D4
prime radicalC2×#14556611C4
cosocleC22×C8×C73C23
hypercenterC2×#350D73
hypocenterC73#13196
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. C2×#17988407C2semidirect
3. C2×#17988370C2semidirect
4. #22611546C2semidirect
5. #22611545C2semidirect
6. C2×#17988362C2semidirect
7. C2×#350×C73C2semidirect
183. C2×#350D73semidirect
187. C73#13196semidirect

Maximal subgroups

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

subgroupindex
C2×#179887022
C2×#179884072
C2×#179883702
#226115462
#226115452
C2×#179883622
C2×#350×C732
#1319673