Finite Group Databasebeta

← #33002859

Subgroups — #33002859

Order 18688.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989004C211yesmaximal, characteristic, complemented
2C2×#17988702C211yesmaximal, characteristic
3C2×#17988370C211yesmaximal, characteristic, complemented
4#22611546C211yesmaximal, characteristic, complemented
5#22608012C211yesmaximal, characteristic, complemented
6#22608008C211yesmaximal, characteristic, complemented
7C2×#350×C73C211yesmaximal, characteristic, complemented
8C2×#14556611C411yescharacteristic
9C2×#14556597C2211yescharacteristic
10#17989004—22no—
11#17989004—22no—
12C2×#14556531—21no—
13C2×#14556531C2211yescharacteristic
14C22×#11924003—21no—
15C22×#11924003C2211yescharacteristic
16#17988702—22no—
17#17988702—22no—
18C2×#14556526C411yescharacteristic
19C2×#14556518C411yescharacteristic
20C2×#14556517C411yescharacteristic
21C2×C8×Dic73C2211yescharacteristic
22#17988370—22no—
23#17988366—21no—
24#17988366—21no—
25C2×#131×C73C2211yescharacteristic
26C2×M32×C73C2211yescharacteristic
27C22×C16×C73C2211yescharacteristic
28#350×C73—22no—
29C2×#11924028C2×C411yescharacteristic
30#14556611—22no—
31#14556611—22no—
32C2×#11924018C811yescharacteristic
33C2×#11924016C811yescharacteristic
34C2×#11924015C811yescharacteristic
35C2×#11924013C811yescharacteristic
36#14556597—21no—
37#14556597—21no—
38#14556597—21no—
39#14556597—21no—
40C2×#11924012C2×C411yescharacteristic
41C2×#11924011—21no—
42C22×#10596831C2×C411yescharacteristic
43C2×C8×D73—21no—
44C2×C4×Dic73C2×C411yescharacteristic
45#14556531—24no—
46#14556531—21no—
47#14556531D412yes—
48C2×#11924003—24no—
49C2×#11924003—21no—
50C2×#11924003—21no—
51C2×#11924003—21no—
52C2×#11924003D411yescharacteristic
53C2×#11924003D411yescharacteristic
54#14556526—22no—
55#14556518—22no—
56#14556517—22no—
57C8×Dic73—21no—
58C8×Dic73—21no—
59C2×#41×C73C2×C411yescharacteristic
60#131×C73—21no—
61#131×C73—21no—
62#131×C73D412yes—
63#131×C73D412yes—
64C2×M16×C73—21no—
65C2×M16×C73C2×C411yescharacteristic
66C22×C8×C73—21no—
67C22×C8×C73C2311yescharacteristic
68M32×C73—21no—
69M32×C73—21no—
70C2×C16×C73—21no—
71C2×C16×C73—21no—
72C2×C16×C73—21no—
73C2×C16×C73—21no—
74#11924028—21no—
75#11924028—21no—
76#11924028—21no—
77#11924028—21no—
78C2×Dic146C2×C811yescharacteristic
79C2×D292C2×C811yescharacteristic
80C2×C22⋊D73—21no—
81C22×Dic73—21no—
82C2×C4×D73—21no—
83#11924018—22no—
84#11924016—22no—
85#11924015—22no—
86#11924013—22no—
87#11924012—21no—
88#11924012—21no—
89#11924011—41no—
90#11924011—41no—
91C2×#10596831—21no—
92C2×#10596831—21no—
93C2×#10596831—21no—
94C2×#10596831C2×C811yescharacteristic
95C2×#10596831C2×C811yescharacteristic
96C8×D73—41no—
97C8×D73—41no—
98C4×Dic73—21no—
99C4×Dic73—21no—
100#11924003—21no—
101#11924003—22no—
102#11924003—21no—
103#41×C73—21no—
104#41×C73—21no—
105#41×C73C22⋊C412yes—
106#41×C73M1612yes—
107C2×Q8×C73C2×C811yescharacteristic
108C2×D4×C73—21no—
109C2×D4×C73C2×C811yescharacteristic
110C22×C4×C73—21no—
111C22×C4×C73C22×C411yescharacteristic
112M16×C73—21no—
113M16×C73—22no—
114M16×C73—22no—
115M16×C73C22⋊C412yes—
116C2×C8×C73—21no—
117C2×C8×C73—22no—
118C2×C8×C73—22no—
119C2×C8×C73C2×D411yescharacteristic
120C2×C8×C73C2×D411yescharacteristic
121C2×C8×C73C2×D411yescharacteristic
122C2×C8×C73C2×D411yescharacteristic
123C2×C8×C73#4111yescharacteristic
124C2×C8×C73#4111yescharacteristic
125C16×C73—41no—
126C16×C73—41no—
127C23×C73—21no—
128C23×C73#13111yescharacteristic
129C22×D73—21no—
130Q8×C73—21no—
131Q8×C73C22⋊C812yes—
132D4×C73—22no—
133D4×C73—22no—
134D4×C73—21no—
135D4×C73C22⋊C812yes—
136C2×C4×C73—21no—
137C2×C4×C73—22no—
138C2×C4×C73—22no—
139C2×C4×C73C2×C22⋊C411yescharacteristic
140C2×C4×C73C4×D411yescharacteristic
141C2×C4×C73C4×D411yescharacteristic
142C2×C4×C73C22×C811yescharacteristic
143C2×C4×C73C2×M1611yescharacteristic
144C2×C4×C73#13111yescharacteristic
145C22⋊D73—41no—
146C22⋊D73—41no—
147C2×Dic73—22no—
148C2×Dic73—21no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151D292—21no—
152D292—21no—
153C4×D73—41no—
154C4×D73—41no—
155Dic146—21no—
156Dic146—21no—
157C8×C73—22no—
158C8×C73#12011yescharacteristic
159C8×C73#12111yescharacteristic
160C8×C73#12111yescharacteristic
161C8×C73#12311yescharacteristic
162#10596831—21no—
163#10596831—21no—
164#10596831—41no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—22no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73#40811yescharacteristic
171C22×C73C8×D411yescharacteristic
172C22×C73#43511yescharacteristic
173C2×D73—41no—
174C2×D73—41no—
175C2×D73—41no—
176C4×C73—22no—
177C4×C73#38611yescharacteristic
178C4×C73C2×C22⋊C811yescharacteristic
179C4×C73C8×D411yescharacteristic
180C4×C73#43511yescharacteristic
181Dic73—42no—
182Dic73—41no—
183#12980—731nomaximal, Sylow
184C2×C73—21no—
185C2×C73—21no—
186C2×C73—42no—
187C2×C73#186911yescharacteristic
188C2×C73#217011yescharacteristic
189C2×C73#217111yescharacteristic
190D73—81no—
191C2×#504—731no—
192C2×#443—731no—
193C2×#350—731no—
194C2×#350D7311yescharacteristic, complemented
195#2113—731no—
196#1376—731no—
197#1374—731no—
198C73#1298011yescharacteristic, complemented, Sylow
199C2×#135—731no—
200C2×#131—731no—
201C2×#131C2×D7311yescharacteristic
202#504—1462no—
203#504—1462no—
204C2×M32—731no—
205C2×M32—1461no—
206C2×M32C2×D7311yescharacteristic
207C22×C16—731no—
208C22×C16—1461no—
209C22×C16C2×D7311yescharacteristic
210#443—1462no—
211#443—1462no—
212C2×#108—731no—
213C2×#104—731no—
214C2×#104—731no—
215C2×C4×C8—731no—
216#350—22no—
217#350—1462no—
218C22⋊C16—1461no—
219C22⋊C16—1461no—
220C2×#41—731no—
221C2×#41C4×D7311yescharacteristic
222#135—1462no—
223#135—1462no—
224C2×Q16—731no—
225C2×SD16—731no—
226C2×SD16—731no—
227C2×D8—731no—
228#131—21no—
229#131—21no—
230#131—1461no—
231#131—1461no—
232#131—1461no—
233#131—1461no—
234#131D29212yes—
235#131C22⋊D7312yes—
236C2×M16—21no—
237C2×M16—731no—
238C2×M16—1461no—
239C2×M16C4×D7311yescharacteristic
240C22×C8—21no—
241C22×C8—731no—
242C22×C8—1461no—
243C22×C8C22×D7311yescharacteristic
244C2×C42—731no—
245M32—21no—
246M32—21no—
247M32—732no—
248M32—1464no—
249M32—1461no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—21no—
253C2×C16—21no—
254C2×C16—731no—
255C2×C16—731no—
256C2×C16—1464no—
257C2×C16—1461no—
258C2×C16—1461no—
259C2×C16—1461no—
260#108—1462no—
261#104—1462no—
262#104—1462no—
263C4×C8—1461no—
264C4×C8—1461no—
265#41—21no—
266#41—21no—
267#41—1461no—
268#41—1461no—
269#41—1461no—
270#41—1461no—
271#41#1192400512yes—
272#41#1192401112yes—
273C2×Q8—731no—
274C2×Q8C8×D7311yescharacteristic
275C2×D4—21no—
276C2×D4—731no—
277C2×D4—1461no—
278C2×D4C8×D7311yescharacteristic
279C22×C4—21no—
280C22×C4—1461no—
281C22×C4—1461no—
282C22×C4C2×C4×D7311yescharacteristic
283Q16—1462no—
284SD16—1462no—
285SD16—1462no—
286D8—1462no—
287M16—21no—
288M16—22no—
289M16—22no—
290M16—2921no—
291M16—2921no—
292M16—1461no—
293M16—1461no—
294M16#1192400512yes—
295C2×C8—21no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—2921no—
299C2×C8—2921no—
300C2×C8—731no—
301C2×C8—731no—
302C2×C8—1461no—
303C2×C8—1461no—
304C2×C8—1461no—
305C2×C8D4×D7311yescharacteristic
306C2×C8D4×D7311yescharacteristic
307C2×C8C2×C22⋊D7311yescharacteristic
308C2×C8C2×D29211yescharacteristic
309C2×C8#1192402711yescharacteristic
310C2×C8#1192402711yescharacteristic
311C42—1461no—
312C42—1461no—
313C16—41no—
314C16—41no—
315C16—1461no—
316C16—1461no—
317C16—1462no—
318C23—21no—
319C23—1461no—
320C23#1455659911yescharacteristic
321Q8—21no—
322Q8—1461no—
323Q8—1461no—
324Q8#1455650312yes—
325D4—22no—
326D4—22no—
327D4—21no—
328D4—2921no—
329D4—2921no—
330D4—1461no—
331D4—1461no—
332D4#1455650312yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—2921no—
337C2×C4—2921no—
338C2×C4—2921no—
339C2×C4—2921no—
340C2×C4—1462no—
341C2×C4—1461no—
342C2×C4C2×#1192400511yescharacteristic
343C2×C4#1455655111yescharacteristic
344C2×C4#1455655111yescharacteristic
345C2×C4C2×C8×D7311yescharacteristic
346C2×C4C2×#1192401111yescharacteristic
347C2×C4#1455659911yescharacteristic
348C8—22no—
349C8—2921no—
350C8—1461no—
351C8—1461no—
352C8#1455656111yescharacteristic
353C8#1455656311yescharacteristic
354C8#1455656311yescharacteristic
355C8#1455657511yescharacteristic
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—2921no—
362C22—2921no—
363C22—2921no—
364C22#1798855511yescharacteristic
365C22#1798865011yescharacteristic
366C22#1798865511yescharacteristic
367C4—22no—
368C4—2922no—
369C4—2921no—
370C4#1798846411yescharacteristic
371C4C2×#1455650311yescharacteristic
372C4#1798865011yescharacteristic
373C4#1798865511yescharacteristic
374C2—21no—
375C2—21no—
376C2—42no—
377C2—5841no—
378C2#2261022111yescharacteristic
379C2#2261176511yescharacteristic
380C2#2261177011yescharacteristic
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#12980
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
1. C2×#17989004C2semidirect
3. C2×#17988370C2semidirect
4. #22611546C2semidirect
5. #22608012C2semidirect
6. #22608008C2semidirect
7. C2×#350×C73C2semidirect
194. C2×#350D73semidirect
198. C73#12980semidirect

Maximal subgroups

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

subgroupindex
C2×#179890042
C2×#179887022
C2×#179883702
#226115462
#226080122
#226080082
C2×#350×C732
#1298073