Finite Group Databasebeta

← #34013464

Subgroups — #34013464

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×#17989645C211yesmaximal, characteristic, complemented
2C2×#17989485C211yesmaximal, characteristic, complemented
3C2×#17989485C211yesmaximal, characteristic, complemented
4#22626161C211yesmaximal, characteristic, complemented
5#22624976C211yesmaximal, characteristic, complemented
6#22624970C211yesmaximal, characteristic, complemented
7C2×#17988704C211yesmaximal, characteristic
8#17989645—22no—
9#17989645—22no—
10C2×#14556665—21no—
11C2×#14556665C2211yescharacteristic
12C2×#14556665C2211yescharacteristic
13C22×#11924031—21no—
14C22×#11924031C2211yescharacteristic
15C22×#11924031C2211yescharacteristic
16#17989485—22no—
17#17989485—22no—
18C22⋊#11924031—21no—
19C22⋊#11924031—21no—
20C2×#14556598C2211yescharacteristic
21C2×#14556598C2211yescharacteristic
22#17988704—22no—
23#17988704—22no—
24C2×#14556527C411yescharacteristic
25C2×#14556518C411yescharacteristic
26C2×#14556518C411yescharacteristic
27C2×C8×Dic73C2211yescharacteristic
28C2×#135×C73C411yescharacteristic
29#14556665—24no—
30#14556665—21no—
31#14556665—21no—
32#14556665—21no—
33#14556665D412yes—
34C2×#11924031—24no—
35C2×#11924031—21no—
36C2×#11924031—21no—
37C2×#11924031—21no—
38C2×#11924031—21no—
39C2×#11924031—21no—
40C2×#11924031—21no—
41C2×#11924031—21no—
42C2×#11924031D411yescharacteristic
43C2×#11924031D411yescharacteristic
44#14556598—21no—
45#14556598—21no—
46#14556598—21no—
47#14556598—21no—
48#14556598—21no—
49#14556598—21no—
50#14556598D412yes—
51#14556598D412yes—
52C2×#11924012—21no—
53C2×#11924012—21no—
54C2×#11924012C2×C411yescharacteristic
55C2×#11924012C2×C411yescharacteristic
56C22×#10596831—21no—
57C22×#10596831—21no—
58C22×#10596831C2311yescharacteristic
59C2×C4×Dic73C2×C411yescharacteristic
60#14556527—22no—
61#14556518—22no—
62#14556518—22no—
63C8×Dic73—21no—
64C8×Dic73—21no—
65C2×#41×C73C2×C411yescharacteristic
66C2×#41×C73C2×C411yescharacteristic
67#135×C73—22no—
68#135×C73—22no—
69C2×Q16×C73C811yescharacteristic
70C2×SD16×C73C811yescharacteristic
71C2×SD16×C73C811yescharacteristic
72C2×D8×C73C811yescharacteristic
73C22×C8×C73C2×C411yescharacteristic
74#11924031—21no—
75#11924031—22no—
76#11924031—21no—
77#11924031—41no—
78#11924031—41no—
79C22×Dic73—21no—
80#11924012—21no—
81#11924012—22no—
82#11924012—22no—
83#11924012—21no—
84#11924012—21no—
85#11924012—41no—
86#11924012—41no—
87#11924012C22⋊C412yes—
88C2×#10596831—21no—
89C2×#10596831—22no—
90C2×#10596831—22no—
91C2×#10596831—21no—
92C2×#10596831—41no—
93C2×#10596831—41no—
94C2×#10596831C2×D411yescharacteristic
95C2×#10596831C2×D411yescharacteristic
96C2×#10596831C2×D411yescharacteristic
97C2×#10596831C2×D411yescharacteristic
98C2×#10596831#4111yescharacteristic
99C2×#10596831#4111yescharacteristic
100C4×Dic73—21no—
101C4×Dic73—21no—
102#41×C73—21no—
103#41×C73—21no—
104#41×C73—21no—
105#41×C73—21no—
106#41×C73—21no—
107#41×C73—21no—
108#41×C73C22⋊C412yes—
109#41×C73M1612yes—
110C2×Q8×C73C2×C811yescharacteristic
111C2×Q8×C73C2×C811yescharacteristic
112C2×D4×C73—21no—
113C2×D4×C73—21no—
114C2×D4×C73C2×C811yescharacteristic
115C2×D4×C73C2×C811yescharacteristic
116C22×C4×C73—21no—
117C22×C4×C73—21no—
118C22×C4×C73C22×C411yescharacteristic
119Q16×C73—22no—
120SD16×C73—22no—
121SD16×C73—22no—
122D8×C73—22no—
123C2×C8×C73—21no—
124C2×C8×C73—21no—
125C2×C8×C73C2×C811yescharacteristic
126C2×C8×C73C2×C811yescharacteristic
127C23×C73—21no—
128C23×C73—21no—
129C23×C73#13111yescharacteristic
130Q8×C73—21no—
131Q8×C73—21no—
132Q8×C73—21no—
133Q8×C73C22⋊C812yes—
134D4×C73—22no—
135D4×C73—22no—
136D4×C73—21no—
137D4×C73—21no—
138D4×C73—21no—
139D4×C73—41no—
140D4×C73—41no—
141D4×C73C22⋊C812yes—
142C2×C4×C73—21no—
143C2×C4×C73—22no—
144C2×C4×C73—22no—
145C2×C4×C73—21no—
146C2×C4×C73—41no—
147C2×C4×C73—41no—
148C2×C4×C73C2×C22⋊C411yescharacteristic
149C2×C4×C73C4×D411yescharacteristic
150C2×C4×C73C4×D411yescharacteristic
151C2×C4×C73C22×C811yescharacteristic
152C2×C4×C73C2×M1611yescharacteristic
153C2×C4×C73#13111yescharacteristic
154C2×Dic73—22no—
155C2×Dic73—41no—
156C2×Dic73—41no—
157C8×C73—21no—
158C8×C73—21no—
159#10596831—22no—
160#10596831—41no—
161#10596831#12011yescharacteristic
162#10596831#12111yescharacteristic
163#10596831#12111yescharacteristic
164#10596831#12311yescharacteristic
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—22no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73—41no—
171C22×C73—41no—
172C22×C73—41no—
173C22×C73#40811yescharacteristic
174C22×C73C8×D411yescharacteristic
175C22×C73#43511yescharacteristic
176C4×C73—22no—
177C4×C73—41no—
178C4×C73#38611yescharacteristic
179C4×C73C2×C22⋊C811yescharacteristic
180C4×C73C8×D411yescharacteristic
181C4×C73#43511yescharacteristic
182Dic73—42no—
183#12980—731nomaximal, Sylow
184C2×C73—21no—
185C2×C73—21no—
186C2×C73—42no—
187C2×C73—81no—
188C2×C73#186911yescharacteristic
189C2×C73#217011yescharacteristic
190C2×C73#217111yescharacteristic
191C2×#504—731no—
192C2×#443—731no—
193C2×#350—731no—
194C2×#350—731no—
195#2113—731no—
196#1376—731no—
197#1374—731no—
198C73#1298011yescharacteristic, complemented, Sylow
199C2×#135#6440811yescharacteristic
200C2×#131—731no—
201C2×#131—731no—
202#504—1462no—
203#504—1462no—
204C2×M32—731no—
205C2×M32—731no—
206C2×M32—1461no—
207C22×C16—731no—
208C22×C16—731no—
209C22×C16—1461no—
210#443—1462no—
211#443—1462no—
212C2×#108—731no—
213C2×#104—731no—
214C2×#104—731no—
215C2×C4×C8—731no—
216#350—1462no—
217#350—1462no—
218C22⋊C16—1461no—
219C22⋊C16—1461no—
220C2×#41C2×#6440811yescharacteristic
221C2×#41C2×#6440811yescharacteristic
222#135—22no—
223#135—22no—
224C2×Q16#1059683311yescharacteristic
225C2×SD16#1059683311yescharacteristic
226C2×SD16#1059683311yescharacteristic
227C2×D8#1059683311yescharacteristic
228#131—732no—
229#131—732no—
230#131—1461no—
231#131—1461no—
232#131—1461no—
233#131—1461no—
234#131—1461no—
235#131—1461no—
236C2×M16—731no—
237C2×M16—731no—
238C2×M16—1461no—
239C2×M16—1461no—
240C22×C8—731no—
241C22×C8—1461no—
242C22×C8—1461no—
243C22×C8C2×#6440811yescharacteristic
244C2×C42—731no—
245M32—732no—
246M32—1461no—
247M32—1461no—
248M32—1461no—
249M32—1464no—
250C2×C16—731no—
251C2×C16—731no—
252C2×C16—1461no—
253C2×C16—1461no—
254C2×C16—1461no—
255C2×C16—1461no—
256C2×C16—1461no—
257C2×C16—1461no—
258C2×C16—1461no—
259C2×C16—1464no—
260#108—1462no—
261#104—1462no—
262#104—1462no—
263C4×C8—1461no—
264C4×C8—1461no—
265#41—21no—
266#41—21no—
267#41—21no—
268#41—21no—
269#41—21no—
270#41—21no—
271#41C22⋊#6440812yes—
272#41#1192403712yes—
273C2×Q8C2×#1059683311yescharacteristic
274C2×Q8C2×#1059683311yescharacteristic
275C2×D4—21no—
276C2×D4—21no—
277C2×D4C2×#1059683311yescharacteristic
278C2×D4C2×#1059683311yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—1461no—
282C22×C4C22×#6440811yescharacteristic
283Q16—22no—
284SD16—22no—
285SD16—22no—
286D8—22no—
287M16—2921no—
288M16—2921no—
289M16—732no—
290M16—1461no—
291M16—1461no—
292M16—1462no—
293M16—1462no—
294M16—1461no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—2921no—
298C2×C8—2921no—
299C2×C8—731no—
300C2×C8—731no—
301C2×C8—731no—
302C2×C8—731no—
303C2×C8—731no—
304C2×C8—731no—
305C2×C8—1461no—
306C2×C8—1462no—
307C2×C8—1462no—
308C2×C8—1461no—
309C2×C8C2×#1059683311yescharacteristic
310C2×C8C2×#1059683311yescharacteristic
311C42—1461no—
312C42—1461no—
313C16—2921no—
314C16—2921no—
315C16—1461no—
316C16—1461no—
317C16—1462no—
318C23—21no—
319C23—21no—
320C23#1455667811yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8C22⋊#1059683312yes—
325D4—22no—
326D4—22no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—41no—
331D4—41no—
332D4C22⋊#1059683312yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—2921no—
340C2×C4—2921no—
341C2×C4—1462no—
342C2×C4C2×C22⋊#6440811yescharacteristic
343C2×C4D4×#6440811yescharacteristic
344C2×C4D4×#6440811yescharacteristic
345C2×C4C22×#1059683311yescharacteristic
346C2×C4C2×#1192403711yescharacteristic
347C2×C4#1455667811yescharacteristic
348C8—21no—
349C8—21no—
350C8—2921no—
351C8—731no—
352C8—731no—
353C8—731no—
354C8—731no—
355C8—1462no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22#1798956011yescharacteristic
365C22D4×#1059683311yescharacteristic
366C22#1798961811yescharacteristic
367C4—22no—
368C4—41no—
369C4—2922no—
370C4#1798953511yescharacteristic
371C4C2×C22⋊#1059683311yescharacteristic
372C4D4×#1059683311yescharacteristic
373C4#1798961811yescharacteristic
374C2—21no—
375C2—21no—
376C2—42no—
377C2—81no—
378C2#2262590411yescharacteristic
379C2#2262631811yescharacteristic
380C2#2262632111yescharacteristic
subgroupG/H
centerC2×C4D4×#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
Fitting, prime radicalC2×#135×C73C4
socleC22×C73C8×D4
cosocleC22×#10596831C23
hypercenterC2×#135#64408
hypocenterC73#12980
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#17989645C2semidirect
2. C2×#17989485C2semidirect
3. C2×#17989485C2semidirect
4. #22626161C2semidirect
5. #22624976C2semidirect
6. #22624970C2semidirect
198. C73#12980semidirect

Maximal subgroups

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

subgroupindex
C2×#179896452
C2×#179894852
#226261612
#226249762
#226249702
C2×#179887042
#1298073