Finite Group Databasebeta

← #33001920

Subgroups — #33001920

Order 18688.

450 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618353C211yesmaximal, characteristic
2#22611686C211yesmaximal, characteristic, complemented
3C2×#17988405C211yesmaximal, characteristic, complemented
4C2×#17988372C211yesmaximal, characteristic
5C2×#17988370C211yesmaximal, characteristic
6#22608020C211yesmaximal, characteristic, complemented
7C73×#1379C211yesmaximal, characteristic, complemented
8C2×#14556599C411yescharacteristic
9C2×#14556597C2211yescharacteristic
10#17989055C411yescharacteristic
11C2×#14556531C2211yescharacteristic
12C22×#11924003C2211yescharacteristic
13#17988544—21no—
14#17988543C411yescharacteristic
15#17988541—21no—
16#17988539—21no—
17M16×Dic73C411yescharacteristic
18C2×C8×Dic73C2211yescharacteristic
19C4×C8×D73—21no—
20#17988405—21no—
21#17988405—21no—
22#17988405—21no—
23#17988405—21no—
24#17988372—22no—
25#17988370—22no—
26C2×M32×C73C2211yescharacteristic
27C22×C16×C73C2211yescharacteristic
28#405×C73C2211yescharacteristic
29C2×#11924028C2×C411yescharacteristic
30#14556599—22no—
31#14556599—22no—
32#14556597—21no—
33#14556597—21no—
34#14556597D412yes—
35#14556597Q812yes—
36C2×#11924012C2×C411yescharacteristic
37C2×#11924011—21no—
38C2×#11924011—21no—
39C22×#10596831C2×C411yescharacteristic
40C2×C8×D73—21no—
41C2×C8×D73—21no—
42#14556556C811yescharacteristic
43#14556556C811yescharacteristic
44#14556553C811yescharacteristic
45#14556553C811yescharacteristic
46#14556551—21no—
47#14556551—21no—
48#14556548—21no—
49C2×C4×Dic73C2×C411yescharacteristic
50C42×D73—21no—
51#14556531—21no—
52#14556531—21no—
53C2×#11924003—21no—
54C2×#11924003—21no—
55C2×#11924003—21no—
56C2×#11924003—21no—
57#14556502—21no—
58#14556501—21no—
59C4×#10596831—21no—
60C8×Dic73—21no—
61C8×Dic73D411yescharacteristic
62C8×Dic73D411yescharacteristic
63C8×Dic73D411yescharacteristic
64C8×Dic73D411yescharacteristic
65C2×M16×C73C2×C411yescharacteristic
66C22×C8×C73C2311yescharacteristic
67#117×C73C2×C411yescharacteristic
68M32×C73—21no—
69M32×C73—21no—
70C2×C16×C73—21no—
71C2×C16×C73—21no—
72C2×C16×C73—21no—
73C2×C16×C73—21no—
74#97×C73—21no—
75C4×C8×C73—21no—
76#11924028—21no—
77#11924028—21no—
78#11924028C4⋊C412yes—
79#11924028M1612yes—
80C2×Dic146C2×C811yescharacteristic
81C2×D292C2×C811yescharacteristic
82C2×C22⋊D73—21no—
83C22×Dic73M1611yescharacteristic
84C22×Dic73M1611yescharacteristic
85C2×C4×D73—21no—
86C2×C4×D73—21no—
87C2×C4×D73—21no—
88#11924012—21no—
89#11924012C4⋊C412yes—
90#11924011—24no—
91#11924011—22no—
92#11924011—22no—
93C2×#10596831—21no—
94C2×#10596831—21no—
95C2×#10596831—21no—
96C2×#10596831C22⋊C411yescharacteristic
97C2×#10596831C22⋊C411yescharacteristic
98C8×D73—24no—
99C8×D73—22no—
100C8×D73—22no—
101#11924007—21no—
102#11924007—21no—
103#11924005—21no—
104#11924005—21no—
105C4×Dic73—21no—
106C4×Dic73—21no—
107C4×Dic73C22⋊C411yescharacteristic
108C4×Dic73C22⋊C411yescharacteristic
109C4×Dic73C2×C811yescharacteristic
110C4×Dic73C2×C811yescharacteristic
111#11924003—41no—
112#11924003—41no—
113C22×C4×C73C22×C411yescharacteristic
114M16×C73—21no—
115M16×C73M1612yes—
116C2×C8×C73—21no—
117C2×C8×C73C2×D411yescharacteristic
118C2×C8×C73C2×D411yescharacteristic
119C2×C8×C73C2×D411yescharacteristic
120C2×C8×C73C2×Q811yescharacteristic
121C2×C8×C73#4111yescharacteristic
122C2×C8×C73#4111yescharacteristic
123C4⋊C4×C73C2×C811yescharacteristic
124C4⋊C4×C73C2×C811yescharacteristic
125C22⋊C4×C73—21no—
126C42×C73—21no—
127C16×C73—41no—
128C16×C73—41no—
129C23×C73C2×M1611yescharacteristic
130C22×D73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73C2×C22⋊C411yescharacteristic
134C2×C4×C73C2×C4⋊C411yescharacteristic
135C2×C4×C73#11711yescharacteristic
136C2×C4×C73C22×C811yescharacteristic
137C2×C4×C73C2×M1611yescharacteristic
138C2×C4×C73C2×M1611yescharacteristic
139C22⋊D73—22no—
140C22⋊D73—22no—
141C2×Dic73—21no—
142C2×Dic73—22no—
143C2×Dic73—41no—
144C2×Dic73C22⋊C811yescharacteristic
145C2×Dic73C22⋊C811yescharacteristic
146C2×Dic73C22⋊C811yescharacteristic
147C2×Dic73C22⋊C811yescharacteristic
148D292—21no—
149D292C4⋊C812yes—
150C4×D73—22no—
151C4×D73—22no—
152C4×D73—42no—
153C4×D73—42no—
154Dic146—21no—
155Dic146C4⋊C812yes—
156C8×C73—22no—
157C8×C73#12111yescharacteristic
158C8×C73#12111yescharacteristic
159C8×C73C22⋊Q811yescharacteristic
160C8×C73C22⋊Q811yescharacteristic
161#10596831—22no—
162#10596831—21no—
163#10596831—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73C2×C22⋊C811yescharacteristic
167C22×C73#42311yescharacteristic
168C22×C73#43211yescharacteristic
169C2×D73—22no—
170C2×D73—41no—
171C2×D73—41no—
172C4×C73—41no—
173C4×C73—41no—
174C4×C73#38011yescharacteristic
175C4×C73#40711yescharacteristic
176C4×C73C2×C4⋊C811yescharacteristic
177C4×C73#43111yescharacteristic
178Dic73—22no—
179Dic73—21no—
180Dic73—21no—
181Dic73—21no—
182Dic73#35012yescomplemented
183#12787—731nomaximal, Sylow
184C2×C73—21no—
185C2×C73—21no—
186C2×C73#179711yescharacteristic
187C2×C73C2×#35011yescharacteristic
188C2×C73#211711yescharacteristic
189D73—42no—
190C4×#131—731no—
191#2150—731no—
192C2×C4⋊C16—731no—
193C2×#350—731no—
194C2×#350—731no—
195#1379—731no—
196#1379D7311yescharacteristic, complemented
197C73#1278711yescharacteristic, complemented, Sylow
198C2×#131—731no—
199C2×#131—731no—
200C4×#41—731no—
201C2×M32—731no—
202C2×M32C2×D7311yescharacteristic
203C22×C16—731no—
204C22×C16C2×D7311yescharacteristic
205#405—731no—
206#405—1461no—
207#405—1461no—
208#405C2×D7311yescharacteristic
209C4×M16—731no—
210C4×M16—1461no—
211C2×C4×C8—731no—
212C2×C4×C8—1461no—
213C4⋊C16—1461no—
214C4⋊C16—1461no—
215C4⋊C16—1461no—
216C4⋊C16—1461no—
217#350—1462no—
218#350—1462no—
219C2×#41—731no—
220#131—732no—
221#131—732no—
222#131—1462no—
223#131—1462no—
224#131—1461no—
225#131—1461no—
226C2×M16—731no—
227C2×M16—1461no—
228C2×M16—1461no—
229C2×M16C4×D7311yescharacteristic
230C22×C8—731no—
231C22×C8—1461no—
232C22×C8—1461no—
233C22×C8C22×D7311yescharacteristic
234C4×Q8—731no—
235C4×Q8—731no—
236C4×D4—731no—
237C4×D4—731no—
238C4×D4—1461no—
239C4×D4—1461no—
240#117—1461no—
241#117C4×D7311yescharacteristic
242C2×C42—731no—
243C2×C42—1461no—
244M32—21no—
245M32—21no—
246M32—1461no—
247M32—1461no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—1461no—
253C2×C16—1461no—
254C2×C16—1461no—
255C2×C16—1461no—
256#97—21no—
257#97—1461no—
258#97—1461no—
259C4×C8—21no—
260C4×C8—731no—
261C4×C8—731no—
262C4×C8—731no—
263C4×C8—731no—
264C4×C8—1461no—
265C4×C8—1461no—
266#41—732no—
267#41—732no—
268#41—1461no—
269#41—1461no—
270C2×Q8—731no—
271C2×D4—731no—
272C2×D4—1461no—
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—1461no—
276C22×C4—1461no—
277C22×C4—1461no—
278C22×C4C2×C4×D7311yescharacteristic
279M16—21no—
280M16—732no—
281M16—1464no—
282M16—1461no—
283M16—1462no—
284M16—1462no—
285M16#1192401112yes—
286C2×C8—21no—
287C2×C8—731no—
288C2×C8—731no—
289C2×C8—1464no—
290C2×C8—1461no—
291C2×C8—1461no—
292C2×C8—1461no—
293C2×C8—1462no—
294C2×C8—1462no—
295C2×C8D4×D7311yescharacteristic
296C2×C8D4×D7311yescharacteristic
297C2×C8D4×D7311yescharacteristic
298C2×C8Q8×D7311yescharacteristic
299C2×C8#1192402811yescharacteristic
300C2×C8#1192402811yescharacteristic
301C4⋊C4—1461no—
302C4⋊C4—1461no—
303C4⋊C4C8×D7311yescharacteristic
304C4⋊C4C8×D7311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—1461no—
307C22⋊C4—1461no—
308C42—21no—
309C42—731no—
310C42—731no—
311C42—731no—
312C42—731no—
313C42—1461no—
314C42—1461no—
315C16—41no—
316C16—41no—
317C16—2921no—
318C16—2921no—
319C23—1461no—
320C23M16×D7311yescharacteristic
321Q8—732no—
322Q8—1461no—
323D4—732no—
324D4—1462no—
325D4—1462no—
326D4—1461no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—2922no—
330C2×C4—2922no—
331C2×C4—2921no—
332C2×C4—731no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—731no—
336C2×C4—1462no—
337C2×C4—1461no—
338C2×C4—1462no—
339C2×C4—1462no—
340C2×C4C22⋊C4×D7311yescharacteristic
341C2×C4C4⋊C4×D7311yescharacteristic
342C2×C4#1455654811yescharacteristic
343C2×C4C2×C8×D7311yescharacteristic
344C2×C4M16×D7311yescharacteristic
345C2×C4C2×#1192401111yescharacteristic
346C8—22no—
347C8—1462no—
348C8—1461no—
349C8—1461no—
350C8#1455656411yescharacteristic
351C8#1455656411yescharacteristic
352C8#1455656911yescharacteristic
353C8#1455656911yescharacteristic
354C22—21no—
355C22—21no—
356C22—2921no—
357C22—2921no—
358C22—1462no—
359C22C22⋊C8×D7311yescharacteristic
360C22#1798860911yescharacteristic
361C22#1798864211yescharacteristic
362C4—41no—
363C4—41no—
364C4—732no—
365C4—1461no—
366C4—1461no—
367C4—1461no—
368C4—1462no—
369C4#1798844611yescharacteristic
370C4#1798854911yescharacteristic
371C4C4⋊C8×D7311yescharacteristic
372C4#1798863811yescharacteristic
373C2—21no—
374C2—21no—
375C2—2922no—
376C2#2260991011yescharacteristic
377C2#350×D7311yescharacteristic
378C2#2261155711yescharacteristic
subgroupG/H
centerC2×C8D4×D73
commutatorC2×C4×C73C22×C8
FrattiniC22×C8C22×D73
FittingC73×#1379C2
socleC22×C73C2×C22⋊C8
prime radicalC2×#11924028C2×C4
cosocleC22×C8×C73C23
hypercenter#1379D73
hypocenterC73#12787
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1379

Complements

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

NH ≅ G/Ntype
2. #22611686C2semidirect
3. C2×#17988405C2semidirect
6. #22608020C2semidirect
7. C73×#1379C2semidirect
182. Dic73#350semidirect
196. #1379D73semidirect
197. C73#12787semidirect

Maximal subgroups

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

subgroupindex
#226183532
#226116862
C2×#179884052
C2×#179883722
C2×#179883702
#226080202
C73×#13792
#1278773