Finite Group Databasebeta

← #33069961

Subgroups — #33069961

Order 18688.

638 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619740C211yesmaximal, characteristic
2#22619740C211yesmaximal, characteristic
3C8×#11924028C211yesmaximal, characteristic
4#22609386C214yesmaximal, complemented
5#22609379C214yesmaximal, complemented
6#22608690C211yesmaximal, characteristic, complemented
7#22608616C211yesmaximal, characteristic, complemented
8#22608612C211yesmaximal, characteristic, complemented
9C2×#487×C73C211yesmaximal, characteristic, complemented
10C4×#11924028C2211yescharacteristic
11#17988879—21no—
12#17988879C2212yes—
13#17988874—21no—
14#17988874C2212yes—
15#17988869—21no—
16#17988869C2212yes—
17#17988864—21no—
18#17988864C2212yes—
19C8×Dic146C2212yes—
20C8×D292C2212yes—
21C8×C22⋊D73—22no—
22#17988640C2211yescharacteristic
23#17988638—21no—
24#17988627—21no—
25#17988627—21no—
26#17988611C2211yescharacteristic
27#17988611C2211yescharacteristic
28#17988586—21no—
29#17988586—21no—
30C4×C8×D73—21no—
31#17988340C2214yes—
32#17988336C2214yes—
33#17988333C2214yes—
34C2×C4⋊Q8×C73C2211yescharacteristic
35C2×C4⋊Q8×C73C2211yescharacteristic
36#487×C73—21no—
37#487×C73—21no—
38#487×C73C2214yes—
39C2×#103×C73—22no—
40C2×C4×C8×C73C2211yescharacteristic
41C2×#11924028D411yescharacteristic
42C2×#11924012—21no—
43C2×#11924012—21no—
44C2×C8×D73—22no—
45C4×Dic146D411yescharacteristic
46C4×Dic146C2311yescharacteristic
47C4×D292D411yescharacteristic
48C4×D292C2311yescharacteristic
49C4×C22⋊D73—21no—
50C4×C22⋊D73—21no—
51#14556550D411yescharacteristic
52#14556548—21no—
53C42×D73—21no—
54#14556524—22no—
55#14556524—22no—
56#14556522—22no—
57#14556522—22no—
58C4⋊#10596831—21no—
59C4⋊#10596831—21no—
60C4⋊#10596831C2312yes—
61C4⋊#10596831C2312yes—
62C4⋊#10596831C2312yes—
63#14556520—22no—
64#14556514—22no—
65#14556514—22no—
66#14556511—22no—
67#14556511—22no—
68C22⋊#10596831—21no—
69#14556503—22no—
70C4×#10596831—21no—
71C8×Dic73—22no—
72C22×Q8×C73—21no—
73C22×Q8×C73—21no—
74C22×C8×C73D412yes—
75C4⋊Q8×C73—21no—
76C4⋊Q8×C73—21no—
77C4⋊Q8×C73—21no—
78C4⋊Q8×C73—21no—
79C4⋊Q8×C73—21no—
80C4⋊Q8×C73—21no—
81C4⋊Q8×C73C2312yes—
82C4⋊Q8×C73C2312yes—
83C2×C4⋊C4×C73—21no—
84C2×C4⋊C4×C73—21no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—21no—
87C2×C42×C73C2311yescharacteristic
88#103×C73—24no—
89#103×C73—24no—
90C4×C8×C73D411yescharacteristic
91C4×C8×C73D411yescharacteristic
92C4×C8×C73C2312yes—
93#11924028—22no—
94#11924028Q1614yes—
95C2×Dic146C2×D411yescharacteristic
96C2×D292C2×D411yescharacteristic
97C2×C22⋊D73—21no—
98C2×C4×D73—21no—
99C2×C4×D73—21no—
100C2×C4×D73—21no—
101#11924012—42no—
102#11924012—42no—
103C2×#10596831—22no—
104C2×#10596831—22no—
105C2×#10596831—22no—
106C8×D73—44no—
107C4⋊Dic73C2×D411yescharacteristic
108C4⋊Dic73C2×D411yescharacteristic
109#11924007—21no—
110#11924007—21no—
111C22⋊Dic73—21no—
112#11924005—21no—
113#11924005—21no—
114C4×Dic73—21no—
115C4×Dic73—21no—
116C4×Dic73—21no—
117C2×Q8×C73—22no—
118C2×Q8×C73—22no—
119C2×Q8×C73—44no—
120C2×Q8×C73—41no—
121C2×Q8×C73—41no—
122C2×Q8×C73—82no—
123C22×C4×C73—41no—
124C22×C4×C73—41no—
125C22×C4×C73C2×D411yescharacteristic
126C22×C4×C73C2×D411yescharacteristic
127C22×C4×C73#4111yescharacteristic
128C2×C8×C73—42no—
129C2×C8×C73C2×D412yes—
130C2×C8×C73C2×D412yes—
131C4⋊C4×C73—22no—
132C4⋊C4×C73—22no—
133C4⋊C4×C73—22no—
134C4⋊C4×C73—22no—
135C4⋊C4×C73—41no—
136C4⋊C4×C73—41no—
137C4⋊C4×C73—41no—
138C4⋊C4×C73—41no—
139C42×C73C2×D411yescharacteristic
140C42×C73C2×D411yescharacteristic
141C42×C73#4111yescharacteristic
142C42×C73C2411yescharacteristic
143C23×C73#12111yescharacteristic
144C22×D73—21no—
145Q8×C73—44no—
146Q8×C73—82no—
147Q8×C73—82no—
148Q8×C73—82no—
149C2×C4×C73—22no—
150C2×C4×C73—22no—
151C2×C4×C73—42no—
152C2×C4×C73—42no—
153C2×C4×C73—82no—
154C2×C4×C73—82no—
155C2×C4×C73#12111yescharacteristic
156C2×C4×C73#12111yescharacteristic
157C2×C4×C73#12111yescharacteristic
158C2×C4×C73C2×Q1612yes—
159C2×C4×C73#13512yes—
160C2×C4×C73C22×D411yescharacteristic
161C2×C4×C73C22×D411yescharacteristic
162C2×C4×C73C2×#4111yescharacteristic
163C22⋊D73—24no—
164C2×Dic73—21no—
165C2×Dic73—21no—
166C2×Dic73—21no—
167D292—21no—
168D292C2×Q1612yes—
169C4×D73—24no—
170C4×D73—42no—
171C4×D73—42no—
172Dic146—21no—
173Dic146C2×Q1612yes—
174C8×C73—22no—
175C8×C73—22no—
176#10596831—42no—
177#10596831—42no—
178#10596831—42no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73#46712yes—
182C22×C73C2×#12111yescharacteristic
183C2×D73—22no—
184C2×D73—41no—
185C2×D73—41no—
186C4×C73—21no—
187C4×C73—21no—
188C4×C73—82no—
189C4×C73—82no—
190C4×C73#46712yes—
191C4×C73#47112yes—
192C4×C73C22×Q1611yescharacteristic
193C4×C73C2×#13511yescharacteristic
194C4×C73#57512yes—
195Dic73—22no—
196Dic73—41no—
197Dic73—41no—
198#19277—731nomaximal, Sylow
199C2×C73—22no—
200C2×C73#304011yescharacteristic
201C2×C73C2×#46711yescharacteristic
202C2×C73C2×#47111yescharacteristic
203D73—42no—
204C2×#487D7311yescharacteristic, complemented
205#3079—731no—
206#3079—731no—
207C8×#41—731no—
208#1684—734no—
209#1683—734no—
210#1567—731no—
211#1549—731no—
212#1548—731no—
213C73#1927711yescharacteristic, complemented, Sylow
214C2×C4⋊Q8C2×D7311yescharacteristic
215C2×C4⋊Q8C2×D7311yescharacteristic
216C4×#41—731no—
217#487—21no—
218#487—21no—
219#487C2×D7314yes—
220#477—732no—
221#477—1461no—
222#476—732no—
223#476—1461no—
224#475—732no—
225#475—1461no—
226#474—732no—
227#474—1461no—
228C8×Q8—732no—
229C8×D4—732no—
230C8×D4—1462no—
231#431—731no—
232#431—1461no—
233#428—1461no—
234#428—1461no—
235#423—731no—
236#423—731no—
237#417—1461no—
238#417—1461no—
239C2×#103—22no—
240C2×C4×C8—1461no—
241C2×C4×C8C2×D7311yescharacteristic
242#335—734no—
243#333—734no—
244#332—734no—
245C2×#41—731no—
246C22×Q8—21no—
247C22×Q8—21no—
248C2×M16—1461no—
249C2×M16—1461no—
250C22×C8—1462no—
251C22×C8C22⋊D7312yes—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8C22×D7312yes—
259C4⋊Q8C22×D7312yes—
260C4×Q8—731no—
261C4×Q8—731no—
262C4×D4—731no—
263C4×D4—731no—
264C4×D4—1461no—
265C4×D4—1461no—
266#117—731no—
267#117—1461no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C42—1461no—
273C2×C42C22×D7311yescharacteristic
274#107—1462no—
275#107—1462no—
276#106—1462no—
277#106—1462no—
278C4⋊C8—732no—
279C4⋊C8—732no—
280C4⋊C8—732no—
281C4⋊C8—1462no—
282C4⋊C8—1461no—
283C4⋊C8—1461no—
284#103—24no—
285#103—24no—
286#103—1462no—
287#103—1462no—
288#102—1462no—
289#102—1462no—
290C22⋊C8—1461no—
291C22⋊C8—1462no—
292C4×C8—1462no—
293C4×C8—1461no—
294C4×C8C22⋊D7311yescharacteristic
295C4×C8C22⋊D7311yescharacteristic
296C4×C8C22×D7312yes—
297#41—734no—
298#41—1462no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—44no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—82no—
305C2×Q8—731no—
306C2×D4—731no—
307C2×D4—1461no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—1461no—
311C22×C4—1461no—
312C22×C4—1461no—
313C22×C4D4×D7311yescharacteristic
314C22×C4C2×C22⋊D7311yescharacteristic
315C22×C4#1192402711yescharacteristic
316M16—2922no—
317M16—2922no—
318C2×C8—42no—
319C2×C8—2924no—
320C2×C8—1462no—
321C2×C8—1462no—
322C2×C8—1462no—
323C2×C8C2×C22⋊D7312yes—
324C2×C8C2×C22⋊D7312yes—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—731no—
334C4⋊C4—731no—
335C4⋊C4—1461no—
336C4⋊C4—1461no—
337C22⋊C4—1461no—
338C22⋊C4—1461no—
339C22⋊C4—1461no—
340C42—1461no—
341C42—1461no—
342C42—1461no—
343C42D4×D7311yescharacteristic
344C42C2×C22⋊D7311yescharacteristic
345C42#1192402711yescharacteristic
346C42C23×D7311yescharacteristic
347C23—1461no—
348C23#1455656211yescharacteristic
349Q8—44no—
350Q8—82no—
351Q8—82no—
352Q8—82no—
353Q8—732no—
354Q8—1461no—
355D4—732no—
356D4—1464no—
357D4—1461no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—2922no—
365C2×C4—2922no—
366C2×C4—1461no—
367C2×C4—1461no—
368C2×C4—1461no—
369C2×C4—1464no—
370C2×C4#1455656211yescharacteristic
371C2×C4#1455656211yescharacteristic
372C2×C4#1455656211yescharacteristic
373C2×C4Q16×D7312yes—
374C2×C4#1455661412yes—
375C2×C4C2×D4×D7311yescharacteristic
376C2×C4C22×C22⋊D7311yescharacteristic
377C2×C4C2×#1192402711yescharacteristic
378C8—22no—
379C8—22no—
380C8—2922no—
381C8—2922no—
382C8—2922no—
383C22—21no—
384C22—21no—
385C22—2921no—
386C22—2921no—
387C22—1462no—
388C22#1798882512yes—
389C22C2×#1455656211yescharacteristic
390C4—21no—
391C4—21no—
392C4—82no—
393C4—82no—
394C4—2921no—
395C4—2921no—
396C4—1462no—
397C4#1798882512yes—
398C4#1798884712yes—
399C4C2×Q16×D7311yescharacteristic
400C4C2×#1455661411yescharacteristic
401C4#1798938512yes—
402C2—22no—
403C2—2922no—
404C2#2261942111yescharacteristic
405C2C2×#1798882511yescharacteristic
406C2C2×#1798884711yescharacteristic
subgroupG/H
centerC22C2×#14556562
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC2×#487×C73C2
socleC22×C73C2×#121
prime radicalC2×#11924028D4
hypercenterC2×#487D73
hypocenterC73#19277
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. #22609386C2semidirect
5. #22609379C2semidirect
6. #22608690C2semidirect
7. #22608616C2semidirect
8. #22608612C2semidirect
9. C2×#487×C73C2semidirect
204. C2×#487D73semidirect
213. C73#19277semidirect

Maximal subgroups

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

subgroupindex
#226197402
C8×#119240282
#226093862
#226093792
#226086902
#226086162
#226086122
C2×#487×C732
#1927773