Finite Group Databasebeta

← #32977673

Subgroups — #32977673

Order 18688.

818 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989294C211yesmaximal, characteristic
2#22610019C212yesmaximal, complemented
3#22608502C212yesmaximal, complemented
4#22608249C211yesmaximal, characteristic
5C73×#1799C211yesmaximal, characteristic
6#17989294—24no—
7#17989294—24no—
8C2×#14556591C411yescharacteristic, complemented
9C2×#14556582—21no—
10C2×#14556570C411yescharacteristic, complemented
11C2×#14556570C2211yescharacteristic
12C2×#14556568—21no—
13C2×#14556568—21no—
14C2×C4×Dic146C411yescharacteristic, complemented
15C2×D4×Dic73—21no—
16C22×C4⋊Dic73C411yescharacteristic, complemented
17C22×C4⋊Dic73C2211yescharacteristic
18C2×C22⋊#10596831C2212yes—
19#17988349—24no—
20#17988323—24no—
21#17988313—21no—
22#17988311—21no—
23C2×C4×D4×C73C2211yescharacteristic
24C2×#99×C73—21no—
25#380×C73C2212yes—
26#342×C73—21no—
27C22×Dic146—21no—
28C22×Dic146C2×C411yescharacteristic
29C23×Dic73—21no—
30C23×Dic73—21no—
31C22×#10596831—22no—
32#14556591—22no—
33#14556591—22no—
34#14556582—28no—
35#14556570—22no—
36#14556570—22no—
37#14556570—22no—
38#14556570D414yes—
39#14556568—28no—
40#14556568—28no—
41C4×Dic146—22no—
42C4×Dic146—22no—
43D4×Dic73—28no—
44C2×C4⋊Dic73—22no—
45C2×C4⋊Dic73—22no—
46C2×C4⋊Dic73—21no—
47C2×C4⋊Dic73—21no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73—21no—
50C2×C4⋊Dic73C2×C411yescharacteristic
51C2×C4⋊Dic73C2×C411yescharacteristic
52C2×C4⋊Dic73C2×C411yescharacteristic
53C2×C4⋊Dic73D414yes—
54C2×#11924007—21no—
55C2×#11924007—21no—
56C2×#11924007—21no—
57C2×C22⋊Dic73—21no—
58C2×C22⋊Dic73—21no—
59C2×C4×Dic73—21no—
60C22⋊#10596831—22no—
61C22⋊#10596831—22no—
62C22×D4×C73D411yescharacteristic
63C23×C4×C73C2×C411yescharacteristic
64C23×C4×C73C2311yescharacteristic
65C4×D4×C73—22no—
66C4×D4×C73—22no—
67C2×C4⋊C4×C73—22no—
68C2×C4⋊C4×C73D411yescharacteristic
69C2×C22⋊C4×C73—22no—
70C2×C22⋊C4×C73D411yescharacteristic
71C2×C22⋊C4×C73D411yescharacteristic
72C2×C42×C73C2×C411yescharacteristic
73#99×C73—42no—
74#95×C73—22no—
75C2×Dic146—21no—
76C2×Dic146—24no—
77C2×Dic146—42no—
78C2×Dic146—82no—
79C2×Dic146C22⋊C412yes—
80C22×Dic73—21no—
81C22×Dic73—21no—
82C22×Dic73—21no—
83C22×Dic73—21no—
84C22×Dic73—24no—
85C22×Dic73—24no—
86C22×Dic73—82no—
87C22×Dic73—82no—
88C2×#10596831—44no—
89C2×#10596831—42no—
90C4⋊Dic73—24no—
91C4⋊Dic73—24no—
92C4⋊Dic73—21no—
93C4⋊Dic73—21no—
94C4⋊Dic73—21no—
95C4⋊Dic73—24no—
96C4⋊Dic73C22⋊C412yes—
97C4⋊Dic73C22⋊C412yes—
98C4⋊Dic73C22⋊C412yes—
99#11924007—24no—
100#11924007—24no—
101#11924007—24no—
102C22⋊Dic73—24no—
103C22⋊Dic73—24no—
104C4×Dic73—24no—
105C24×C73C22⋊C411yescharacteristic
106C24×C73C2×D411yescharacteristic
107C2×D4×C73—22no—
108C2×D4×C73—22no—
109C2×D4×C73SD1612yes—
110C2×D4×C73Q1612yes—
111C22×C4×C73—21no—
112C22×C4×C73—21no—
113C22×C4×C73—42no—
114C22×C4×C73—42no—
115C22×C4×C73—42no—
116C22×C4×C73C22⋊C411yescharacteristic
117C22×C4×C73C22⋊C411yescharacteristic
118C22×C4×C73C22⋊C411yescharacteristic
119C22×C4×C73C22×C411yescharacteristic
120C22×C4×C73C2×D412yes—
121C22×C4×C73C2×D412yes—
122C22×C4×C73C2×D411yescharacteristic
123C4⋊C4×C73—22no—
124C4⋊C4×C73—44no—
125C22⋊C4×C73—22no—
126C22⋊C4×C73—22no—
127C22⋊C4×C73—42no—
128C22⋊C4×C73—42no—
129C42×C73—21no—
130C42×C73—21no—
131C23×C73—21no—
132C23×C73—21no—
133C23×C73—41no—
134C23×C73—41no—
135C23×C73—41no—
136C23×C73—41no—
137C23×C73#10312yes—
138C23×C73C2×C22⋊C411yescharacteristic
139C23×C73#12012yes—
140C23×C73C2×SD1611yescharacteristic
141C23×C73C2×Q1611yescharacteristic
142C23×C73#13712yes—
143D4×C73—24no—
144D4×C73—24no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—24no—
148C2×C4×C73—22no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—42no—
152C2×C4×C73—41no—
153C2×C4×C73—42no—
154C2×C4×C73—42no—
155C2×C4×C73—41no—
156C2×C4×C73—41no—
157C2×C4×C73—82no—
158C2×C4×C73—82no—
159C2×C4×C73—82no—
160C2×C4×C73#10312yes—
161C2×C4×C73C2×C22⋊C411yescharacteristic
162C2×C4×C73C2×C22⋊C411yescharacteristic
163C2×C4×C73#12012yes—
164C2×Dic73—22no—
165C2×Dic73—22no—
166C2×Dic73—22no—
167C2×Dic73—22no—
168C2×Dic73—42no—
169C2×Dic73—42no—
170C2×Dic73—42no—
171C2×Dic73—42no—
172C2×Dic73—84no—
173C2×Dic73—84no—
174Dic146—42no—
175Dic146—42no—
176Dic146—84no—
177#10596831—82no—
178C22×C73—21no—
179C22×C73—22no—
180C22×C73—21no—
181C22×C73—22no—
182C22×C73—22no—
183C22×C73—41no—
184C22×C73—41no—
185C22×C73—42no—
186C22×C73—42no—
187C22×C73—42no—
188C22×C73—41no—
189C22×C73—41no—
190C22×C73#37911yescharacteristic
191C22×C73C2×#10311yescharacteristic
192C22×C73#41911yescharacteristic
193C22×C73#44812yes—
194C22×C73#45112yes—
195C4×C73—22no—
196C4×C73—21no—
197C4×C73—22no—
198C4×C73—41no—
199C4×C73—41no—
200C4×C73—162no—
201C4×C73#41012yes—
202Dic73—42no—
203Dic73—42no—
204Dic73—42no—
205Dic73—42no—
206#8380—731nomaximal, Sylow
207C2×C73—22no—
208C2×C73—21no—
209C2×C73—21no—
210C2×C73—22no—
211C2×C73—42no—
212C2×C73#178211yescharacteristic
213C2×C73#178711yescharacteristic
214C2×C73#179511yescharacteristic
215C2×#554—731no—
216#1824—732no—
217#1799D7311yescharacteristic
218#1520—732no—
219#1459—731no—
220C73#838011yescharacteristic, complemented, Sylow
221#554—1464no—
222#554—1464no—
223C2×C4⋊Q8—731no—
224C2×#125—1461no—
225C2×C22⋊Q8—731no—
226C2×C22⋊Q8—731no—
227C2×C22⋊Q8—1461no—
228C2×C22⋊Q8—1461no—
229C2×C4×Q8—731no—
230C2×C4×D4—1461no—
231C2×C4×D4C2×D7311yescharacteristic
232C22×C4⋊C4—731no—
233C22×C4⋊C4—731no—
234C2×#99—21no—
235C2×C22⋊C8—732no—
236#380C2×D7312yes—
237#342—21no—
238#340—1464no—
239#328—1464no—
240#324—1461no—
241#323—1461no—
242C22×Q8—731no—
243C22×Q8—1461no—
244C22×D4C22⋊D7311yescharacteristic
245C23×C4—1461no—
246C23×C4—1461no—
247C23×C4C4×D7311yescharacteristic
248C23×C4C22×D7311yescharacteristic
249C22×C8—1462no—
250C4⋊Q8—1462no—
251C4⋊Q8—1462no—
252#125—1468no—
253C22⋊Q8—734no—
254C22⋊Q8—1468no—
255C22⋊Q8—1468no—
256C22⋊Q8—1462no—
257C22⋊Q8—1462no—
258C22⋊Q8—1462no—
259C4×Q8—1462no—
260C4×Q8—1462no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—1468no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—731no—
266C2×C4⋊C4—731no—
267C2×C4⋊C4—731no—
268C2×C4⋊C4—734no—
269C2×C4⋊C4—1462no—
270C2×C4⋊C4—1462no—
271C2×C4⋊C4—1461no—
272C2×C4⋊C4—1461no—
273C2×C4⋊C4—1461no—
274C2×C4⋊C4—1461no—
275C2×C4⋊C4—1462no—
276C2×C4⋊C4—1461no—
277C2×C4⋊C4—1461no—
278C2×C4⋊C4D29211yescharacteristic
279C2×C22⋊C4—22no—
280C2×C22⋊C4—1461no—
281C2×C22⋊C4—1461no—
282C2×C22⋊C4D29211yescharacteristic
283C2×C22⋊C4C22⋊D7311yescharacteristic
284C2×C42—1461no—
285C2×C42C4×D7311yescharacteristic
286#99—42no—
287C22⋊C8—1462no—
288C22⋊C8—1462no—
289#95—22no—
290C24#1192400511yescharacteristic
291C24C2×C22⋊D7311yescharacteristic
292C2×Q8—2922no—
293C2×Q8—5842no—
294C2×Q8—732no—
295C2×Q8—1464no—
296C2×Q8—1461no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4#1192401612yes—
300C2×D4#1192401812yes—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—5842no—
307C22×C4—5842no—
308C22×C4—1461no—
309C22×C4—1461no—
310C22×C4—1461no—
311C22×C4—1461no—
312C22×C4—1464no—
313C22×C4—1464no—
314C22×C4#1192400511yescharacteristic
315C22×C4#1192400511yescharacteristic
316C22×C4#1192400511yescharacteristic
317C22×C4C2×C4×D7311yescharacteristic
318C22×C4D4×D7312yes—
319C22×C4D4×D7312yes—
320C22×C4C2×D29211yescharacteristic
321C2×C8—2924no—
322C2×C8—2922no—
323C4⋊C4—22no—
324C4⋊C4—44no—
325C4⋊C4—732no—
326C4⋊C4—732no—
327C4⋊C4—732no—
328C4⋊C4—1464no—
329C4⋊C4—1464no—
330C4⋊C4—1464no—
331C4⋊C4—1464no—
332C4⋊C4—1461no—
333C4⋊C4—1461no—
334C4⋊C4—1461no—
335C4⋊C4—1464no—
336C4⋊C4—1464no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C22⋊C4—1464no—
342C22⋊C4—1464no—
343C42—21no—
344C42—21no—
345C42—1464no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23#1455651412yes—
353C23C2×#1192400511yescharacteristic
354C23#1455655912yes—
355C23C2×#1192401611yescharacteristic
356C23C2×#1192401811yescharacteristic
357C23#1455662112yes—
358Q8—2922no—
359Q8—2922no—
360Q8—5844no—
361D4—24no—
362D4—24no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—2922no—
379C2×C4—2922no—
380C2×C4—2922no—
381C2×C4—2922no—
382C2×C4—5844no—
383C2×C4—5844no—
384C2×C4—1462no—
385C2×C4—1462no—
386C2×C4—1462no—
387C2×C4—1462no—
388C2×C4#1455651412yes—
389C2×C4C22⋊C4×D7311yescharacteristic
390C2×C4C22⋊C4×D7311yescharacteristic
391C2×C4#1455656112yes—
392C8—5842no—
393C22—21no—
394C22—22no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—42no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22#1798844211yescharacteristic
406C22C2×#1455651411yescharacteristic
407C22#1798859511yescharacteristic
408C22#1798872512yes—
409C22#1798874212yes—
410C4—22no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—162no—
416C4—2922no—
417C4—2922no—
418C4—2922no—
419C4—2922no—
420C4#1798855912yes—
421C2—22no—
422C2—21no—
423C2—21no—
424C2—22no—
425C2—42no—
426C2#2260984711yescharacteristic
427C2#2260986511yescharacteristic
428C2#2260989911yescharacteristic
subgroupG/H
centerC22#17988442
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1799C2
socleC22×C73#379
prime radicalC22×D4×C73D4
cosocleC23×C4×C73C23
hypercenter#1799D73
hypocenterC73#8380
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #22610019C2semidirect
3. #22608502C2semidirect
8. C2×#14556591C4semidirect
10. C2×#14556570C4semidirect
14. C2×C4×Dic146C4semidirect
16. C22×C4⋊Dic73C4semidirect
220. C73#8380semidirect

Maximal subgroups

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

subgroupindex
C2×#179892942
#226100192
#226085022
#226082492
C73×#17992
#838073