Finite Group Databasebeta

← #32978663

Subgroups — #32978663

Order 18688.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988471C211yesmaximal, characteristic
2#22609911C211yesmaximal, characteristic
3C2×#17988312C212yesmaximal
4#22607773C212yesmaximal
5C73×#1797C211yesmaximal, characteristic
6C22×#11924007C411yescharacteristic
7C22×#11924007C2211yescharacteristic
8C2×C4⋊#10596831—21no—
9C2×C22⋊#10596831C2212yes—
10#17988471—21no—
11#17988471—21no—
12#17988471—21no—
13#17988471—21no—
14C2×#14556498C411yescharacteristic
15C2×#14556498C411yescharacteristic
16C2×#14556498C411yescharacteristic
17C2×#14556498C2211yescharacteristic
18#17988342—21no—
19#17988312—24no—
20C22×C42×C73C2211yescharacteristic
21C2×C4⋊C8×C73—21no—
22C2×C22⋊C8×C73C2212yes—
23#336×C73—21no—
24C23×Dic73C2×C411yescharacteristic
25C23×Dic73C2×C411yescharacteristic
26C23×Dic73C2×C411yescharacteristic
27C23×Dic73C2×C411yescharacteristic
28C22×#10596831—22no—
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×#11924007—21no—
35C2×#11924007—42no—
36C2×#11924007D412yes—
37C2×#11924007Q812yes—
38C4⋊#10596831—42no—
39C22⋊#10596831—22no—
40C22⋊#10596831—22no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49C23×C4×C73C2×C411yescharacteristic
50C23×C4×C73C2×C411yescharacteristic
51C23×C4×C73C2311yescharacteristic
52C22×C8×C73—22no—
53C2×C42×C73—42no—
54C2×C42×C73D411yescharacteristic
55C2×C42×C73D411yescharacteristic
56C2×C42×C73D411yescharacteristic
57C2×C42×C73D411yescharacteristic
58C4⋊C8×C73—42no—
59C22⋊C8×C73—22no—
60C22⋊C8×C73—22no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—22no—
66C22×Dic73—22no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73—22no—
70C22×Dic73—22no—
71C22×Dic73—41no—
72C22×Dic73—41no—
73C22×Dic73—41no—
74C22×Dic73—41no—
75C22×Dic73—41no—
76C22×Dic73—41no—
77C22×Dic73C4⋊C412yes—
78C22×Dic73C4⋊C412yes—
79C2×#10596831—42no—
80C2×#10596831—42no—
81C2×#10596831—42no—
82#11924007—22no—
83#11924007—22no—
84#11924007—22no—
85#11924007—22no—
86#11924007—42no—
87#11924007—42no—
88C24×C73C22×C411yescharacteristic
89C22×C4×C73—22no—
90C22×C4×C73—22no—
91C22×C4×C73—22no—
92C22×C4×C73—22no—
93C22×C4×C73—41no—
94C22×C4×C73—41no—
95C22×C4×C73—41no—
96C22×C4×C73—41no—
97C22×C4×C73C22⋊C411yescharacteristic
98C22×C4×C73C22⋊C411yescharacteristic
99C22×C4×C73C22⋊C411yescharacteristic
100C22×C4×C73C22⋊C411yescharacteristic
101C22×C4×C73C2×D411yescharacteristic
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73C2×D411yescharacteristic
104C22×C4×C73C2×Q811yescharacteristic
105C22×C4×C73#4111yescharacteristic
106C22×C4×C73#4111yescharacteristic
107C2×C8×C73—42no—
108C2×C8×C73—42no—
109C2×C8×C73—42no—
110C42×C73—22no—
111C42×C73—22no—
112C42×C73—41no—
113C42×C73—41no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73C2×C22⋊C411yescharacteristic
119C23×C73C2×C4⋊C411yescharacteristic
120C23×C73#11711yescharacteristic
121C23×C73#13112yes—
122C23×C73#13112yes—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—41no—
140C2×C4×C73—41no—
141C2×C4×C73—44no—
142C2×C4×C73—44no—
143C2×C4×C73#9912yes—
144C2×C4×C73#10112yes—
145C2×C4×C73#12111yescharacteristic
146C2×C4×C73#12111yescharacteristic
147C2×C4×C73C22⋊Q811yescharacteristic
148C2×C4×C73C22⋊Q811yescharacteristic
149C2×Dic73—22no—
150C2×Dic73—22no—
151C2×Dic73—24no—
152C2×Dic73—42no—
153C2×Dic73—41no—
154C2×Dic73—41no—
155C2×Dic73—41no—
156C2×Dic73—41no—
157C2×Dic73—42no—
158C2×Dic73—42no—
159C2×Dic73—41no—
160C2×Dic73—41no—
161C2×Dic73—41no—
162C2×Dic73—41no—
163C2×Dic73—41no—
164C2×Dic73—41no—
165C2×Dic73—82no—
166C2×Dic73—82no—
167C8×C73—82no—
168#10596831—82no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—22no—
174C22×C73—22no—
175C22×C73—22no—
176C22×C73—22no—
177C22×C73#38011yescharacteristic
178C22×C73#40811yescharacteristic
179C22×C73#40811yescharacteristic
180C22×C73C2×#9911yescharacteristic
181C22×C73#41011yescharacteristic
182C22×C73C2×#10111yescharacteristic
183C22×C73#41311yescharacteristic
184C22×C73#42412yes—
185C22×C73#43312yes—
186C4×C73—21no—
187C4×C73—21no—
188C4×C73—21no—
189C4×C73—21no—
190C4×C73—22no—
191C4×C73—22no—
192C4×C73—41no—
193C4×C73—41no—
194Dic73—42no—
195Dic73—42no—
196Dic73—81no—
197Dic73—81no—
198#8562—731nomaximal, Sylow
199C2×C73—22no—
200C2×C73—22no—
201C2×C73#146811yescharacteristic
202C2×C73#147011yescharacteristic
203C2×C73#147211yescharacteristic
204C2×C73#147311yescharacteristic
205C2×C73#179811yescharacteristic
206C2×C73#179911yescharacteristic
207C2×C73#180111yescharacteristic
208C2×#387—731no—
209#1797—731no—
210#1797D7311yescharacteristic
211C2×#324—732no—
212#1280—732no—
213C73#856211yescharacteristic, complemented, Sylow
214C22×C4⋊C4—731no—
215C22×C4⋊C4—731no—
216C22×C42C2×D7311yescharacteristic
217C2×C4⋊C8—21no—
218C2×C4⋊C8—1461no—
219C2×C22⋊C8—732no—
220C2×C22⋊C8C2×D7312yes—
221#387—1461no—
222#387—1461no—
223#387—1461no—
224#387—1461no—
225C2×#95—731no—
226C2×#95—731no—
227C2×#95—731no—
228C2×#95—731no—
229#336—21no—
230#336—1461no—
231#324—1464no—
232C23×C4—731no—
233C23×C4—731no—
234C23×C4—731no—
235C23×C4—731no—
236C23×C4C4×D7311yescharacteristic
237C23×C4C4×D7311yescharacteristic
238C23×C4C22×D7311yescharacteristic
239C22×C8—22no—
240C22×C8—1462no—
241C2×C4⋊C4—2922no—
242C2×C4⋊C4—732no—
243C2×C4⋊C4—732no—
244C2×C4⋊C4—1461no—
245C2×C4⋊C4—1461no—
246C2×C4⋊C4—1461no—
247C2×C4⋊C4—1461no—
248C2×C4⋊C4—1461no—
249C2×C4⋊C4—1461no—
250C2×C42—42no—
251C2×C42D29211yescharacteristic
252C2×C42D29211yescharacteristic
253C2×C42C22⋊D7311yescharacteristic
254C2×C42C22⋊D7311yescharacteristic
255C4⋊C8—42no—
256C4⋊C8—2922no—
257C22⋊C8—22no—
258C22⋊C8—22no—
259C22⋊C8—1462no—
260C22⋊C8—1462no—
261#95—1461no—
262#95—1461no—
263#95—1461no—
264#95—1461no—
265#95—1461no—
266#95—1461no—
267#95—1461no—
268#95—1461no—
269C24C2×C4×D7311yescharacteristic
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—2921no—
279C22×C4—2921no—
280C22×C4—2921no—
281C22×C4—2921no—
282C22×C4—2921no—
283C22×C4—2921no—
284C22×C4—732no—
285C22×C4—732no—
286C22×C4—1461no—
287C22×C4—1461no—
288C22×C4—1461no—
289C22×C4—1461no—
290C22×C4—1461no—
291C22×C4—1461no—
292C22×C4—1462no—
293C22×C4—1462no—
294C22×C4—1462no—
295C22×C4—1462no—
296C22×C4#1192400511yescharacteristic
297C22×C4#1192400511yescharacteristic
298C22×C4#1192400511yescharacteristic
299C22×C4#1192400511yescharacteristic
300C22×C4D4×D7311yescharacteristic
301C22×C4C2×C22⋊D7311yescharacteristic
302C22×C4C2×D29211yescharacteristic
303C22×C4Q8×D7311yescharacteristic
304C22×C4#1192402711yescharacteristic
305C22×C4#1192402911yescharacteristic
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—2922no—
310C2×C8—2922no—
311C2×C8—2922no—
312C4⋊C4—2922no—
313C4⋊C4—2922no—
314C4⋊C4—1462no—
315C4⋊C4—1462no—
316C4⋊C4—1462no—
317C4⋊C4—1462no—
318C42—22no—
319C42—22no—
320C42—41no—
321C42—41no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23C2×#1192400511yescharacteristic
327C23C4⋊C4×D7311yescharacteristic
328C23#1455654911yescharacteristic
329C23#1455659712yes—
330C23#1455659912yes—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—2922no—
352C2×C4—2922no—
353C2×C4—2921no—
354C2×C4—2921no—
355C2×C4—2921no—
356C2×C4—2921no—
357C2×C4—2922no—
358C2×C4—2921no—
359C2×C4—2921no—
360C2×C4—2921no—
361C2×C4—2921no—
362C2×C4—2921no—
363C2×C4—2921no—
364C2×C4—5842no—
365C2×C4—5842no—
366C2×C4—1464no—
367C2×C4—1462no—
368C2×C4—1462no—
369C2×C4#1455650512yes—
370C2×C4#1455650912yes—
371C2×C4#1455656211yescharacteristic
372C2×C4#1455656611yescharacteristic
373C2×C4#1455656711yescharacteristic
374C2×C4#1455657111yescharacteristic
375C8—82no—
376C8—5842no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—21no—
384C22—21no—
385C22#1798844411yescharacteristic
386C22#1798855311yescharacteristic
387C22#1798855511yescharacteristic
388C22C2×#1455650511yescharacteristic
389C22#1798856011yescharacteristic
390C22C2×#1455650911yescharacteristic
391C22#1798856911yescharacteristic
392C22#1798861212yes—
393C22#1798864712yes—
394C4—22no—
395C4—22no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—2922no—
403C4—2922no—
404C4—5841no—
405C4—5841no—
406C2—22no—
407C2—22no—
408C2#2260828011yescharacteristic
409C2#2260828811yescharacteristic
410C2#2260829411yescharacteristic
411C2#2260829811yescharacteristic
412C2#2260991211yescharacteristic
413C2#2260991611yescharacteristic
414C2#2260992411yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutator, prime radicalC24×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1797C2
socleC23×C73C2×C22⋊C4
cosocleC23×C4×C73C23
hypercenter#1797D73
hypocenterC73#8562
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
213. C73#8562semidirect

Maximal subgroups

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

subgroupindex
C2×#179884712
#226099112
C2×#179883122
#226077732
C73×#17972
#856273