Finite Group Databasebeta

← #32972561

Subgroups — #32972561

Order 18688.

844 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22609841C211yesmaximal, characteristic
2#22608154C211yesmaximal, characteristic
3C73×C22⋊#95C211yesmaximal, characteristic
4C22×C22⋊Dic73—21no—
5C2×C22⋊#10596831—21no—
6C2×C22⋊#10596831—21no—
7C2×C22⋊#10596831C412yescomplemented
8C2×#14556498—21no—
9C2×#14556498C412yescomplemented
10C24×C4×C73C2211yescharacteristic
11C22×C22⋊C4×C73—21no—
12C2×#95×C73—21no—
13C2×#95×C73C412yescomplemented
14C23×Dic73—22no—
15C22×#10596831—22no—
16C2×C22⋊Dic73—24no—
17C2×C22⋊Dic73—42no—
18C2×C22⋊Dic73—41no—
19C2×C22⋊Dic73—41no—
20C22⋊#10596831—42no—
21C22⋊#10596831—42no—
22C22⋊#10596831—42no—
23#14556498—42no—
24#14556498—42no—
25C25×C73D411yescharacteristic
26C23×C4×C73—22no—
27C23×C4×C73—42no—
28C23×C4×C73—42no—
29C23×C4×C73—42no—
30C23×C4×C73C2×C411yescharacteristic
31C23×C4×C73C2×C411yescharacteristic
32C23×C4×C73C2×C411yescharacteristic
33C23×C4×C73D411yescharacteristic
34C23×C4×C73D411yescharacteristic
35C23×C4×C73Q811yescharacteristic
36C2×C22⋊C4×C73—24no—
37C2×C22⋊C4×C73—42no—
38C2×C22⋊C4×C73—41no—
39C2×C22⋊C4×C73—41no—
40#95×C73—42no—
41#95×C73—42no—
42C22×Dic73—24no—
43C22×Dic73—42no—
44C22×Dic73—42no—
45C22×Dic73—42no—
46C22×Dic73—42no—
47C22×Dic73—42no—
48C22×Dic73—42no—
49C2×#10596831—42no—
50C2×#10596831—42no—
51C2×#10596831—42no—
52C22⋊Dic73—44no—
53C22⋊Dic73—44no—
54C24×C73—22no—
55C24×C73—22no—
56C24×C73—22no—
57C24×C73—22no—
58C24×C73—41no—
59C24×C73—41no—
60C24×C73C22⋊C411yescharacteristic
61C24×C73C22⋊C411yescharacteristic
62C24×C73C4⋊C411yescharacteristic
63C24×C73D811yescharacteristic
64C24×C73SD1611yescharacteristic
65C24×C73SD1611yescharacteristic
66C24×C73Q1611yescharacteristic
67C22×C4×C73—22no—
68C22×C4×C73—22no—
69C22×C4×C73—22no—
70C22×C4×C73—22no—
71C22×C4×C73—22no—
72C22×C4×C73—22no—
73C22×C4×C73—22no—
74C22×C4×C73—24no—
75C22×C4×C73—41no—
76C22×C4×C73—41no—
77C22×C4×C73—41no—
78C22×C4×C73—41no—
79C22×C4×C73—41no—
80C22×C4×C73—41no—
81C22×C4×C73—41no—
82C22×C4×C73—41no—
83C22×C4×C73—41no—
84C22×C4×C73—41no—
85C22×C4×C73—41no—
86C22×C4×C73—416no—
87C22×C4×C73—42no—
88C22×C4×C73—42no—
89C22×C4×C73—42no—
90C22×C4×C73—42no—
91C22×C4×C73—42no—
92C22×C4×C73—42no—
93C22×C4×C73C4211yescharacteristic
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C4⋊C411yescharacteristic
96C22×C4×C73C4⋊C411yescharacteristic
97C22⋊C4×C73—44no—
98C22⋊C4×C73—44no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—22no—
108C23×C73—22no—
109C23×C73—22no—
110C23×C73—22no—
111C23×C73—22no—
112C23×C73—22no—
113C23×C73—22no—
114C23×C73—22no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—41no—
122C23×C73—41no—
123C23×C73—41no—
124C23×C73—41no—
125C23×C73—44no—
126C23×C73—44no—
127C23×C73—44no—
128C23×C73—44no—
129C23×C73#9511yescharacteristic
130C23×C73#9912yes—
131C23×C73#9912yes—
132C23×C73#10211yescharacteristic
133C23×C73#10211yescharacteristic
134C23×C73#10311yescharacteristic
135C23×C73#10311yescharacteristic
136C23×C73#10412yes—
137C23×C73#10412yes—
138C23×C73#10611yescharacteristic
139C23×C73#10711yescharacteristic
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—44no—
152C2×C4×C73—44no—
153C2×C4×C73—44no—
154C2×C4×C73—44no—
155C2×C4×C73—44no—
156C2×C4×C73—44no—
157C2×C4×C73—44no—
158C2×C4×C73—44no—
159C2×C4×C73—44no—
160C2×C4×C73—82no—
161C2×C4×C73—82no—
162C2×C4×C73—82no—
163C2×C4×C73—82no—
164C2×C4×C73#9912yes—
165C2×Dic73—44no—
166C2×Dic73—44no—
167C2×Dic73—44no—
168C2×Dic73—82no—
169C2×Dic73—82no—
170C2×Dic73—82no—
171C2×Dic73—82no—
172#10596831—82no—
173C22×C73—22no—
174C22×C73—22no—
175C22×C73—22no—
176C22×C73—22no—
177C22×C73—21no—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73—21no—
183C22×C73—21no—
184C22×C73—21no—
185C22×C73—22no—
186C22×C73—22no—
187C22×C73—22no—
188C22×C73—22no—
189C22×C73—21no—
190C22×C73—21no—
191C22×C73—21no—
192C22×C73—21no—
193C22×C73—21no—
194C22×C73—21no—
195C22×C73—44no—
196C22×C73—44no—
197C22×C73—44no—
198C22×C73—44no—
199C22×C73—41no—
200C22×C73—41no—
201C22×C73—41no—
202C22×C73—41no—
203C22×C73#32712yes—
204C22×C73#32712yes—
205C22×C73#32812yes—
206C22×C73#32812yes—
207C22×C73H(3,ℤ/4)11yescharacteristic
208C22×C73#33911yescharacteristic
209C22×C73#33911yescharacteristic
210C22×C73#34011yescharacteristic
211C22×C73#34211yescharacteristic
212C22×C73#34211yescharacteristic
213C22×C73#34211yescharacteristic
214C4×C73—22no—
215C4×C73—41no—
216C4×C73—41no—
217C4×C73—41no—
218C4×C73—84no—
219Dic73—84no—
220#7035—731nomaximal, Sylow
221C2×C73—22no—
222C2×C73—22no—
223C2×C73—22no—
224C2×C73—22no—
225C2×C73—41no—
226C2×C73—41no—
227C2×C73#128411yescharacteristic
228C2×C73#128411yescharacteristic
229C2×C73#128911yescharacteristic
230C2×C73#129411yescharacteristic
231C2×C73#129411yescharacteristic
232C2×C73#129711yescharacteristic
233C2×C73#130411yescharacteristic
234#1779—731no—
235C22⋊#95—731no—
236C22⋊#95D7311yescharacteristic
237C73#703511yescharacteristic, complemented, Sylow
238C24×C4C2×D7311yescharacteristic
239C22×C22⋊C4—21no—
240C22×C22⋊C4—1461no—
241C2×C22⋊C8—732no—
242C2×C22⋊C8—1461no—
243C2×C22⋊C8—1461no—
244C2×#95—21no—
245C2×#95—732no—
246C2×#95—1461no—
247C2×#95Dic7312yescomplemented
248C25C22⋊D7311yescharacteristic
249C23×C4—22no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—1462no—
254C23×C4Dic14611yescharacteristic
255C23×C4C4×D7311yescharacteristic
256C23×C4C4×D7311yescharacteristic
257C23×C4D29211yescharacteristic
258C23×C4C2×Dic7311yescharacteristic
259C23×C4C22⋊D7311yescharacteristic
260C22×C8—1462no—
261C2×C22⋊C4—24no—
262C2×C22⋊C4—42no—
263C2×C22⋊C4—41no—
264C2×C22⋊C4—41no—
265C2×C22⋊C4—2922no—
266C2×C22⋊C4—2921no—
267C2×C22⋊C4—2921no—
268C2×C22⋊C4—1464no—
269C22⋊C8—2922no—
270C22⋊C8—2922no—
271C22⋊C8—2922no—
272#95—42no—
273#95—42no—
274#95—2922no—
275#95—2922no—
276C24—22no—
277C24—22no—
278C24—22no—
279C24—22no—
280C24—41no—
281C24—41no—
282C24#1192400511yescharacteristic
283C24C22⋊Dic7311yescharacteristic
284C24#1192400711yescharacteristic
285C24#1192401311yescharacteristic
286C24#1192401511yescharacteristic
287C24#1192401611yescharacteristic
288C24#1192401811yescharacteristic
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—24no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—416no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—2922no—
316C22×C4—2922no—
317C22×C4—2922no—
318C22×C4—2922no—
319C22×C4—2922no—
320C22×C4—2922no—
321C22×C4—1464no—
322C22×C4C4×Dic7311yescharacteristic
323C22×C4#1192400511yescharacteristic
324C22×C4#1192400711yescharacteristic
325C22×C4C4⋊Dic7311yescharacteristic
326C2×C8—2922no—
327C2×C8—2922no—
328C2×C8—2922no—
329C22⋊C4—44no—
330C22⋊C4—44no—
331C22⋊C4—2924no—
332C22⋊C4—2924no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—22no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—44no—
360C23—44no—
361C23—44no—
362C23—44no—
363C23#1455649811yescharacteristic
364C23#1455650512yes—
365C23#1455650612yes—
366C23#1455651111yescharacteristic
367C23#1455651211yescharacteristic
368C23#1455651411yescharacteristic
369C23#1455651511yescharacteristic
370C23#1455651812yes—
371C23#1455651912yes—
372C23#1455652211yescharacteristic
373C23#1455652411yescharacteristic
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4—2924no—
399C2×C4—2924no—
400C2×C4—2924no—
401C2×C4—5842no—
402C2×C4—5842no—
403C2×C4—5842no—
404C2×C4—5842no—
405C2×C4#1455650512yes—
406C8—5842no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—44no—
430C22—44no—
431C22—44no—
432C22—44no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22#1798832012yes—
438C22#1798832112yes—
439C22#1798832312yes—
440C22#1798832412yes—
441C22#1798834311yescharacteristic
442C22#1798834611yescharacteristic
443C22#1798834711yescharacteristic
444C22#1798834911yescharacteristic
445C22#1798835311yescharacteristic
446C22#1798835311yescharacteristic
447C22#1798835411yescharacteristic
448C4—22no—
449C4—41no—
450C4—41no—
451C4—41no—
452C4—84no—
453C4—5844no—
454C2—22no—
455C2—22no—
456C2—22no—
457C2—22no—
458C2—41no—
459C2—41no—
460C2#2260778311yescharacteristic
461C2#2260778411yescharacteristic
462C2#2260779811yescharacteristic
463C2#2260780911yescharacteristic
464C2#2260781011yescharacteristic
465C2#2260781711yescharacteristic
466C2#2260783511yescharacteristic
subgroupG/H
centerC23#14556498
commutatorC22×C4×C73C42
FrattiniC24×C4C2×D73
FittingC73×C22⋊#95C2
socleC23×C73#95
prime radicalC25×C73D4
cosocleC24×C4×C73C22
hypercenterC22⋊#95D73
hypocenterC73#7035
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
7. C2×C22⋊#10596831C4semidirect
9. C2×#14556498C4semidirect
13. C2×#95×C73C4semidirect
237. C73#7035semidirect
247. C2×#95Dic73semidirect

Maximal subgroups

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

subgroupindex
#226098412
#226081542
C73×C22⋊#952
#703573