Finite Group Databasebeta

← #22616675

Subgroups — #22616675

Order 9344.

548 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556578C211yesmaximal, characteristic, complemented
2C2×#14556572C211yesmaximal, characteristic, complemented
3#17988523C211yesmaximal, characteristic, complemented
4#17988515C211yesmaximal, characteristic, complemented
5#17988501C211yesmaximal, characteristic, complemented
6#17988501C211yesmaximal, characteristic, complemented
7#17988499C211yesmaximal, characteristic, complemented
8#17988491C211yesmaximal, characteristic, complemented
9#17988490C211yesmaximal, characteristic, complemented
10#17988484C211yesmaximal, characteristic, complemented
11#17988481C211yesmaximal, characteristic, complemented
12#17988480C211yesmaximal, characteristic, complemented
13#17988467C211yesmaximal, characteristic, complemented
14#17988462C211yesmaximal, characteristic, complemented
15#392×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17C23×Dic73C2211yescharacteristic
18#14556578—24no—
19#14556572—24no—
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×C22⋊Dic73C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×C22⋊Dic73C2211yescharacteristic
35C2×C22⋊Dic73C2211yescharacteristic
36C2×C22⋊Dic73C2211yescharacteristic
37C2×C4×Dic73C2211yescharacteristic
38C2×C4×Dic73C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C22×D4×C73C2211yescharacteristic
47C22×D4×C73C2211yescharacteristic
48C22×D4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C2×Dic146—22no—
54C2×Dic146—22no—
55C2×Dic146—41no—
56C22×Dic73—22no—
57C22×Dic73—41no—
58C22×Dic73—41no—
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C4⋊Dic73—41no—
68C4⋊Dic73—41no—
69#11924007—22no—
70#11924007—22no—
71#11924007—22no—
72#11924007—41no—
73C22⋊Dic73—22no—
74C22⋊Dic73—22no—
75C22⋊Dic73—22no—
76C22⋊Dic73—22no—
77C22⋊Dic73—22no—
78C22⋊Dic73—41no—
79C22⋊Dic73—41no—
80C22⋊Dic73—41no—
81C22⋊Dic73—41no—
82C22⋊Dic73—41no—
83C22⋊Dic73D414yescomplemented
84C4×Dic73—22no—
85C4×Dic73—41no—
86C24×C73C2311yescharacteristic
87C24×C73C2311yescharacteristic
88C24×C73C2311yescharacteristic
89C2×D4×C73—22no—
90C2×D4×C73—22no—
91C2×D4×C73—22no—
92C2×D4×C73—22no—
93C2×D4×C73—41no—
94C2×D4×C73—41no—
95C2×D4×C73—41no—
96C2×D4×C73—41no—
97C2×D4×C73—41no—
98C22×C4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C22⋊C4×C73—22no—
103C22⋊C4×C73—22no—
104C22⋊C4×C73—41no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—21no—
123C23×C73—21no—
124C23×C73—21no—
125C23×C73C2×D412yes—
126C23×C73C2411yescharacteristic
127D4×C73—44no—
128D4×C73—44no—
129D4×C73—44no—
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—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73#4112yes—
141C2×C4×C73#4112yes—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—21no—
151C2×Dic73—21no—
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73—21no—
157C2×Dic73—21no—
158C2×Dic73—21no—
159C2×Dic73—21no—
160C2×Dic73—21no—
161C2×Dic73—21no—
162C2×Dic73—21no—
163C2×Dic73—21no—
164C2×Dic73—44no—
165C2×Dic73C2×D412yes—
166C2×Dic73C2×D412yes—
167Dic146—44no—
168C22×C73—22no—
169C22×C73—22no—
170C22×C73—22no—
171C22×C73—41no—
172C22×C73—41no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73—41no—
177C22×C73—41no—
178C22×C73—41no—
179C22×C73—41no—
180C22×C73—41no—
181C22×C73—41no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73—41no—
185C22×C73—41no—
186C22×C73—41no—
187C22×C73—41no—
188C22×C73—41no—
189C22×C73C22×D411yescharacteristic
190C22×C73C2×#4111yescharacteristic
191C22×C73C2×#4111yescharacteristic
192C22×C73H(5,𝔽2)11yescharacteristic
193C22×C73H(5,𝔽2)11yescharacteristic
194C22×C73H(5,𝔽2)11yescharacteristic
195C22×C732−1+411yescharacteristic
196C4×C73—22no—
197C4×C73—22no—
198C4×C73—41no—
199C4×C73—41no—
200Dic73—22no—
201Dic73—22no—
202Dic73—41no—
203Dic73—41no—
204Dic73—41no—
205Dic73—41no—
206Dic73—41no—
207Dic73—41no—
208C2×C73—42no—
209C2×C73—81no—
210C2×C73—81no—
211C2×C73#53511yescharacteristic
212C2×C73#53811yescharacteristic
213C2×C73#54211yescharacteristic
214C2×C73#54611yescharacteristic
215C2×C73#54711yescharacteristic
216C2×C73#55911yescharacteristic
217C2×C73#56211yescharacteristic
218#2710—731nomaximal, Sylow
219C73#271011yescharacteristic, complemented, Sylow
220C2×#124—731no—
221C2×#123—731no—
222#399—731no—
223#397—731no—
224#394—731no—
225#394—731no—
226#393—731no—
227#392D7311yescharacteristic
228#391—731no—
229#390—731no—
230#389—731no—
231#388—731no—
232#388—731no—
233#386—731no—
234#385—731no—
235C22×Q8—731no—
236C22×D4C2×D7311yescharacteristic
237C22×D4C2×D7311yescharacteristic
238C22×D4C2×D7311yescharacteristic
239C23×C4—731no—
240#124—1464no—
241#123—1464no—
242C2×C4⋊C4—731no—
243C2×C4⋊C4—731no—
244C2×C4⋊C4—731no—
245C2×C4⋊C4—731no—
246C2×C4⋊C4—731no—
247C2×C4⋊C4—731no—
248C2×C22⋊C4—731no—
249C2×C22⋊C4—731no—
250C2×C22⋊C4—731no—
251C2×C22⋊C4—731no—
252C2×C22⋊C4—731no—
253C2×C22⋊C4—731no—
254C2×C22⋊C4—731no—
255C2×C22⋊C4—731no—
256C2×C22⋊C4—731no—
257C2×C22⋊C4—731no—
258C2×C22⋊C4—731no—
259C2×C22⋊C4C2×D7311yescharacteristic
260C2×C22⋊C4C2×D7311yescharacteristic
261C2×C22⋊C4C2×D7311yescharacteristic
262C2×C42—731no—
263C2×C42—731no—
264#95—731no—
265#95—731no—
266#95—731no—
267#95—731no—
268#95—731no—
269#95—731no—
270#95—731no—
271#95C2×D7311yescharacteristic
272C24C22×D7311yescharacteristic
273C24C22×D7311yescharacteristic
274C24C22×D7311yescharacteristic
275C2×Q8—2921no—
276C2×Q8—1462no—
277C2×Q8—1462no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C22×C4—2921no—
288C22×C4—2921no—
289C22×C4—731no—
290C22×C4—731no—
291C22×C4—731no—
292C22×C4—731no—
293C22×C4—731no—
294C22×C4—731no—
295C22×C4—731no—
296C22×C4—731no—
297C22×C4—1462no—
298C22×C4C22×D7311yescharacteristic
299C22×C4C22×D7311yescharacteristic
300C22×C4C22×D7311yescharacteristic
301C22×C4C22×D7311yescharacteristic
302C4⋊C4—2921no—
303C4⋊C4—2921no—
304C4⋊C4—2921no—
305C4⋊C4—1462no—
306C4⋊C4—1462no—
307C4⋊C4—1462no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—41no—
311C22⋊C4—2921no—
312C22⋊C4—2921no—
313C22⋊C4—2921no—
314C22⋊C4—2921no—
315C22⋊C4—2921no—
316C22⋊C4—734no—
317C22⋊C4—1462no—
318C22⋊C4—1462no—
319C22⋊C4—1462no—
320C22⋊C4—1462no—
321C22⋊C4—1462no—
322C42—2921no—
323C42—1462no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23D4×D7312yes—
345C23C23×D7311yescharacteristic
346Q8—2924no—
347D4—44no—
348D4—44no—
349D4—44no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—2924no—
361C2×C4—732no—
362C2×C4—732no—
363C2×C4—1461no—
364C2×C4—1461no—
365C2×C4—1461no—
366C2×C4—1461no—
367C2×C4—1461no—
368C2×C4—1461no—
369C2×C4—1461no—
370C2×C4—1461no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4—1461no—
374C2×C4—1461no—
375C2×C4—1461no—
376C2×C4—1461no—
377C2×C4—1461no—
378C2×C4—1461no—
379C2×C4—1461no—
380C2×C4—1461no—
381C2×C4—1461no—
382C2×C4—1461no—
383C2×C4—1461no—
384C2×C4—1461no—
385C2×C4#1192402712yes—
386C2×C4#1192402712yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22C2×D4×D7311yescharacteristic
409C22C2×#1192402711yescharacteristic
410C22C2×#1192402711yescharacteristic
411C22#1455663611yescharacteristic
412C22#1455663611yescharacteristic
413C22#1455663611yescharacteristic
414C22#1455663811yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—2921no—
420C4—2921no—
421C4—2921no—
422C4—2921no—
423C4—2921no—
424C4—2921no—
425C4—1462no—
426C4—1462no—
427C2—42no—
428C2—81no—
429C2—81no—
430C2#1798915211yescharacteristic
431C2#1798917211yescharacteristic
432C2#1798920411yescharacteristic
433C2#1798922411yescharacteristic
434C2#1798923711yescharacteristic
435C2#1798932311yescharacteristic
436C2#1798933211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2710
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14556578C2semidirect
2. C2×#14556572C2semidirect
3. #17988523C2semidirect
4. #17988515C2semidirect
5. #17988501C2semidirect
6. #17988501C2semidirect
7. #17988499C2semidirect
8. #17988491C2semidirect
9. #17988490C2semidirect
10. #17988484C2semidirect
11. #17988481C2semidirect
12. #17988480C2semidirect
13. #17988467C2semidirect
14. #17988462C2semidirect
83. C22⋊Dic73D4semidirect
219. C73#2710semidirect