Finite Group Databasebeta

← #22616643

Subgroups — #22616643

Order 9344.

568 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556572C211yesmaximal, characteristic, complemented
2#17988525C211yesmaximal, characteristic, complemented
3#17988518C211yesmaximal, characteristic, complemented
4#17988515C211yesmaximal, characteristic, complemented
5#17988515C211yesmaximal, characteristic, complemented
6#17988501C211yesmaximal, characteristic, complemented
7#17988501C211yesmaximal, characteristic, complemented
8#17988467C211yesmaximal, characteristic, complemented
9#17988467C211yesmaximal, characteristic, complemented
10#17988467C211yesmaximal, characteristic, complemented
11#17988460C211yesmaximal, characteristic, complemented
12#17988460C211yesmaximal, characteristic, complemented
13#17988459C211yesmaximal, characteristic, complemented
14#17988445C211yesmaximal, characteristic, complemented
15C2×#121×C73C211yesmaximal, characteristic
16C23×Dic73C2211yescharacteristic
17C23×Dic73C2211yescharacteristic
18#14556572—24no—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
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
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45C22×D4×C73C2211yescharacteristic
46C22×D4×C73C2211yescharacteristic
47C22×D4×C73C2211yescharacteristic
48C23×C4×C73C2211yescharacteristic
49#121×C73—24no—
50C2×C4⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic
53C22×Dic73—22no—
54C22×Dic73—22no—
55C22×Dic73—41no—
56C22×Dic73—41no—
57C22×Dic73—41no—
58C22×Dic73—41no—
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67#11924007—22no—
68#11924007—22no—
69#11924007—41no—
70#11924007—41no—
71#11924007—41no—
72#11924007—41no—
73C22⋊Dic73—22no—
74C22⋊Dic73—22no—
75C22⋊Dic73—22no—
76C22⋊Dic73—22no—
77C22⋊Dic73—22no—
78C22⋊Dic73—22no—
79C22⋊Dic73—41no—
80C22⋊Dic73—41no—
81C22⋊Dic73—41no—
82C22⋊Dic73—41no—
83C24×C73C2311yescharacteristic
84C24×C73C2311yescharacteristic
85C24×C73C2311yescharacteristic
86C2×D4×C73—22no—
87C2×D4×C73—22no—
88C2×D4×C73—22no—
89C2×D4×C73—22no—
90C2×D4×C73—41no—
91C2×D4×C73—41no—
92C2×D4×C73—41no—
93C2×D4×C73—41no—
94C2×D4×C73D414yes—
95C22×C4×C73—22no—
96C22×C4×C73—41no—
97C22×C4×C73—41no—
98C22×C4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C4⋊C4×C73—22no—
103C22⋊C4×C73—22no—
104C22⋊C4×C73—22no—
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×C73C2×D412yes—
124C23×C73C2×D412yes—
125C23×C73#4112yes—
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—21no—
141C2×C4×C73—44no—
142C2×C4×C73C2×D412yes—
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—21no—
165C2×Dic73—21no—
166C2×Dic73—44no—
167C2×Dic73—44no—
168C2×Dic73#4112yes—
169C22×C73—22no—
170C22×C73—22no—
171C22×C73—22no—
172C22×C73—22no—
173C22×C73—22no—
174C22×C73—22no—
175C22×C73—22no—
176C22×C73—22no—
177C22×C73—22no—
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×C73—41no—
190C22×C73C22×D411yescharacteristic
191C22×C73C2×#4111yescharacteristic
192C22×C73C2×#4111yescharacteristic
193C22×C73H(5,𝔽2)11yescharacteristic
194C22×C73H(5,𝔽2)11yescharacteristic
195C22×C73H(5,𝔽2)11yescharacteristic
196C22×C732−1+411yescharacteristic
197C4×C73—22no—
198C4×C73—41no—
199C4×C73—41no—
200C4×C73—41no—
201Dic73—22no—
202Dic73—41no—
203Dic73—41no—
204Dic73—41no—
205Dic73—41no—
206Dic73—41no—
207Dic73—41no—
208Dic73—41no—
209C2×C73—42no—
210C2×C73—42no—
211C2×C73—42no—
212C2×C73#53411yescharacteristic
213C2×C73#53811yescharacteristic
214C2×C73#53911yescharacteristic
215C2×C73#54611yescharacteristic
216C2×C73#54711yescharacteristic
217C2×C73#55311yescharacteristic
218C2×C73#56211yescharacteristic
219#2708—731nomaximal, Sylow
220C73#270811yescharacteristic, complemented, Sylow
221C2×#123—731no—
222C2×#121D7311yescharacteristic
223#400—731no—
224#398—731no—
225#397—731no—
226#397—731no—
227#394—731no—
228#394—731no—
229#386—731no—
230#386—731no—
231#386—731no—
232#385—731no—
233#385—731no—
234#385—731no—
235#380—731no—
236C22×D4C2×D7311yescharacteristic
237C22×D4C2×D7311yescharacteristic
238C22×D4C2×D7311yescharacteristic
239C23×C4—731no—
240C23×C4—731no—
241C23×C4C2×D7311yescharacteristic
242#123—1464no—
243#121—24no—
244C2×C4⋊C4—731no—
245C2×C4⋊C4—731no—
246C2×C4⋊C4—731no—
247C2×C4⋊C4—731no—
248C2×C4⋊C4—731no—
249C2×C4⋊C4—731no—
250C2×C4⋊C4C2×D7311yescharacteristic
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⋊C4—731no—
260C2×C22⋊C4—731no—
261C2×C22⋊C4C2×D7311yescharacteristic
262C2×C22⋊C4C2×D7311yescharacteristic
263#95—731no—
264#95—731no—
265#95—731no—
266#95—731no—
267#95—731no—
268#95—731no—
269#95—731no—
270#95—731no—
271#95—731no—
272#95—731no—
273C24C22×D7311yescharacteristic
274C24C22×D7311yescharacteristic
275C24C22×D7311yescharacteristic
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4C22⋊D7314yes—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—2921no—
289C22×C4—2921no—
290C22×C4—2921no—
291C22×C4—2921no—
292C22×C4—731no—
293C22×C4—731no—
294C22×C4—731no—
295C22×C4—731no—
296C22×C4—731no—
297C22×C4—731no—
298C22×C4—731no—
299C22×C4—731no—
300C22×C4—1462no—
301C22×C4—1462no—
302C22×C4C22×D7311yescharacteristic
303C22×C4C22×D7311yescharacteristic
304C22×C4C22×D7311yescharacteristic
305C22×C4C22×D7311yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—2921no—
308C4⋊C4—2921no—
309C4⋊C4—2921no—
310C4⋊C4—2921no—
311C4⋊C4—1462no—
312C4⋊C4—1462no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—2921no—
316C22⋊C4—2921no—
317C22⋊C4—2921no—
318C22⋊C4—2921no—
319C22⋊C4—1462no—
320C22⋊C4—1462no—
321C22⋊C4—1462no—
322C22⋊C4—1462no—
323C22⋊C4—1462no—
324C22⋊C4—1462no—
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—
343C23C2×C22⋊D7312yes—
344C23C2×C22⋊D7312yes—
345C23#1192402712yes—
346C23C23×D7311yescharacteristic
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—21no—
361C2×C4—44no—
362C2×C4—2924no—
363C2×C4—2924no—
364C2×C4—732no—
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—1461no—
386C2×C4—1461no—
387C2×C4—1461no—
388C2×C4C2×C22⋊D7312yes—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22C22×C22⋊D7311yescharacteristic
411C22#41×D7311yescharacteristic
412C22C2×#1192402711yescharacteristic
413C22#1455663611yescharacteristic
414C22#1455663611yescharacteristic
415C22#1455663611yescharacteristic
416C22#1455663811yescharacteristic
417C4—22no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—2921no—
422C4—2921no—
423C4—2921no—
424C4—2921no—
425C4—2921no—
426C4—2921no—
427C4—2921no—
428C4—1462no—
429C2—42no—
430C2—42no—
431C2—42no—
432C2#1798914611yescharacteristic
433C2#1798916911yescharacteristic
434C2#1798918211yescharacteristic
435C2#1798923111yescharacteristic
436C2#1798923611yescharacteristic
437C2#1798928011yescharacteristic
438C2#1798933211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#121×C73C2
hypercenterC2×#121D73
hypocenterC73#2708
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14556572C2semidirect
2. #17988525C2semidirect
3. #17988518C2semidirect
4. #17988515C2semidirect
5. #17988515C2semidirect
6. #17988501C2semidirect
7. #17988501C2semidirect
8. #17988467C2semidirect
9. #17988467C2semidirect
10. #17988467C2semidirect
11. #17988460C2semidirect
12. #17988460C2semidirect
13. #17988459C2semidirect
14. #17988445C2semidirect
220. C73#2708semidirect