Finite Group Databasebeta

← #22616608

Subgroups — #22616608

Order 9344.

540 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556584C211yesmaximal, characteristic, complemented
2C2×#14556574C211yesmaximal, characteristic, complemented
3#17988524C211yesmaximal, characteristic, complemented
4#17988510C211yesmaximal, characteristic, complemented
5#17988510C211yesmaximal, characteristic, complemented
6#17988503C211yesmaximal, characteristic, complemented
7#17988502C211yesmaximal, characteristic, complemented
8#17988495C211yesmaximal, characteristic
9#17988490C211yesmaximal, characteristic, complemented
10#17988487C211yesmaximal, characteristic, complemented
11#17988484C211yesmaximal, characteristic, complemented
12#17988476C211yesmaximal, characteristic, complemented
13#17988470C211yesmaximal, characteristic, complemented
14#17988447C211yesmaximal, characteristic, complemented
15#386×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18#14556584—24no—
19#14556574—24no—
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊Dic73C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×C22⋊Dic73C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic
40C2×C4×Dic73C2211yescharacteristic
41C2×C4×Dic73C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C22×D4×C73C2211yescharacteristic
47C23×C4×C73C2211yescharacteristic
48C2×C22⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×C22⋊D73—22no—
55C2×C22⋊D73—22no—
56C2×C22⋊D73—41no—
57C2×C22⋊D73—41no—
58C2×C22⋊D73—41no—
59C2×C22⋊D73—41no—
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C4⋊Dic73—22no—
68C4⋊Dic73—22no—
69C4⋊Dic73—41no—
70C4⋊Dic73—41no—
71#11924007—22no—
72#11924007—22no—
73#11924007—41no—
74#11924007—41no—
75#11924007D414yescomplemented
76C22⋊Dic73—22no—
77C22⋊Dic73—22no—
78C22⋊Dic73—22no—
79C22⋊Dic73—41no—
80C22⋊Dic73—41no—
81C22⋊Dic73—41no—
82#11924005—22no—
83#11924005—22no—
84#11924005—22no—
85#11924005—41no—
86#11924005—41no—
87C4×Dic73—22no—
88C4×Dic73—41no—
89C24×C73C2311yescharacteristic
90C24×C73C2311yescharacteristic
91C2×D4×C73—22no—
92C2×D4×C73—22no—
93C2×D4×C73—41no—
94C22×C4×C73—22no—
95C22×C4×C73—22no—
96C22×C4×C73—41no—
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C22⋊C4×C73—22no—
103C22⋊C4×C73—41no—
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#4112yes—
119C23×C73C2411yescharacteristic
120C22×D73—21no—
121C22×D73—21no—
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—21no—
125C22×D73—21no—
126C22×D73—21no—
127D4×C73—44no—
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—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—44no—
142C2×C4×C73C2×D412yes—
143C2×C4×C73#4112yes—
144C22⋊D73—44no—
145C22⋊D73—44no—
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×Dic73C2×D412yes—
166C2×Dic73C2×D412yes—
167C22×C73—22no—
168C22×C73—22no—
169C22×C73—22no—
170C22×C73—41no—
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×C73C22×D411yescharacteristic
182C22×C73C2×#4111yescharacteristic
183C22×C73C2×#4111yescharacteristic
184C22×C73H(5,𝔽2)11yescharacteristic
185C22×C73H(5,𝔽2)11yescharacteristic
186C22×C73H(5,𝔽2)11yescharacteristic
187C22×C732−1+411yescharacteristic
188C2×D73—41no—
189C2×D73—41no—
190C2×D73—41no—
191C2×D73—41no—
192C2×D73—41no—
193C2×D73—41no—
194C2×D73—41no—
195C4×C73—22no—
196C4×C73—22no—
197C4×C73—41no—
198C4×C73—41no—
199C4×C73—41no—
200Dic73—22no—
201Dic73—22no—
202Dic73—41no—
203Dic73—41no—
204Dic73—41no—
205Dic73—41no—
206Dic73—41no—
207C2×C73—42no—
208C2×C73—81no—
209C2×C73#53711yescharacteristic
210C2×C73#53911yescharacteristic
211C2×C73#54211yescharacteristic
212C2×C73#54611yescharacteristic
213C2×C73#55011yescharacteristic
214C2×C73#55111yescharacteristic
215C2×C73#56011yescharacteristic
216D73—81no—
217#2705—731nomaximal, Sylow
218C73#270511yescharacteristic, complemented, Sylow
219C2×#126—731no—
220C2×#123—731no—
221#399—731no—
222#396—731no—
223#396—731no—
224#394—731no—
225#394—731no—
226#392—731no—
227#390—731no—
228#390—731no—
229#389—731no—
230#388—731no—
231#387—731no—
232#386D7311yescharacteristic, complemented
233#380—731no—
234C22×D4—731no—
235C22×D4—731no—
236C22×D4C2×D7311yescharacteristic
237C23×C4C2×D7311yescharacteristic
238#126—1464no—
239#123—1464no—
240C2×C4⋊C4—731no—
241C2×C4⋊C4—731no—
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×C4⋊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⋊C4—731no—
260C2×C22⋊C4C2×D7311yescharacteristic
261C2×C22⋊C4C2×D7311yescharacteristic
262C2×C22⋊C4C2×D7311yescharacteristic
263C2×C42—731no—
264C2×C42—731no—
265#95—731no—
266#95—731no—
267#95—731no—
268#95—731no—
269#95C2×D7311yescharacteristic
270#95C2×D7311yescharacteristic
271C24—731no—
272C24C22×D7311yescharacteristic
273C24C22×D7311yescharacteristic
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—2921no—
278C2×D4—2921no—
279C2×D4—2921no—
280C2×D4—2921no—
281C2×D4—1462no—
282C2×D4—1462no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—41no—
286C22×C4—731no—
287C22×C4—731no—
288C22×C4—731no—
289C22×C4—731no—
290C22×C4—731no—
291C22×C4—731no—
292C22×C4—731no—
293C22×C4C22×D7311yescharacteristic
294C22×C4C22×D7311yescharacteristic
295C22×C4C22×D7311yescharacteristic
296C22×C4C22×D7311yescharacteristic
297C22×C4C22×D7311yescharacteristic
298C4⋊C4—2921no—
299C4⋊C4—2921no—
300C4⋊C4—2921no—
301C4⋊C4—2921no—
302C4⋊C4—734no—
303C4⋊C4—1462no—
304C4⋊C4—1462no—
305C4⋊C4—1462no—
306C4⋊C4—1462no—
307C22⋊C4—22no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—2921no—
311C22⋊C4—2921no—
312C22⋊C4—2921no—
313C22⋊C4—2921no—
314C22⋊C4—2921no—
315C22⋊C4—1462no—
316C22⋊C4—1462no—
317C22⋊C4—1462no—
318C22⋊C4—1462no—
319C22⋊C4—1462no—
320C22⋊C4—1462no—
321C42—2921no—
322C42—1462no—
323C23—21no—
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—1461no—
337C23—1461no—
338C23—1461no—
339C23—1461no—
340C23—1461no—
341C23—1461no—
342C23—1461no—
343C23#1192402712yes—
344C23C23×D7311yescharacteristic
345D4—44no—
346D4—2924no—
347D4—2924no—
348C2×C4—21no—
349C2×C4—21no—
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—732no—
363C2×C4—732no—
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×C4D4×D7312yes—
384C2×C4#1192402812yes—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—2921no—
400C22—2921no—
401C22—2921no—
402C22—2921no—
403C22—2921no—
404C22—2921no—
405C22—2921no—
406C22C2×D4×D7311yescharacteristic
407C22C2×#1192402711yescharacteristic
408C22C2×#1192402811yescharacteristic
409C22#1455663611yescharacteristic
410C22#1455663611yescharacteristic
411C22#1455663711yescharacteristic
412C22#1455663811yescharacteristic
413C4—22no—
414C4—22no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4—2921no—
419C4—2921no—
420C4—2921no—
421C4—2921no—
422C4—2921no—
423C4—1462no—
424C4—1462no—
425C2—42no—
426C2—81no—
427C2—5841no—
428C2#1798916611yescharacteristic
429C2#1798918111yescharacteristic
430C2#1798920211yescharacteristic
431C2#1798922411yescharacteristic
432C2#1798925811yescharacteristic
433C2#1798926311yescharacteristic
434C2#1798932511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#386×C73C2
hypercenter#386D73
hypocenterC73#2705
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#14556584C2semidirect
2. C2×#14556574C2semidirect
3. #17988524C2semidirect
4. #17988510C2semidirect
5. #17988510C2semidirect
6. #17988503C2semidirect
7. #17988502C2semidirect
9. #17988490C2semidirect
10. #17988487C2semidirect
11. #17988484C2semidirect
12. #17988476C2semidirect
13. #17988470C2semidirect
14. #17988447C2semidirect
15. #386×C73C2semidirect
75. #11924007D4semidirect
218. C73#2705semidirect
232. #386D73semidirect