Finite Group Databasebeta

← #22613486

Subgroups — #22613486

Order 9344.

666 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556574C211yesmaximal, characteristic, complemented
2C2×#14556563C211yesmaximal, characteristic
3C2×D4×Dic73C211yesmaximal, characteristic, complemented
4#17988520C211yesmaximal, characteristic, complemented
5#17988515C211yesmaximal, characteristic, complemented
6#17988509C211yesmaximal, characteristic, complemented
7#17988502C211yesmaximal, characteristic, complemented
8#17988482C211yesmaximal, characteristic, complemented
9#17988477C211yesmaximal, characteristic, complemented
10#17988464C211yesmaximal, characteristic, complemented
11#17988464C211yesmaximal, characteristic, complemented
12#17988459C211yesmaximal, characteristic, complemented
13#17988445C211yesmaximal, characteristic, complemented
14C2×#14556498C211yesmaximal, characteristic, complemented
15C2×#123×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C23×Dic73C2211yescharacteristic
19C23×Dic73C2211yescharacteristic
20C23×Dic73C2211yescharacteristic
21#14556574—24no—
22#14556563—24no—
23D4×Dic73—24no—
24C2×C4⋊Dic73C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×C4×Dic73C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46#14556498C2211yescharacteristic
47C22×D4×C73C2211yescharacteristic
48C23×C4×C73C2211yescharacteristic
49#123×C73—24no—
50C2×C4⋊C4×C73C2211yescharacteristic
51C2×C4⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic
53C2×C22⋊C4×C73C2211yescharacteristic
54C2×C22⋊C4×C73C2211yescharacteristic
55C23×D73C2311yescharacteristic
56C2×C22⋊D73—22no—
57C2×C22⋊D73—22no—
58C2×C22⋊D73—22no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—22no—
61C2×C22⋊D73—41no—
62C22×Dic73—22no—
63C22×Dic73—22no—
64C22×Dic73—22no—
65C22×Dic73—22no—
66C22×Dic73—22no—
67C22×Dic73—22no—
68C22×Dic73—41no—
69C22×Dic73—41no—
70C22×Dic73—41no—
71C22×Dic73C2311yescharacteristic
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C22×Dic73C2311yescharacteristic
77C22×Dic73C2311yescharacteristic
78C4⋊Dic73—22no—
79#11924007—22no—
80#11924007—22no—
81#11924007—22no—
82#11924007—22no—
83#11924007—41no—
84C22⋊Dic73—22no—
85C22⋊Dic73—22no—
86C22⋊Dic73D414yescomplemented
87#11924005—22no—
88#11924005—22no—
89#11924005—22no—
90#11924005—22no—
91#11924005—41no—
92C4×Dic73—22no—
93C24×C73C2311yescharacteristic
94C24×C73C2311yescharacteristic
95C2×D4×C73—22no—
96C2×D4×C73—22no—
97C2×D4×C73D414yes—
98C22×C4×C73—22no—
99C22×C4×C73—22no—
100C22×C4×C73—22no—
101C22×C4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105C22×C4×C73C2311yescharacteristic
106C4⋊C4×C73—22no—
107C4⋊C4×C73—22no—
108C22⋊C4×C73—22no—
109C22⋊C4×C73—22no—
110C22⋊C4×C73—22no—
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×C73C2×D412yes—
122C23×C73C2×D412yes—
123C23×C73C2×D412yes—
124C23×C73#4112yes—
125C23×C73C2411yescharacteristic
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—21no—
129C22×D73—21no—
130C22×D73—21no—
131C22×D73—21no—
132C22×D73—21no—
133D4×C73—28no—
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—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—44no—
149C2×C4×C73C2×D412yes—
150C22⋊D73—44no—
151C22⋊D73—44no—
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—21no—
167C2×Dic73—21no—
168C2×Dic73—21no—
169C2×Dic73—44no—
170C2×Dic73—44no—
171C2×Dic73—44no—
172C2×Dic73C2×D412yes—
173C2×Dic73C2×D412yes—
174C2×Dic73#4112yes—
175C2×Dic73#4112yes—
176C22×C73—22no—
177C22×C73—22no—
178C22×C73—22no—
179C22×C73—22no—
180C22×C73—22no—
181C22×C73—22no—
182C22×C73—22no—
183C22×C73—22no—
184C22×C73—22no—
185C22×C73—41no—
186C22×C73—41no—
187C22×C73—41no—
188C22×C73—41no—
189C22×C73#12114yes—
190C22×C73C22×D411yescharacteristic
191C22×C73C22×D411yescharacteristic
192C22×C73C2×#4111yescharacteristic
193C22×C73C2×#4111yescharacteristic
194C22×C73C2×#4111yescharacteristic
195C22×C73H(5,𝔽2)11yescharacteristic
196C22×C732−1+411yescharacteristic
197C2×D73—41no—
198C2×D73—41no—
199C2×D73—41no—
200C2×D73—41no—
201C2×D73—41no—
202C2×D73—41no—
203C2×D73—41no—
204C4×C73—22no—
205C4×C73—41no—
206C4×C73—41no—
207C4×C73—41no—
208C4×C73—41no—
209Dic73—22no—
210Dic73—22no—
211Dic73—22no—
212Dic73—22no—
213Dic73—41no—
214Dic73—41no—
215Dic73—41no—
216C2×C73—24no—
217C2×C73—42no—
218C2×C73C2×#12111yescharacteristic
219C2×C73#52911yescharacteristic
220C2×C73#53911yescharacteristic
221C2×C73#54611yescharacteristic
222C2×C73#54611yescharacteristic
223C2×C73#54711yescharacteristic
224C2×C73#54711yescharacteristic
225D73—81no—
226#2425—731nomaximal, Sylow
227C73#242511yescharacteristic, complemented, Sylow
228C2×#123—731no—
229C2×#123D7311yescharacteristic, complemented
230C2×#121—731no—
231C2×C4×D4—731no—
232#398—731no—
233#397—731no—
234#396—731no—
235#394—731no—
236#389—731no—
237#388—731no—
238#386—731no—
239#386—731no—
240#385—731no—
241#380—731no—
242C2×#95—731no—
243C22×D4—731no—
244C22×D4—731no—
245C22×D4C2×D7311yescharacteristic
246C23×C4—731no—
247C23×C4—731no—
248C23×C4—731no—
249C23×C4C2×D7311yescharacteristic
250#123—24no—
251#123—1464no—
252#121—1464no—
253C4×D4—1464no—
254C2×C4⋊C4—731no—
255C2×C4⋊C4—731no—
256C2×C4⋊C4—731no—
257C2×C4⋊C4—731no—
258C2×C4⋊C4—731no—
259C2×C4⋊C4—731no—
260C2×C4⋊C4C2×D7311yescharacteristic
261C2×C4⋊C4C2×D7311yescharacteristic
262C2×C22⋊C4—731no—
263C2×C22⋊C4—731no—
264C2×C22⋊C4—731no—
265C2×C22⋊C4—731no—
266C2×C22⋊C4—731no—
267C2×C22⋊C4—731no—
268C2×C22⋊C4—731no—
269C2×C22⋊C4—731no—
270C2×C22⋊C4C2×D7311yescharacteristic
271C2×C22⋊C4C2×D7311yescharacteristic
272C2×C22⋊C4C2×D7311yescharacteristic
273C2×C42—731no—
274#95—731no—
275#95—731no—
276#95—731no—
277#95—731no—
278#95—731no—
279#95—731no—
280#95—731no—
281#95—731no—
282C24—731no—
283C24C22×D7311yescharacteristic
284C24C22×D7311yescharacteristic
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—2921no—
288C2×D4—1462no—
289C2×D4—1462no—
290C2×D4—1462no—
291C2×D4—1462no—
292C2×D4—1462no—
293C2×D4C22⋊D7314yes—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—2921no—
298C22×C4—2921no—
299C22×C4—2921no—
300C22×C4—731no—
301C22×C4—731no—
302C22×C4—731no—
303C22×C4—731no—
304C22×C4—731no—
305C22×C4—731no—
306C22×C4—731no—
307C22×C4—1462no—
308C22×C4—1462no—
309C22×C4—1462no—
310C22×C4—1462no—
311C22×C4—1462no—
312C22×C4—1462no—
313C22×C4C22×D7311yescharacteristic
314C22×C4C22×D7311yescharacteristic
315C22×C4C22×D7311yescharacteristic
316C22×C4C22×D7311yescharacteristic
317C22×C4C22×D7311yescharacteristic
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—2921no—
321C4⋊C4—1462no—
322C4⋊C4—1462no—
323C4⋊C4—1462no—
324C4⋊C4—1462no—
325C4⋊C4—1462no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—2921no—
330C22⋊C4—734no—
331C22⋊C4—1462no—
332C22⋊C4—1462no—
333C22⋊C4—1462no—
334C22⋊C4—1462no—
335C22⋊C4—1462no—
336C22⋊C4—1462no—
337C42—1462no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—1461no—
349C23—1461no—
350C23—1461no—
351C23—1461no—
352C23—1461no—
353C23—1461no—
354C23—1461no—
355C23D4×D7312yes—
356C23C2×C22⋊D7312yes—
357C23C2×C22⋊D7312yes—
358C23#1192402712yes—
359C23C23×D7311yescharacteristic
360D4—28no—
361D4—2924no—
362D4—2924no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—44no—
378C2×C4—2924no—
379C2×C4—2924no—
380C2×C4—2924no—
381C2×C4—732no—
382C2×C4—732no—
383C2×C4—732no—
384C2×C4—732no—
385C2×C4—1461no—
386C2×C4—1461no—
387C2×C4—1461no—
388C2×C4—1461no—
389C2×C4—1461no—
390C2×C4—1461no—
391C2×C4—1461no—
392C2×C4—1461no—
393C2×C4—1461no—
394C2×C4—1461no—
395C2×C4—1461no—
396C2×C4—1461no—
397C2×C4—1461no—
398C2×C4—1461no—
399C2×C4—1461no—
400C2×C4—1461no—
401C2×C4—1461no—
402C2×C4C2×C22⋊D7312yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—2921no—
417C22—2921no—
418C22—2921no—
419C22—2921no—
420C22—2921no—
421C22—2921no—
422C22—2921no—
423C22#1455656314yes—
424C22C2×D4×D7311yescharacteristic
425C22C22×C22⋊D7311yescharacteristic
426C22#41×D7311yescharacteristic
427C22#41×D7311yescharacteristic
428C22C2×#1192402711yescharacteristic
429C22#1455663711yescharacteristic
430C22#1455663811yescharacteristic
431C4—22no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—2921no—
437C4—2921no—
438C4—2921no—
439C4—1462no—
440C4—1462no—
441C4—1462no—
442C4—1462no—
443C2—24no—
444C2—42no—
445C2—5841no—
446C2C2×#1455656311yescharacteristic
447C2#1798911411yescharacteristic
448C2#1798918111yescharacteristic
449C2#1798922511yescharacteristic
450C2#1798922911yescharacteristic
451C2#1798923511yescharacteristic
452C2#1798923611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#123×C73C2
hypercenterC2×#123D73
hypocenterC73#2425
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#14556574C2semidirect
3. C2×D4×Dic73C2semidirect
4. #17988520C2semidirect
5. #17988515C2semidirect
6. #17988509C2semidirect
7. #17988502C2semidirect
8. #17988482C2semidirect
9. #17988477C2semidirect
10. #17988464C2semidirect
11. #17988464C2semidirect
12. #17988459C2semidirect
13. #17988445C2semidirect
14. C2×#14556498C2semidirect
15. C2×#123×C73C2semidirect
86. C22⋊Dic73D4semidirect
227. C73#2425semidirect
229. C2×#123D73semidirect