Finite Group Databasebeta

← #22614293

Subgroups — #22614293

Order 9344.

632 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556590C211yesmaximal, characteristic, complemented
2C2×#14556579C211yesmaximal, characteristic, complemented
3C2×#14556577C211yesmaximal, characteristic, complemented
4C2×#14556564C211yesmaximal, characteristic
5#17988504C211yesmaximal, characteristic, complemented
6#17988503C211yesmaximal, characteristic, complemented
7#17988500C211yesmaximal, characteristic, complemented
8#17988499C211yesmaximal, characteristic, complemented
9#17988487C211yesmaximal, characteristic, complemented
10#17988487C211yesmaximal, characteristic, complemented
11#17988479C211yesmaximal, characteristic, complemented
12#17988446C211yesmaximal, characteristic, complemented
13C4×#11924007C211yesmaximal, characteristic, complemented
14#17988434C211yesmaximal, characteristic, complemented
15#388×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C22×D292C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20C22×C22⋊D73C2211yescharacteristic
21C22×C4×D73C2211yescharacteristic
22#14556590—24no—
23#14556579—24no—
24#14556577—24no—
25#14556564—24no—
26C2×C4⋊Dic73C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic
40C2×#11924005C2211yescharacteristic
41C2×C4×Dic73C2211yescharacteristic
42C2×C4×Dic73C2211yescharacteristic
43C2×C4×Dic73C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46#14556498C2211yescharacteristic
47#14556498C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C42×C73C2211yescharacteristic
53#95×C73C2211yescharacteristic
54#95×C73C2211yescharacteristic
55C23×D73C2311yescharacteristic
56C23×D73C2311yescharacteristic
57C2×Dic146—22no—
58C2×Dic146—22no—
59C2×Dic146—22no—
60C2×Dic146—22no—
61C2×Dic146—41no—
62C2×Dic146—41no—
63C2×D292—22no—
64C2×D292—22no—
65C2×D292—41no—
66C2×C22⋊D73—22no—
67C2×C22⋊D73—22no—
68C2×C22⋊D73—22no—
69C2×C22⋊D73—22no—
70C2×C22⋊D73—22no—
71C2×C22⋊D73—41no—
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C22×Dic73C2311yescharacteristic
77C22×Dic73C2311yescharacteristic
78C2×C4×D73—22no—
79C2×C4×D73—22no—
80C2×C4×D73—22no—
81C4⋊Dic73—22no—
82#11924007—22no—
83#11924007—22no—
84#11924007D414yes—
85C22⋊Dic73—22no—
86C22⋊Dic73—41no—
87#11924005—22no—
88#11924005—22no—
89#11924005—22no—
90#11924005—22no—
91#11924005—22no—
92#11924005—22no—
93#11924005—22no—
94#11924005—41no—
95#11924005D414yescomplemented
96C4×Dic73—22no—
97C4×Dic73—22no—
98C4×Dic73—22no—
99C24×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105C22×C4×C73C2311yescharacteristic
106C4⋊C4×C73—22no—
107C22⋊C4×C73—22no—
108C22⋊C4×C73—22no—
109C22⋊C4×C73—22no—
110C42×C73—22no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73C2411yescharacteristic
119C22×D73—21no—
120C22×D73—21no—
121C22×D73—21no—
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—21no—
125C22×D73—21no—
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—21no—
129C22×D73—21no—
130C22×D73—21no—
131C22×D73—21no—
132C22×D73C2×D412yes—
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—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×C73C2×D412yes—
149C2×C4×C73C2×D412yes—
150C2×C4×C73#4112yes—
151C22⋊D73—44no—
152C22⋊D73—44no—
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×Dic73C2×D412yes—
167C2×Dic73C2×D412yes—
168C2×Dic73C2×D412yes—
169C2×Dic73#4112yes—
170C2×Dic73#4112yes—
171D292—44no—
172C4×D73—44no—
173Dic146—44no—
174Dic146—44no—
175C22×C73—41no—
176C22×C73—41no—
177C22×C73—41no—
178C22×C73—41no—
179C22×C73—41no—
180C22×C73—41no—
181C22×C73—41no—
182C22×C73C22×D411yescharacteristic
183C22×C73C22×D411yescharacteristic
184C22×C73C2×#4111yescharacteristic
185C22×C73C2×#4111yescharacteristic
186C22×C73C2×#4111yescharacteristic
187C22×C73H(5,𝔽2)11yescharacteristic
188C22×C732−1+411yescharacteristic
189C2×D73—22no—
190C2×D73—22no—
191C2×D73—22no—
192C2×D73—41no—
193C2×D73—41no—
194C2×D73—41no—
195C2×D73—41no—
196C2×D73—41no—
197C2×D73—41no—
198C2×D73—41no—
199C2×D73—41no—
200C2×D73—41no—
201C2×D73—41no—
202C2×D73—41no—
203C4×C73—22no—
204C4×C73—22no—
205C4×C73—22no—
206C4×C73—41no—
207C4×C73—41no—
208C4×C73—41no—
209Dic73—22no—
210Dic73—22no—
211Dic73—41no—
212Dic73—41no—
213Dic73—41no—
214Dic73#12414yescomplemented
215C2×C73—81no—
216C2×C73C2×#12411yescharacteristic
217C2×C73#53211yescharacteristic
218C2×C73#54211yescharacteristic
219C2×C73D4211yescharacteristic
220C2×C73#54711yescharacteristic
221C2×C73#54811yescharacteristic
222C2×C73#55511yescharacteristic
223D73—42no—
224D73—81no—
225#2491—731nomaximal, Sylow
226C73#249111yescharacteristic, complemented, Sylow
227C2×C4⋊Q8—731no—
228C2×#124—731no—
229C2×#124—731no—
230C2×#121—731no—
231#394—731no—
232#394—731no—
233#393—731no—
234#393—731no—
235#390—731no—
236#390—731no—
237#388—731no—
238#388D7311yescharacteristic, complemented
239#380—731no—
240C4×C4⋊C4—731no—
241C4×C22⋊C4—731no—
242C22×Q8—731no—
243C22×Q8—731no—
244C22×D4—731no—
245C22×D4—731no—
246C22×D4—731no—
247C23×C4—731no—
248C4⋊Q8—1464no—
249#124—1464no—
250#124—1464no—
251#121—1464no—
252C2×C4⋊C4—731no—
253C2×C4⋊C4—731no—
254C2×C4⋊C4—731no—
255C2×C4⋊C4—731no—
256C2×C4⋊C4C2×D7311yescharacteristic
257C2×C22⋊C4—731no—
258C2×C22⋊C4—731no—
259C2×C22⋊C4—731no—
260C2×C22⋊C4—731no—
261C2×C22⋊C4—731no—
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⋊C4C2×D7311yescharacteristic
269C2×C22⋊C4C2×D7311yescharacteristic
270C2×C22⋊C4C2×D7311yescharacteristic
271C2×C42—731no—
272C2×C42—731no—
273C2×C42—731no—
274C2×C42C2×D7311yescharacteristic
275#95—731no—
276#95—731no—
277#95—731no—
278#95—731no—
279#95C2×D7311yescharacteristic
280#95C2×D7311yescharacteristic
281C24—731no—
282C24—731no—
283C24C22×D7311yescharacteristic
284C2×Q8—2921no—
285C2×Q8—2921no—
286C2×Q8—1462no—
287C2×Q8—1462no—
288C2×Q8—1462no—
289C2×Q8—1462no—
290C2×D4—2921no—
291C2×D4—2921no—
292C2×D4—1462no—
293C2×D4—1462no—
294C2×D4—1462no—
295C2×D4—1462no—
296C2×D4—1462no—
297C2×D4—1462no—
298C2×D4—1462no—
299C22×C4—731no—
300C22×C4—731no—
301C22×C4—731no—
302C22×C4—731no—
303C22×C4—731no—
304C22×C4—731no—
305C22×C4—1462no—
306C22×C4—1462no—
307C22×C4—1462no—
308C22×C4C22×D7311yescharacteristic
309C22×C4C22×D7311yescharacteristic
310C22×C4C22×D7311yescharacteristic
311C22×C4C22×D7311yescharacteristic
312C22×C4C22×D7311yescharacteristic
313C22×C4C22×D7311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—734no—
316C4⋊C4—1462no—
317C4⋊C4—1462no—
318C4⋊C4—1462no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—2921no—
323C22⋊C4—2921no—
324C22⋊C4—734no—
325C22⋊C4—1462no—
326C22⋊C4—1462no—
327C22⋊C4—1462no—
328C22⋊C4—1462no—
329C22⋊C4—1462no—
330C22⋊C4—1462no—
331C22⋊C4—1462no—
332C22⋊C4—1462no—
333C42—22no—
334C42—1462no—
335C42—1462no—
336C42—1462no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—732no—
345C23—1461no—
346C23—1461no—
347C23—1461no—
348C23—1461no—
349C23—1461no—
350C23—1461no—
351C23—1461no—
352C23—1461no—
353C23—1461no—
354C23—1461no—
355C23—1461no—
356C23—1461no—
357C23—1461no—
358C23C23×D7311yescharacteristic
359Q8—2924no—
360Q8—2924no—
361D4—2924no—
362D4—2924no—
363D4—2924no—
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—21no—
378C2×C4—21no—
379C2×C4—2924no—
380C2×C4—732no—
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×C4D4×D7312yes—
399C2×C4D4×D7312yes—
400C2×C4#1192402812yes—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—2921no—
409C22—2921no—
410C22—2921no—
411C22—2921no—
412C22—2921no—
413C22—2921no—
414C22—2921no—
415C22—2921no—
416C22—2921no—
417C22—2921no—
418C22—2921no—
419C22—1462no—
420C22—1462no—
421C22—1462no—
422C22C2×D4×D7311yescharacteristic
423C22C2×D4×D7311yescharacteristic
424C22#41×D7311yescharacteristic
425C22#41×D7311yescharacteristic
426C22C2×#1192402811yescharacteristic
427C22#1455663711yescharacteristic
428C22#1455663811yescharacteristic
429C4—22no—
430C4—22no—
431C4—22no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—2921no—
436C4—2921no—
437C4—2921no—
438C4—734no—
439C4—1462no—
440C4—1462no—
441C2—81no—
442C2—2922no—
443C2—5841no—
444C2#124×D7311yescharacteristic
445C2#1798913411yescharacteristic
446C2#1798920311yescharacteristic
447C2#1798922111yescharacteristic
448C2#1798923511yescharacteristic
449C2#1798924611yescharacteristic
450C2#1798930011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#388×C73C2
hypercenter#388D73
hypocenterC73#2491
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14556590C2semidirect
2. C2×#14556579C2semidirect
3. C2×#14556577C2semidirect
5. #17988504C2semidirect
6. #17988503C2semidirect
7. #17988500C2semidirect
8. #17988499C2semidirect
9. #17988487C2semidirect
10. #17988487C2semidirect
11. #17988479C2semidirect
12. #17988446C2semidirect
13. C4×#11924007C2semidirect
14. #17988434C2semidirect
15. #388×C73C2semidirect
95. #11924005D4semidirect
214. Dic73#124semidirect
226. C73#2491semidirect
238. #388D73semidirect