Finite Group Databasebeta

← #22615004

Subgroups — #22615004

Order 9344.

696 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556578C211yesmaximal, characteristic, complemented
2C2×#14556577C211yesmaximal, characteristic, complemented
3C2×#14556563C211yesmaximal, characteristic, complemented
4#17988507C211yesmaximal, characteristic, complemented
5#17988501C211yesmaximal, characteristic, complemented
6#17988495C211yesmaximal, characteristic, complemented
7#17988495C211yesmaximal, characteristic, complemented
8#17988487C211yesmaximal, characteristic, complemented
9#17988477C211yesmaximal, characteristic, complemented
10#17988475C211yesmaximal, characteristic, complemented
11#17988467C211yesmaximal, characteristic, complemented
12#17988466C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
15C2×#121×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C22⋊D73C2211yescharacteristic
20C23×Dic73C2211yescharacteristic
21#14556578—24no—
22#14556577—24no—
23#14556563—24no—
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×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×C4×Dic73C2211yescharacteristic
39C2×C4×Dic73C2211yescharacteristic
40C2×C4×Dic73C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46#14556498C2211yescharacteristic
47C22×D4×C73C2211yescharacteristic
48C22×D4×C73C2211yescharacteristic
49C22×D4×C73C2211yescharacteristic
50C23×C4×C73C2211yescharacteristic
51#121×C73—24no—
52C2×C4⋊C4×C73C2211yescharacteristic
53C2×C22⋊C4×C73C2211yescharacteristic
54C2×C22⋊C4×C73C2211yescharacteristic
55C23×D73C2311yescharacteristic
56C2×Dic146—22no—
57C2×Dic146—22no—
58C2×Dic146—41no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—22no—
61C2×C22⋊D73—22no—
62C2×C22⋊D73—22no—
63C2×C22⋊D73—22no—
64C2×C22⋊D73—41no—
65C2×C22⋊D73—41no—
66C2×C22⋊D73—41no—
67C2×C22⋊D73—41no—
68C22×Dic73—22no—
69C22×Dic73—22no—
70C22×Dic73—41no—
71C22×Dic73C2311yescharacteristic
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C22×Dic73C2311yescharacteristic
77C22×Dic73C2311yescharacteristic
78#11924007—22no—
79#11924007—41no—
80C22⋊Dic73—22no—
81C22⋊Dic73—22no—
82C22⋊Dic73—22no—
83C22⋊Dic73—22no—
84C22⋊Dic73—22no—
85C22⋊Dic73—22no—
86C22⋊Dic73—22no—
87C22⋊Dic73D414yescomplemented
88#11924005—22no—
89#11924005—22no—
90#11924005—22no—
91#11924005—22no—
92C4×Dic73—22no—
93C4×Dic73—22no—
94C4×Dic73—41no—
95C24×C73C2311yescharacteristic
96C24×C73C2311yescharacteristic
97C24×C73C2311yescharacteristic
98C2×D4×C73—22no—
99C2×D4×C73—22no—
100C2×D4×C73—22no—
101C2×D4×C73—22no—
102C2×D4×C73—22no—
103C2×D4×C73—22no—
104C2×D4×C73—41no—
105C2×D4×C73—41no—
106C2×D4×C73—41no—
107C22×C4×C73—22no—
108C22×C4×C73—22no—
109C22×C4×C73—41no—
110C22×C4×C73C2311yescharacteristic
111C22×C4×C73C2311yescharacteristic
112C22×C4×C73C2311yescharacteristic
113C22×C4×C73C2311yescharacteristic
114C4⋊C4×C73—22no—
115C22⋊C4×C73—22no—
116C22⋊C4×C73D414yescomplemented
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×C73—21no—
126C23×C73—21no—
127C23×C73—21no—
128C23×C73—21no—
129C23×C73—21no—
130C23×C73—21no—
131C23×C73—21no—
132C23×C73—21no—
133C23×C73—21no—
134C23×C73—21no—
135C23×C73—21no—
136C23×C73C2×D412yes—
137C23×C73C2×D412yes—
138C23×C73C2411yescharacteristic
139C22×D73—21no—
140C22×D73—21no—
141C22×D73—21no—
142C22×D73—21no—
143C22×D73—21no—
144C22×D73—21no—
145C22×D73—21no—
146D4×C73—44no—
147D4×C73—44no—
148D4×C73—44no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—21no—
154C2×C4×C73—21no—
155C2×C4×C73—21no—
156C2×C4×C73—21no—
157C2×C4×C73—21no—
158C2×C4×C73—44no—
159C2×C4×C73C2×D412yes—
160C2×C4×C73C2×D412yes—
161C2×C4×C73#4112yes—
162C22⋊D73—44no—
163C22⋊D73—44no—
164C22⋊D73—44no—
165C2×Dic73—21no—
166C2×Dic73—21no—
167C2×Dic73—21no—
168C2×Dic73—21no—
169C2×Dic73—21no—
170C2×Dic73—21no—
171C2×Dic73—21no—
172C2×Dic73—21no—
173C2×Dic73—21no—
174C2×Dic73—21no—
175C2×Dic73—21no—
176C2×Dic73—21no—
177C2×Dic73—21no—
178C2×Dic73—21no—
179C2×Dic73—21no—
180C2×Dic73—21no—
181C2×Dic73—21no—
182C2×Dic73—44no—
183C2×Dic73C2×D412yes—
184C2×Dic73C2×D412yes—
185C2×Dic73#4112yes—
186C2×Dic73#4112yes—
187Dic146—44no—
188C22×C73—22no—
189C22×C73—22no—
190C22×C73—22no—
191C22×C73—22no—
192C22×C73—22no—
193C22×C73—22no—
194C22×C73—41no—
195C22×C73—41no—
196C22×C73—41no—
197C22×C73—41no—
198C22×C73—41no—
199C22×C73—41no—
200C22×C73—41no—
201C22×C73—41no—
202C22×C73—41no—
203C22×C73—41no—
204C22×C73—41no—
205C22×C73—41no—
206C22×C73—41no—
207C22×C73—41no—
208C22×C73—41no—
209C22×C73C22×D411yescharacteristic
210C22×C73C22×D411yescharacteristic
211C22×C73C2×#4111yescharacteristic
212C22×C73C2×#4111yescharacteristic
213C22×C73C2×#4111yescharacteristic
214C22×C73H(5,𝔽2)11yescharacteristic
215C22×C73H(5,𝔽2)11yescharacteristic
216C2×D73—41no—
217C2×D73—41no—
218C2×D73—41no—
219C2×D73—41no—
220C2×D73—41no—
221C2×D73—41no—
222C2×D73—41no—
223C4×C73—22no—
224C4×C73—22no—
225C4×C73—22no—
226C4×C73—41no—
227Dic73—22no—
228Dic73—22no—
229Dic73—22no—
230Dic73—22no—
231Dic73—41no—
232Dic73—41no—
233Dic73—41no—
234C2×C73—42no—
235C2×C73—42no—
236C2×C73—81no—
237C2×C73#53211yescharacteristic
238C2×C73#53211yescharacteristic
239C2×C73#53811yescharacteristic
240C2×C73D4211yescharacteristic
241C2×C73#54611yescharacteristic
242C2×C73#54611yescharacteristic
243C2×C73#55511yescharacteristic
244D73—81no—
245#2555—731nomaximal, Sylow
246C73#255511yescharacteristic, complemented, Sylow
247C2×#124—731no—
248C2×#124—731no—
249C2×#121—731no—
250C2×#121D7311yescharacteristic, complemented
251#395—731no—
252#394—731no—
253#392—731no—
254#392—731no—
255#390—731no—
256#388—731no—
257#388—731no—
258#386—731no—
259#386—731no—
260C4×C22⋊C4—731no—
261C4×C22⋊C4—731no—
262C22×Q8—731no—
263C22×D4—731no—
264C22×D4—731no—
265C22×D4—731no—
266C22×D4C2×D7311yescharacteristic
267C22×D4C2×D7311yescharacteristic
268C22×D4C2×D7311yescharacteristic
269C23×C4—731no—
270C23×C4C2×D7311yescharacteristic
271#124—1464no—
272#124—1464no—
273#121—24no—
274#121—1464no—
275C2×C4⋊C4—731no—
276C2×C4⋊C4—731no—
277C2×C4⋊C4C2×D7311yescharacteristic
278C2×C22⋊C4—731no—
279C2×C22⋊C4—731no—
280C2×C22⋊C4—731no—
281C2×C22⋊C4—731no—
282C2×C22⋊C4—731no—
283C2×C22⋊C4—731no—
284C2×C22⋊C4—731no—
285C2×C22⋊C4—731no—
286C2×C22⋊C4—731no—
287C2×C22⋊C4—731no—
288C2×C22⋊C4—731no—
289C2×C22⋊C4—731no—
290C2×C22⋊C4C2×D7311yescharacteristic
291C2×C22⋊C4C2×D7311yescharacteristic
292C2×C42—731no—
293C2×C42—731no—
294C2×C42—731no—
295#95—731no—
296#95—731no—
297#95—731no—
298#95—731no—
299#95—731no—
300#95—731no—
301C24—731no—
302C24C22×D7311yescharacteristic
303C24C22×D7311yescharacteristic
304C24C22×D7311yescharacteristic
305C2×Q8—2921no—
306C2×Q8—1462no—
307C2×Q8—1462no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—2921no—
318C2×D4—2921no—
319C2×D4—2921no—
320C2×D4—2921no—
321C2×D4—1462no—
322C2×D4—1462no—
323C2×D4—1462no—
324C2×D4—1462no—
325C2×D4—1462no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—41no—
329C22×C4—2921no—
330C22×C4—731no—
331C22×C4—731no—
332C22×C4—731no—
333C22×C4—731no—
334C22×C4—731no—
335C22×C4—731no—
336C22×C4—731no—
337C22×C4—1462no—
338C22×C4—1462no—
339C22×C4C22×D7311yescharacteristic
340C22×C4C22×D7311yescharacteristic
341C22×C4C22×D7311yescharacteristic
342C22×C4C22×D7311yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—2921no—
345C4⋊C4—1462no—
346C22⋊C4—22no—
347C22⋊C4—734no—
348C22⋊C4—1462no—
349C22⋊C4—1462no—
350C22⋊C4—1462no—
351C22⋊C4—1462no—
352C22⋊C4—1462no—
353C22⋊C4—1462no—
354C22⋊C4—1462no—
355C22⋊C4—1462no—
356C22⋊C4—1462no—
357C22⋊C4—1462no—
358C22⋊C4—1462no—
359C22⋊C4C22⋊D7314yescomplemented
360C42—2921no—
361C42—1462no—
362C42—1462no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—1461no—
383C23—1461no—
384C23—1461no—
385C23—1461no—
386C23—1461no—
387C23—1461no—
388C23—1461no—
389C23D4×D7312yes—
390C23C2×C22⋊D7312yes—
391C23C23×D7311yescharacteristic
392Q8—2924no—
393D4—44no—
394D4—44no—
395D4—44no—
396D4—2924no—
397D4—2924no—
398D4—2924no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—44no—
409C2×C4—2924no—
410C2×C4—732no—
411C2×C4—732no—
412C2×C4—732no—
413C2×C4—732no—
414C2×C4—1461no—
415C2×C4—1461no—
416C2×C4—1461no—
417C2×C4—1461no—
418C2×C4—1461no—
419C2×C4—1461no—
420C2×C4—1461no—
421C2×C4—1461no—
422C2×C4—1461no—
423C2×C4—1461no—
424C2×C4—1461no—
425C2×C4—1461no—
426C2×C4—1461no—
427C2×C4—1461no—
428C2×C4—1461no—
429C2×C4—1461no—
430C2×C4—1461no—
431C2×C4C2×C22⋊D7312yes—
432C2×C4C2×C22⋊D7312yes—
433C2×C4#1192402712yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—2921no—
456C22—2921no—
457C22—2921no—
458C22—2921no—
459C22—2921no—
460C22—2921no—
461C22—2921no—
462C22C2×D4×D7311yescharacteristic
463C22C22×C22⋊D7311yescharacteristic
464C22#41×D7311yescharacteristic
465C22#41×D7311yescharacteristic
466C22C2×#1192402711yescharacteristic
467C22#1455663611yescharacteristic
468C22#1455663611yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—2921no—
474C4—2921no—
475C4—2921no—
476C4—1462no—
477C4—1462no—
478C4—1462no—
479C4—1462no—
480C2—42no—
481C2—42no—
482C2—81no—
483C2—5841no—
484C2#1798913211yescharacteristic
485C2#1798913311yescharacteristic
486C2#1798916911yescharacteristic
487C2D4×C22⋊D7311yescharacteristic
488C2#1798922611yescharacteristic
489C2#1798923111yescharacteristic
490C2#1798930111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#121×C73C2
hypercenterC2×#121D73
hypocenterC73#2555
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14556578C2semidirect
2. C2×#14556577C2semidirect
3. C2×#14556563C2semidirect
4. #17988507C2semidirect
5. #17988501C2semidirect
6. #17988495C2semidirect
7. #17988495C2semidirect
8. #17988487C2semidirect
9. #17988477C2semidirect
10. #17988475C2semidirect
11. #17988467C2semidirect
12. #17988466C2semidirect
13. C22⋊C4×Dic73C2semidirect
14. C4×C22⋊Dic73C2semidirect
15. C2×#121×C73C2semidirect
87. C22⋊Dic73D4semidirect
116. C22⋊C4×C73D4semidirect
246. C73#2555semidirect
250. C2×#121D73semidirect
359. C22⋊C4C22⋊D73semidirect