Finite Group Databasebeta

← #33239708

Subgroups — #33239708

Order 18688.

484 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618899C211yesmaximal, characteristic
2#22611839C211yesmaximal, characteristic, complemented
3#22611838C211yesmaximal, characteristic, complemented
4#22611761C211yesmaximal, characteristic, complemented
5#22611759C211yesmaximal, characteristic, complemented
6#22611757C211yesmaximal, characteristic, complemented
7#22611754C211yesmaximal, characteristic, complemented
8#22611753C211yesmaximal, characteristic, complemented
9#22611736C211yesmaximal, characteristic, complemented
10#22611735C211yesmaximal, characteristic, complemented
11#22611731C211yesmaximal, characteristic, complemented
12#22611691C211yesmaximal, characteristic, complemented
13#22611688C211yesmaximal, characteristic, complemented
14#22611686C211yesmaximal, characteristic, complemented
15C73×#2169C211yesmaximal, characteristic, complemented
16#17989117C411yescharacteristic
17C2×#14556531C2211yescharacteristic
18C2×#14556530C2211yescharacteristic
19C22×#11924003C2211yescharacteristic
20C2×C16×D73C2211yescharacteristic
21#17988716C411yescharacteristic
22C8×Dic146C2211yescharacteristic
23#17988662C411yescharacteristic
24#17988659C411yescharacteristic
25#17988655C411yescharacteristic
26C8×C22⋊D73C2211yescharacteristic
27C8×C22⋊D73C2211yescharacteristic
28#17988647C411yescharacteristic
29#17988645C411yescharacteristic
30#17988641C411yescharacteristic
31#17988542C2211yescharacteristic
32#17988541C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34C4⋊#11924003C2211yescharacteristic
35#17988405C2211yescharacteristic
36#17988405C2211yescharacteristic
37#17988405C2211yescharacteristic
38#17988405C2211yescharacteristic
39#17988405C2211yescharacteristic
40#17988405C2211yescharacteristic
41#17988405C2211yescharacteristic
42#17988405C2211yescharacteristic
43C22⋊#11924003C2211yescharacteristic
44C22⋊#11924003C2211yescharacteristic
45#17988366C2211yescharacteristic
46#17988366C2211yescharacteristic
47#17988363C2211yescharacteristic
48#17988362C2211yescharacteristic
49#17988362C2211yescharacteristic
50#17988362C2211yescharacteristic
51C16×Dic73C2211yescharacteristic
52C2×M32×C73C2211yescharacteristic
53C2×M32×C73C2211yescharacteristic
54C8×D4×C73C2211yescharacteristic
55C4⋊C16×C73C2211yescharacteristic
56C22⋊C16×C73C2211yescharacteristic
57C22⋊C16×C73C2211yescharacteristic
58C4×C16×C73C2211yescharacteristic
59C2×#11924012C2×C411yescharacteristic
60C2×#11924011C2×C411yescharacteristic
61C22×#10596831C2×C411yescharacteristic
62C2×C8×D73C2311yescharacteristic
63#14556586C811yescharacteristic
64#14556584C811yescharacteristic
65#14556581C811yescharacteristic
66#14556577C811yescharacteristic
67#14556575C811yescharacteristic
68#14556572C811yescharacteristic
69#14556568C811yescharacteristic
70#14556563C811yescharacteristic
71C4×Dic146C2×C411yescharacteristic
72C4×C22⋊D73C2×C411yescharacteristic
73C4×C22⋊D73C2×C411yescharacteristic
74#14556550C2×C411yescharacteristic
75#14556548C2×C411yescharacteristic
76C2×C4×Dic73C2×C411yescharacteristic
77#14556531—41no—
78#14556530—41no—
79C2×#11924003—41no—
80C2×#11924003C2311yescharacteristic
81C2×#11924003C2311yescharacteristic
82C2×#11924003C2311yescharacteristic
83C2×#11924003C2311yescharacteristic
84C16×D73—41no—
85C4⋊#10596831C2×C411yescharacteristic
86#14556520C2×C411yescharacteristic
87#14556520C2×C411yescharacteristic
88#14556520C2×C411yescharacteristic
89#14556520C2×C411yescharacteristic
90C22⋊#10596831C2×C411yescharacteristic
91C22⋊#10596831C2×C411yescharacteristic
92#14556503C2×C411yescharacteristic
93#14556503C2×C411yescharacteristic
94#14556502C2×C411yescharacteristic
95#14556501C2×C411yescharacteristic
96#14556501C2×C411yescharacteristic
97#14556501C2×C411yescharacteristic
98C8×Dic73C2×C411yescharacteristic
99C8×Dic73C2×C411yescharacteristic
100C8×Dic73C2311yescharacteristic
101C8×Dic73C2311yescharacteristic
102C8×Dic73C2311yescharacteristic
103C22×C8×C73C2311yescharacteristic
104C22×C8×C73C2311yescharacteristic
105C4×D4×C73C2×C411yescharacteristic
106M32×C73—41no—
107M32×C73—41no—
108C2×C16×C73C2311yescharacteristic
109C2×C16×C73C2311yescharacteristic
110C2×C16×C73C2311yescharacteristic
111C2×C16×C73C2311yescharacteristic
112C4⋊C8×C73C2×C411yescharacteristic
113C22⋊C8×C73C2×C411yescharacteristic
114C22⋊C8×C73C2×C411yescharacteristic
115C4×C8×C73C2311yescharacteristic
116C2×Dic146C2×C811yescharacteristic
117C2×C22⋊D73C2×C811yescharacteristic
118C2×C22⋊D73C2×C811yescharacteristic
119C22×Dic73C2×C811yescharacteristic
120C22×Dic73C2×C811yescharacteristic
121C2×C4×D73C22×C411yescharacteristic
122#11924012—41no—
123#11924011—41no—
124C2×#10596831—41no—
125C2×#10596831C22×C411yescharacteristic
126C2×#10596831C22×C411yescharacteristic
127C2×#10596831C22×C411yescharacteristic
128C2×#10596831C22×C411yescharacteristic
129C8×D73—21no—
130C8×D73—21no—
131C4⋊Dic73C2×C811yescharacteristic
132C4⋊Dic73C2×C811yescharacteristic
133C4⋊Dic73C2×C811yescharacteristic
134#11924007C2×C811yescharacteristic
135#11924007C2×C811yescharacteristic
136#11924007C2×C811yescharacteristic
137#11924007C2×C811yescharacteristic
138#11924007C2×C811yescharacteristic
139#11924007C2×C811yescharacteristic
140C22⋊Dic73C2×C811yescharacteristic
141C22⋊Dic73C2×C811yescharacteristic
142C22⋊Dic73C2×C811yescharacteristic
143C22⋊Dic73C2×C811yescharacteristic
144#11924005C2×C811yescharacteristic
145#11924005C2×C811yescharacteristic
146#11924005C2×C811yescharacteristic
147#11924005C2×C811yescharacteristic
148C4×Dic73C2×C811yescharacteristic
149C4×Dic73C2×C811yescharacteristic
150C4×Dic73C22×C411yescharacteristic
151C4×Dic73C22×C411yescharacteristic
152C4×Dic73C22×C411yescharacteristic
153#11924003—21no—
154#11924003—21no—
155#11924003—21no—
156#11924003—21no—
157C2×D4×C73C2×C811yescharacteristic
158C22×C4×C73C22×C411yescharacteristic
159C22×C4×C73C22×C411yescharacteristic
160C2×C8×C73—21no—
161C2×C8×C73—21no—
162C2×C8×C73—21no—
163C2×C8×C73—21no—
164C2×C8×C73C22×C411yescharacteristic
165C2×C8×C73C22×C411yescharacteristic
166C2×C8×C73C22×C411yescharacteristic
167C2×C8×C73C2411yescharacteristic
168C4⋊C4×C73C2×C811yescharacteristic
169C22⋊C4×C73C2×C811yescharacteristic
170C22⋊C4×C73C2×C811yescharacteristic
171C42×C73C22×C411yescharacteristic
172C16×C73—21no—
173C16×C73—21no—
174C16×C73—21no—
175C16×C73—21no—
176C23×C73C22×C811yescharacteristic
177C23×C73C22×C811yescharacteristic
178C22×D73C22×C811yescharacteristic
179D4×C73—41no—
180C2×C4×C73—21no—
181C2×C4×C73—21no—
182C2×C4×C73—21no—
183C2×C4×C73—21no—
184C2×C4×C73C22×C811yescharacteristic
185C2×C4×C73C22×C811yescharacteristic
186C2×C4×C73C22×C811yescharacteristic
187C2×C4×C73C22×C811yescharacteristic
188C2×C4×C73C23×C411yescharacteristic
189C22⋊D73—41no—
190C22⋊D73—41no—
191C2×Dic73—41no—
192C2×Dic73—41no—
193C2×Dic73C22×C811yescharacteristic
194C2×Dic73C22×C811yescharacteristic
195C2×Dic73C22×C811yescharacteristic
196C2×Dic73C22×C811yescharacteristic
197C2×Dic73C22×C811yescharacteristic
198C2×Dic73C22×C811yescharacteristic
199C2×Dic73C22×C811yescharacteristic
200C4×D73—21no—
201C4×D73—21no—
202Dic146—41no—
203C8×C73—21no—
204C8×C73—21no—
205C8×C73—21no—
206C8×C73H(5,𝔽2)11yescharacteristic
207C8×C732−1+411yescharacteristic
208#10596831—21no—
209#10596831—21no—
210#10596831—21no—
211#10596831—21no—
212C22×C73—21no—
213C22×C73—21no—
214C22×C73—21no—
215C22×C73—21no—
216C22×C73—21no—
217C22×C73—21no—
218C22×C73C23×C811yescharacteristic
219C2×D73—21no—
220C2×D73—21no—
221C2×D73—21no—
222C4×C73—21no—
223C4×C73—21no—
224C4×C73—21no—
225C4×C73—21no—
226C4×C73#52011yescharacteristic
227C4×C73#56811yescharacteristic
228Dic73—21no—
229Dic73—21no—
230Dic73—21no—
231Dic73—21no—
232Dic73—21no—
233Dic73—21no—
234Dic73—21no—
235#33509—731nomaximal, Sylow
236C2×C73—41no—
237C2×C73—41no—
238C2×C73#298811yescharacteristic
239C2×C73#340711yescharacteristic
240C2×C73#340711yescharacteristic
241D73—41no—
242#2966—731no—
243#2183—731no—
244#2183—731no—
245#2169—731no—
246#2169D7311yescharacteristic, complemented
247#2168—731no—
248#2168—731no—
249#2168—731no—
250#2168—731no—
251#2164—731no—
252#2164—731no—
253#2163—731no—
254#2151—731no—
255#2151—731no—
256#2150—731no—
257C73#3350911yescharacteristic, complemented, Sylow
258#529—731no—
259C2×M32—731no—
260C2×M32—731no—
261C2×M32C2×D7311yescharacteristic
262C2×M32C2×D7311yescharacteristic
263C22×C16—731no—
264C22×C16—731no—
265#446—731no—
266C8×Q8—731no—
267#436—731no—
268#435—731no—
269#435—731no—
270C8×D4—731no—
271C8×D4—731no—
272C8×D4C2×D7311yescharacteristic
273#433—731no—
274#433—731no—
275#432—731no—
276#405—731no—
277#405—731no—
278C2×C4×C8—731no—
279C4⋊C16—731no—
280C4⋊C16—731no—
281C4⋊C16—731no—
282C4⋊C16—731no—
283C4⋊C16—731no—
284C4⋊C16—731no—
285C4⋊C16—731no—
286C4⋊C16—731no—
287C4⋊C16—731no—
288C4⋊C16C2×D7311yescharacteristic
289C22⋊C16—731no—
290C22⋊C16—731no—
291C22⋊C16—731no—
292C22⋊C16—731no—
293C22⋊C16C2×D7311yescharacteristic
294C22⋊C16C2×D7311yescharacteristic
295#346—731no—
296#346—731no—
297#346—731no—
298#346—731no—
299C4×C16—731no—
300C4×C16C2×D7311yescharacteristic
301C2×M16—731no—
302C2×M16—731no—
303C22×C8—731no—
304C22×C8—731no—
305C22×C8C22×D7311yescharacteristic
306C22×C8C22×D7311yescharacteristic
307#126—731no—
308#126—731no—
309#125—731no—
310#124—731no—
311#123—731no—
312#123—731no—
313C22⋊Q8—731no—
314#121—731no—
315C4×Q8—731no—
316C4×D4—731no—
317C4×D4—731no—
318C4×D4C4×D7311yescharacteristic
319#117—731no—
320#117—731no—
321C2×C42—731no—
322M32—41no—
323M32—41no—
324M32—2921no—
325M32—2921no—
326C2×C16—2921no—
327C2×C16—2921no—
328C2×C16—731no—
329C2×C16—731no—
330C2×C16—731no—
331C2×C16—731no—
332C2×C16C22×D7311yescharacteristic
333C2×C16C22×D7311yescharacteristic
334C2×C16C22×D7311yescharacteristic
335C2×C16C22×D7311yescharacteristic
336C4⋊C8—731no—
337C4⋊C8—731no—
338C4⋊C8—731no—
339C4⋊C8—731no—
340C4⋊C8—731no—
341C4⋊C8C4×D7311yescharacteristic
342C22⋊C8—731no—
343C22⋊C8—731no—
344C22⋊C8—731no—
345C22⋊C8—731no—
346C22⋊C8C4×D7311yescharacteristic
347C22⋊C8C4×D7311yescharacteristic
348#97—731no—
349#97—731no—
350#97—731no—
351#97—731no—
352C4×C8—731no—
353C4×C8—731no—
354C4×C8—731no—
355C4×C8—731no—
356C4×C8—731no—
357C4×C8C22×D7311yescharacteristic
358C2×Q8—731no—
359C2×D4—731no—
360C2×D4—731no—
361C2×D4C8×D7311yescharacteristic
362C22×C4—731no—
363C22×C4—731no—
364C22×C4—731no—
365C22×C4C2×C4×D7311yescharacteristic
366C22×C4C2×C4×D7311yescharacteristic
367M16—2921no—
368M16—2921no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—2921no—
374C2×C8—731no—
375C2×C8—731no—
376C2×C8—731no—
377C2×C8—731no—
378C2×C8—1461no—
379C2×C8—1461no—
380C2×C8C2×C4×D7311yescharacteristic
381C2×C8C2×C4×D7311yescharacteristic
382C2×C8C2×C4×D7311yescharacteristic
383C2×C8C23×D7311yescharacteristic
384C4⋊C4—731no—
385C4⋊C4—731no—
386C4⋊C4—731no—
387C4⋊C4—731no—
388C4⋊C4—731no—
389C4⋊C4—731no—
390C4⋊C4—731no—
391C4⋊C4—731no—
392C4⋊C4—731no—
393C4⋊C4C8×D7311yescharacteristic
394C22⋊C4—731no—
395C22⋊C4—731no—
396C22⋊C4—731no—
397C22⋊C4—731no—
398C22⋊C4—731no—
399C22⋊C4—731no—
400C22⋊C4—731no—
401C22⋊C4—731no—
402C22⋊C4C8×D7311yescharacteristic
403C22⋊C4C8×D7311yescharacteristic
404C42—731no—
405C42—731no—
406C42—731no—
407C42—731no—
408C42—731no—
409C42C2×C4×D7311yescharacteristic
410C16—21no—
411C16—21no—
412C16—21no—
413C16—21no—
414C16—1461no—
415C16—1461no—
416C16—1461no—
417C16—1461no—
418C23—731no—
419C23C2×C8×D7311yescharacteristic
420C23C2×C8×D7311yescharacteristic
421Q8—2921no—
422D4—41no—
423D4—2921no—
424D4—2921no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—2921no—
430C2×C4—2921no—
431C2×C4—731no—
432C2×C4—731no—
433C2×C4—731no—
434C2×C4—731no—
435C2×C4—731no—
436C2×C4—731no—
437C2×C4—731no—
438C2×C4—1461no—
439C2×C4—1461no—
440C2×C4C2×C8×D7311yescharacteristic
441C2×C4C2×C8×D7311yescharacteristic
442C2×C4C2×C8×D7311yescharacteristic
443C2×C4C2×C8×D7311yescharacteristic
444C2×C4C22×C4×D7311yescharacteristic
445C8—21no—
446C8—21no—
447C8—21no—
448C8—1461no—
449C8—1461no—
450C8—1461no—
451C8—1461no—
452C8#1455663611yescharacteristic
453C8#1455663811yescharacteristic
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—1461no—
461C22—1461no—
462C22—1461no—
463C22C22×C8×D7311yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—1461no—
469C4—1461no—
470C4—1461no—
471C4—1461no—
472C4—1461no—
473C4—1461no—
474C4—1461no—
475C4#1798906611yescharacteristic
476C4#1798935211yescharacteristic
477C2—41no—
478C2—41no—
479C2—2921no—
480C2#2261903811yescharacteristic
481C2#2262303211yescharacteristic
482C2#2262303311yescharacteristic
subgroupG/H
center, FrattiniC2×C8C23×D73
commutator, socleC22×C73C23×C8
FittingC73×#2169C2
prime radical#14556563C8
cosocleC2×C8×C73C24
hypercenter#2169D73
hypocenterC73#33509
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ #2169

Complements

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

NH ≅ G/Ntype
2. #22611839C2semidirect
3. #22611838C2semidirect
4. #22611761C2semidirect
5. #22611759C2semidirect
6. #22611757C2semidirect
7. #22611754C2semidirect
8. #22611753C2semidirect
9. #22611736C2semidirect
10. #22611735C2semidirect
11. #22611731C2semidirect
12. #22611691C2semidirect
13. #22611688C2semidirect
14. #22611686C2semidirect
15. C73×#2169C2semidirect
246. #2169D73semidirect
257. C73#33509semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226188992
#226118392
#226118382
#226117612
#226117592
#226117572
#226117542
#226117532
#226117362
#226117352
#226117312
#226116912
#226116882
#226116862
C73×#21692
#3350973