Finite Group Databasebeta

← C2×#22608561 #33054009

Subgroups — C2×#22608561 #33054009

Order 18688.

986 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989122C211yesmaximal, characteristic
2C2×#17988642C211yesmaximal, characteristic, complemented
3C2×#17988642C211yesmaximal, characteristic, complemented
4#22608561C218yesmaximal, direct product factor
5C2×#17988329C211yesmaximal, characteristic, complemented
6C2×#17988326C211yesmaximal, characteristic, complemented
7C2×#17988326C211yesmaximal, characteristic, complemented
8C2×#330×C73C211yesmaximal, characteristic, complemented
9#17989122—22no—
10#17989122—22no—
11#17989122C414yes—
12#17989122C2214yes—
13C2×#14556586—21no—
14C2×#14556579C2211yescharacteristic
15C2×#14556576—21no—
16C2×#14556571C411yescharacteristic
17C2×#14556566C411yescharacteristic
18C2×#14556556C411yescharacteristic
19C2×#14556553—21no—
20C2×#14556553C411yescharacteristic
21C2×#14556549—21no—
22C2×C42×D73C2211yescharacteristic
23#17988642—22no—
24#17988642—22no—
25#17988642C2214yescomplemented
26#17988642C2214yescomplemented
27C2×#14556520—21no—
28C2×#14556520—21no—
29C2×#14556503—21no—
30C2×#14556503—21no—
31C2×#14556502C2211yescharacteristic
32C2×#14556502C2211yescharacteristic
33#17988329C2214yescomplemented
34#17988326C2214yescomplemented
35#17988326C2214yescomplemented
36C2×#125×C73C2211yescharacteristic
37C2×#97×C73C2211yescharacteristic
38C2×#97×C73C2211yescharacteristic
39#330×C73C2214yescomplemented
40C22×Dic146C2×C411yescharacteristic
41C22×D292—21no—
42C22×D292C2×C411yescharacteristic
43C22×C4×D73—21no—
44C22×C4×D73C2×C411yescharacteristic
45C22×C4×D73D411yescharacteristic
46C22×C4×D73D411yescharacteristic
47C22×#10596831—21no—
48C22×#10596831—21no—
49#14556586—24no—
50#14556586—24no—
51#14556579—21no—
52#14556579—21no—
53#14556579C2×C412yes—
54#14556579C2312yes—
55#14556576—24no—
56#14556576—24no—
57#14556571—22no—
58#14556571C2×C414yes—
59#14556566—22no—
60#14556566C2×C414yes—
61#14556556—22no—
62#14556556C2×C414yes—
63#14556553—24no—
64#14556553—24no—
65#14556553—22no—
66#14556553C2×C414yes—
67#14556549—24no—
68#14556549—24no—
69C2×C4⋊Dic73—21no—
70C2×#11924007—21no—
71C2×#11924005—21no—
72C2×#11924005—21no—
73C2×#11924005—21no—
74C2×#11924005—21no—
75C2×#11924005—21no—
76C2×C4×Dic73—21no—
77C2×C4×Dic73C2×C411yescharacteristic
78C2×C4×Dic73D411yescharacteristic
79C2×C4×Dic73D411yescharacteristic
80C42×D73C2×C412yes—
81C42×D73D412yes—
82C42×D73D412yes—
83C42×D73C2312yes—
84#14556520—24no—
85#14556520—24no—
86#14556503—24no—
87#14556503—24no—
88#14556502—21no—
89#14556502—21no—
90#14556502C2312yes—
91#14556502C2312yes—
92C22×C8×C73—21no—
93C22×C8×C73—21no—
94#125×C73—21no—
95#125×C73—21no—
96#125×C73C2×C412yes—
97#125×C73C2312yes—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73C2×C411yescharacteristic
101C2×C4⋊C4×C73C2×C411yescharacteristic
102C2×C42×C73C2311yescharacteristic
103#97×C73—21no—
104#97×C73—21no—
105#97×C73C2312yes—
106#97×C73C2312yes—
107C23×D73—21no—
108C23×D73C22⋊C411yescharacteristic
109C2×Dic146—21no—
110C2×Dic146—42no—
111C2×Dic146C22×C412yes—
112C2×D292—24no—
113C2×D292—21no—
114C2×D292—42no—
115C2×D292—44no—
116C2×D292C22×C412yes—
117C22×Dic73—21no—
118C22×Dic73C22⋊C411yescharacteristic
119C22×Dic73C22⋊C411yescharacteristic
120C22×Dic73C22⋊C411yescharacteristic
121C2×C4×D73—24no—
122C2×C4×D73—42no—
123C2×C4×D73—42no—
124C2×C4×D73—42no—
125C2×C4×D73—44no—
126C2×C4×D73C22⋊C412yes—
127C2×C4×D73C22⋊C412yes—
128C2×C4×D73C22⋊C412yes—
129C2×C4×D73C22×C412yes—
130C2×C4×D73C2×D412yes—
131C2×C4×D73C2×D412yes—
132C2×#10596831—22no—
133C2×#10596831—22no—
134C2×#10596831—42no—
135C2×#10596831—42no—
136C4⋊Dic73—24no—
137#11924007—24no—
138#11924005—24no—
139#11924005—22no—
140#11924005—22no—
141#11924005—22no—
142#11924005—22no—
143#11924005—24no—
144#11924005—24no—
145C4×Dic73—24no—
146C4×Dic73C22⋊C412yes—
147C4×Dic73C22⋊C412yes—
148C4×Dic73C22⋊C412yes—
149C4×Dic73C22×C412yes—
150C4×Dic73C2×D412yes—
151C4×Dic73C2×D412yes—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73C22×C411yescharacteristic
155C22×C4×C73C2×D411yescharacteristic
156C22×C4×C73C2×D411yescharacteristic
157C2×C8×C73—22no—
158C2×C8×C73—22no—
159C2×C8×C73—42no—
160C2×C8×C73—42no—
161C4⋊C4×C73—22no—
162C4⋊C4×C73—22no—
163C4⋊C4×C73—21no—
164C4⋊C4×C73—21no—
165C4⋊C4×C73—22no—
166C4⋊C4×C73—22no—
167C4⋊C4×C73C22×C412yes—
168C4⋊C4×C73C22×C412yes—
169C42×C73C22×C411yescharacteristic
170C42×C73C2×D411yescharacteristic
171C42×C73C2×D411yescharacteristic
172C42×C73C2411yescharacteristic
173C23×C73C2×C22⋊C411yescharacteristic
174C22×D73—22no—
175C22×D73—22no—
176C22×D73—22no—
177C22×D73—22no—
178C22×D73—42no—
179C22×D73—42no—
180C22×D73—42no—
181C22×D73C2×C22⋊C412yes—
182C2×C4×C73—22no—
183C2×C4×C73—22no—
184C2×C4×C73—22no—
185C2×C4×C73—22no—
186C2×C4×C73—22no—
187C2×C4×C73—42no—
188C2×C4×C73—42no—
189C2×C4×C73C2×C22⋊C411yescharacteristic
190C2×C4×C73C2×C22⋊C411yescharacteristic
191C2×C4×C73C2×C22⋊C411yescharacteristic
192C2×C4×C73C23×C411yescharacteristic
193C2×C4×C73C22×D411yescharacteristic
194C2×C4×C73C22×D411yescharacteristic
195C2×Dic73—22no—
196C2×Dic73—22no—
197C2×Dic73—22no—
198C2×Dic73—22no—
199C2×Dic73—42no—
200C2×Dic73C2×C22⋊C412yes—
201C2×Dic73C2×C22⋊C412yes—
202C2×Dic73C2×C22⋊C412yes—
203D292—42no—
204D292—42no—
205D292—48no—
206C4×D73—42no—
207C4×D73—42no—
208C4×D73—42no—
209C4×D73—42no—
210C4×D73—42no—
211C4×D73—42no—
212C4×D73—48no—
213Dic146—42no—
214Dic146—42no—
215C8×C73—42no—
216C8×C73—42no—
217#10596831—42no—
218#10596831—42no—
219C22×C73#41312yes—
220C22×C73#42112yes—
221C22×C73#42112yes—
222C22×C73C22×C22⋊C411yescharacteristic
223C2×D73—22no—
224C2×D73—22no—
225C2×D73—22no—
226C2×D73—44no—
227C2×D73—42no—
228C2×D73—42no—
229C2×D73—42no—
230C2×D73—84no—
231C4×C73—21no—
232C4×C73—21no—
233C4×C73—21no—
234C4×C73—21no—
235C4×C73—21no—
236C4×C73—21no—
237C4×C73—42no—
238C4×C73—42no—
239Dic73—22no—
240Dic73—22no—
241Dic73—22no—
242Dic73—42no—
243C2×#1535—731nomaximal, Sylow
244C2×C73#153514yescomplemented
245C2×C73C2×#41311yescharacteristic
246C2×C73C2×#42111yescharacteristic
247C2×C73C2×#42111yescharacteristic
248D73—42no—
249D73—82no—
250C2×#529—731no—
251C2×#432—731no—
252C2×#432—731no—
253#1535—738no—
254C2×#330—731no—
255C2×#330D7311yescharacteristic, complemented
256C2×#329—731no—
257C2×#329—731no—
258C73C2×#153511yescharacteristic, complemented, Sylow
259#529—734no—
260#529—734no—
261#529—1462no—
262#529—1462no—
263C2×#126—1461no—
264C2×#125C2×D7311yescharacteristic
265C2×#124—731no—
266C2×#123—1461no—
267C2×C22⋊Q8—731no—
268C2×#121—731no—
269C2×C4×Q8—731no—
270C2×C4×D4—731no—
271C2×C4×D4—1461no—
272C2×#117—1461no—
273C22×C42—731no—
274#432—734no—
275#432—734no—
276#432—1462no—
277#432—1462no—
278C2×C4⋊C8—1461no—
279C2×C4⋊C8—1461no—
280C2×C22⋊C8—1461no—
281C2×C22⋊C8—1461no—
282C2×#97—731no—
283C2×#97—731no—
284C2×#97C2×D7311yescharacteristic
285C2×#97C2×D7311yescharacteristic
286#330—734no—
287#330C2×D7314yescomplemented
288#329—734no—
289#329—734no—
290C22×Q8—731no—
291C22×D4—731no—
292C22×D4—1461no—
293C23×C4—731no—
294C23×C4—731no—
295C23×C4—731no—
296C23×C4—1461no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—1461no—
300C22×C8—1461no—
301#126—1464no—
302#126—1464no—
303#125—21no—
304#125—21no—
305#125C4×D7312yes—
306#125C22×D7312yes—
307#124—732no—
308#124—732no—
309#124—1461no—
310#124—1461no—
311#123—1464no—
312#123—1464no—
313C22⋊Q8—734no—
314C22⋊Q8—1462no—
315#121—734no—
316#121—1462no—
317C4×Q8—734no—
318C4×Q8—1462no—
319C4×D4—734no—
320C4×D4—1462no—
321C4×D4—1464no—
322C4×D4—1464no—
323#117—1464no—
324#117—1464no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—1461no—
328C2×C4⋊C4—1461no—
329C2×C4⋊C4C4×D7311yescharacteristic
330C2×C4⋊C4C4×D7311yescharacteristic
331C2×C22⋊C4—1461no—
332C2×C22⋊C4—1461no—
333C2×C22⋊C4—1461no—
334C2×C22⋊C4—1461no—
335C2×C22⋊C4—1461no—
336C2×C42—731no—
337C2×C42—731no—
338C2×C42—731no—
339C2×C42—732no—
340C2×C42—732no—
341C2×C42—732no—
342C2×C42—732no—
343C2×C42—1461no—
344C2×C42C22×D7311yescharacteristic
345C4⋊C8—1464no—
346C4⋊C8—1464no—
347C22⋊C8—1464no—
348C22⋊C8—1464no—
349#97—21no—
350#97—21no—
351#97—732no—
352#97—732no—
353#97—1461no—
354#97—1461no—
355#97C22×D7312yes—
356#97C22×D7312yes—
357C24—731no—
358C24—1461no—
359C2×Q8—2922no—
360C2×Q8—732no—
361C2×Q8—1461no—
362C2×D4—2922no—
363C2×D4—2924no—
364C2×D4—732no—
365C2×D4—1464no—
366C2×D4—1461no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—2922no—
370C22×C4—2922no—
371C22×C4—2922no—
372C22×C4—2924no—
373C22×C4—732no—
374C22×C4—732no—
375C22×C4—732no—
376C22×C4—732no—
377C22×C4—732no—
378C22×C4—732no—
379C22×C4—731no—
380C22×C4—731no—
381C22×C4—731no—
382C22×C4—1464no—
383C22×C4—1461no—
384C22×C4C2×C4×D7311yescharacteristic
385C22×C4D4×D7311yescharacteristic
386C22×C4D4×D7311yescharacteristic
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—42no—
390C2×C8—42no—
391C2×C8—2922no—
392C2×C8—2922no—
393C2×C8—1462no—
394C2×C8—1462no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—1464no—
402C4⋊C4—1464no—
403C4⋊C4C2×C4×D7312yes—
404C4⋊C4C2×C4×D7312yes—
405C22⋊C4—1464no—
406C22⋊C4—1464no—
407C22⋊C4—1464no—
408C22⋊C4—1462no—
409C22⋊C4—1462no—
410C22⋊C4—1462no—
411C22⋊C4—1462no—
412C42—732no—
413C42—732no—
414C42—732no—
415C42—732no—
416C42—732no—
417C42—732no—
418C42—1464no—
419C42C2×C4×D7311yescharacteristic
420C42D4×D7311yescharacteristic
421C42D4×D7311yescharacteristic
422C42C23×D7311yescharacteristic
423C23—2922no—
424C23—2922no—
425C23—2922no—
426C23—732no—
427C23—1462no—
428C23—1462no—
429C23—1462no—
430C23—1462no—
431C23C22⋊C4×D7311yescharacteristic
432Q8—2922no—
433Q8—2922no—
434D4—2922no—
435D4—2922no—
436D4—2928no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—2922no—
445C2×C4—2922no—
446C2×C4—2922no—
447C2×C4—2922no—
448C2×C4—2922no—
449C2×C4—2922no—
450C2×C4—2928no—
451C2×C4—2922no—
452C2×C4—732no—
453C2×C4—732no—
454C2×C4—732no—
455C2×C4—1462no—
456C2×C4—1462no—
457C2×C4—1462no—
458C2×C4—1462no—
459C2×C4C22⋊C4×D7311yescharacteristic
460C2×C4C22⋊C4×D7311yescharacteristic
461C2×C4C22⋊C4×D7311yescharacteristic
462C2×C4C22×C4×D7311yescharacteristic
463C2×C4C2×D4×D7311yescharacteristic
464C2×C4C2×D4×D7311yescharacteristic
465C8—42no—
466C8—42no—
467C8—2922no—
468C8—2922no—
469C22—2924no—
470C22—2922no—
471C22—2922no—
472C22—2922no—
473C22—5844no—
474C22—1462no—
475C22—1462no—
476C22—1462no—
477C22#1798857012yes—
478C22#1798860212yes—
479C22#1798860212yes—
480C22C2×C22⋊C4×D7311yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—42no—
488C4—42no—
489C4—2922no—
490C4—1462no—
491C4—1462no—
492C4—1462no—
493C2—2922no—
494C2—5842no—
495C2#2260856114yesdirect product factor
496C2C2×#1798857011yescharacteristic
497C2C2×#1798860211yescharacteristic
498C2C2×#1798860211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC2×#330×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556566C4
cosocleC42×C73C24
hypercenterC2×#330D73
hypocenterC73C2×#1535
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
2. C2×#17988642C2semidirect
3. C2×#17988642C2semidirect
4. #22608561C2direct (N × H)
5. C2×#17988329C2semidirect
6. C2×#17988326C2semidirect
7. C2×#17988326C2semidirect
8. C2×#330×C73C2semidirect
25. #17988642C22semidirect
26. #17988642C22semidirect
33. #17988329C22semidirect
34. #17988326C22semidirect
35. #17988326C22semidirect
39. #330×C73C22semidirect
244. C2×C73#1535semidirect
255. C2×#330D73semidirect
258. C73C2×#1535semidirect
287. #330C2×D73semidirect
495. C2#22608561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891222
C2×#179886422
#226085612
C2×#179883292
C2×#179883262
C2×#330×C732
C2×#153573