Finite Group Databasebeta

← C2×#22608466 #33053223

Subgroups — C2×#22608466 #33053223

Order 18688.

1098 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989118C211yesmaximal, characteristic
2C2×#17988641C211yesmaximal, characteristic, complemented
3C2×#17988451C211yesmaximal, characteristic, complemented
4#22608466C218yesmaximal, direct product factor
5C2×#17988325C211yesmaximal, characteristic, complemented
6C2×#17988323C211yesmaximal, characteristic, complemented
7C2×#17988321C211yesmaximal, characteristic
8C2×#327×C73C211yesmaximal, characteristic
9#17989118—22no—
10#17989118—22no—
11#17989118C414yescomplemented
12#17989118C2214yes—
13C2×#14556584—21no—
14C2×#14556582C411yescharacteristic, complemented
15C2×#14556578C411yescharacteristic, complemented
16C2×#14556572—21no—
17C2×#14556570C2211yescharacteristic
18C2×#14556556C411yescharacteristic, complemented
19C2×D4×Dic73—21no—
20C2×D4×Dic73C411yescharacteristic, complemented
21C2×#14556547—21no—
22C22×#11924007—21no—
23C22×C4×Dic73C2211yescharacteristic
24#17988641—22no—
25#17988641C2214yescomplemented
26C2×#14556520—21no—
27C2×C22⋊#10596831C2211yescharacteristic
28C2×#14556501—21no—
29#17988451—22no—
30#17988451C2214yescomplemented
31C2×#14556498—21no—
32C2×#14556498C2211yescharacteristic
33#17988325C2214yescomplemented
34#17988323C2214yescomplemented
35#17988321C2214yes—
36C2×#121×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×#95×C73C2211yescharacteristic
39#327×C73C2214yes—
40C22×Dic146C2×C411yescharacteristic
41C23×Dic73—21no—
42C23×Dic73—21no—
43C23×Dic73D411yescharacteristic
44C23×Dic73D411yescharacteristic
45C22×#10596831—21no—
46#14556584—24no—
47#14556584—24no—
48#14556582—22no—
49#14556582C2×C414yescomplemented
50#14556578—22no—
51#14556578C2×C414yescomplemented
52#14556572—24no—
53#14556572—24no—
54#14556570—21no—
55#14556570—21no—
56#14556570C2×C412yes—
57#14556570C2312yes—
58#14556556—22no—
59#14556556C2×C414yescomplemented
60D4×Dic73—24no—
61D4×Dic73—24no—
62D4×Dic73—22no—
63D4×Dic73C2×C414yescomplemented
64#14556547—24no—
65#14556547—24no—
66C2×C4⋊Dic73—21no—
67C2×C4⋊Dic73C2×C411yescharacteristic
68C2×#11924007—21no—
69C2×#11924007—21no—
70C2×#11924007—24no—
71C2×#11924007—21no—
72C2×#11924007—44no—
73C2×C22⋊Dic73—21no—
74C2×C22⋊Dic73—21no—
75C2×C22⋊Dic73—21no—
76C2×C22⋊Dic73—21no—
77C2×C4×Dic73—21no—
78C2×C4×Dic73C2×C411yescharacteristic
79C2×C4×Dic73C2×C411yescharacteristic
80C2×C4×Dic73C2×C412yes—
81C2×C4×Dic73D412yes—
82C2×C4×Dic73D412yes—
83C2×C4×Dic73D411yescharacteristic
84C2×C4×Dic73D411yescharacteristic
85C2×C4×Dic73C2312yes—
86#14556520—24no—
87C22⋊#10596831—21no—
88C22⋊#10596831C2312yes—
89#14556501—24no—
90#14556498—24no—
91#14556498—21no—
92#14556498C2312yes—
93C22×D4×C73—21no—
94C22×D4×C73C2×C411yescharacteristic
95C23×C4×C73—21no—
96C23×C4×C73C2311yescharacteristic
97C22×C8×C73—21no—
98#121×C73—21no—
99#121×C73—21no—
100#121×C73C2×C412yes—
101#121×C73C2312yes—
102C2×C4⋊C4×C73C2×C411yescharacteristic
103C2×C22⋊C4×C73—21no—
104C22⋊C8×C73—21no—
105C22⋊C8×C73C2312yes—
106#95×C73—21no—
107#95×C73C2312yes—
108C2×Dic146—21no—
109C2×Dic146—42no—
110C2×Dic146C22×C412yes—
111C22×Dic73—22no—
112C22×Dic73—22no—
113C22×Dic73—21no—
114C22×Dic73—21no—
115C22×Dic73—24no—
116C22×Dic73—22no—
117C22×Dic73—42no—
118C22×Dic73—44no—
119C22×Dic73—42no—
120C22×Dic73—42no—
121C22×Dic73—42no—
122C22×Dic73C22⋊C411yescharacteristic
123C22×Dic73C22⋊C411yescharacteristic
124C22×Dic73C22⋊C411yescharacteristic
125C22×Dic73C22⋊C411yescharacteristic
126C22×Dic73C22⋊C412yes—
127C22×Dic73C22⋊C412yes—
128C22×Dic73C2×D412yes—
129C22×Dic73C2×D412yes—
130C2×#10596831—22no—
131C2×#10596831—42no—
132C4⋊Dic73—21no—
133C4⋊Dic73—24no—
134C4⋊Dic73C22×C412yes—
135#11924007—22no—
136#11924007—22no—
137#11924007—24no—
138#11924007—24no—
139#11924007—48no—
140C22⋊Dic73—22no—
141C22⋊Dic73—22no—
142C22⋊Dic73—24no—
143C22⋊Dic73—24no—
144C22⋊Dic73—24no—
145C4×Dic73—24no—
146C4×Dic73C22⋊C412yes—
147C4×Dic73C22⋊C412yes—
148C4×Dic73C22⋊C412yes—
149C4×Dic73C22⋊C412yes—
150C4×Dic73C22×C412yes—
151C4×Dic73C22×C412yes—
152C4×Dic73C2×D412yes—
153C4×Dic73C2×D412yes—
154C24×C73—21no—
155C24×C73C2×D411yescharacteristic
156C2×D4×C73—22no—
157C2×D4×C73—22no—
158C2×D4×C73—21no—
159C2×D4×C73—42no—
160C2×D4×C73—42no—
161C2×D4×C73—42no—
162C2×D4×C73C22×C412yes—
163C22×C4×C73—21no—
164C22×C4×C73—22no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73—42no—
168C22×C4×C73—42no—
169C22×C4×C73C22×C411yescharacteristic
170C22×C4×C73C22×C411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2411yescharacteristic
175C2×C8×C73—22no—
176C2×C8×C73—42no—
177C4⋊C4×C73—21no—
178C4⋊C4×C73C22×C412yes—
179C22⋊C4×C73—22no—
180C22⋊C4×C73—22no—
181C23×C73—22no—
182C23×C73—22no—
183C23×C73—22no—
184C23×C73—42no—
185C23×C73—42no—
186C23×C73—42no—
187C23×C73C2×C22⋊C411yescharacteristic
188C23×C73C2×C22⋊C411yescharacteristic
189C23×C73AGL(1,ℤ/8)12yes—
190C23×C73#13712yes—
191C23×C73C22×D411yescharacteristic
192D4×C73—42no—
193D4×C73—42no—
194D4×C73—42no—
195D4×C73—42no—
196D4×C73—44no—
197C2×C4×C73—22no—
198C2×C4×C73—22no—
199C2×C4×C73—22no—
200C2×C4×C73—41no—
201C2×C4×C73—41no—
202C2×C4×C73—41no—
203C2×C4×C73—41no—
204C2×C4×C73—42no—
205C2×C4×C73—42no—
206C2×C4×C73—42no—
207C2×C4×C73—42no—
208C2×C4×C73—84no—
209C2×C4×C73C2×C22⋊C411yescharacteristic
210C2×C4×C73C2×C22⋊C411yescharacteristic
211C2×C4×C73C23×C411yescharacteristic
212C2×C4×C73C22×D411yescharacteristic
213C2×Dic73—22no—
214C2×Dic73—22no—
215C2×Dic73—24no—
216C2×Dic73—22no—
217C2×Dic73—22no—
218C2×Dic73—22no—
219C2×Dic73—22no—
220C2×Dic73—22no—
221C2×Dic73—22no—
222C2×Dic73—42no—
223C2×Dic73—42no—
224C2×Dic73—48no—
225C2×Dic73—42no—
226C2×Dic73—42no—
227C2×Dic73—42no—
228C2×Dic73—42no—
229C2×Dic73—42no—
230C2×Dic73—84no—
231C2×Dic73C2×C22⋊C412yes—
232C2×Dic73C2×C22⋊C412yes—
233C2×Dic73C2×C22⋊C412yes—
234C2×Dic73C2×C22⋊C412yes—
235Dic146—42no—
236Dic146—42no—
237C8×C73—42no—
238#10596831—42no—
239C22×C73—21no—
240C22×C73—21no—
241C22×C73—21no—
242C22×C73—21no—
243C22×C73—24no—
244C22×C73—24no—
245C22×C73—42no—
246C22×C73—42no—
247C22×C73—42no—
248C22×C73—84no—
249C22×C73#41012yes—
250C22×C73#41712yes—
251C22×C73#41712yes—
252C22×C73#42112yes—
253C22×C73C22×C22⋊C411yescharacteristic
254C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
255C22×C73C2×#13711yescharacteristic
256C4×C73—21no—
257C4×C73—21no—
258C4×C73—21no—
259C4×C73—21no—
260C4×C73—42no—
261C4×C73—82no—
262Dic73—22no—
263Dic73—22no—
264Dic73—22no—
265Dic73—22no—
266Dic73—42no—
267Dic73—42no—
268Dic73—82no—
269C2×#1512—731nomaximal, Sylow
270C2×C73—21no—
271C2×C73—21no—
272C2×C73—22no—
273C2×C73—82no—
274C2×C73#151214yescomplemented
275C2×C73C2×#41011yescharacteristic
276C2×C73C2×#41711yescharacteristic
277C2×C73C2×#42111yescharacteristic
278C2×#529—731no—
279C2×#432—731no—
280C2×#382—731no—
281#1512—738no—
282C2×#328—731no—
283C2×#328—731no—
284C2×#327—731no—
285C2×#327D7311yescharacteristic
286C73C2×#151211yescharacteristic, complemented, Sylow
287#529—734no—
288#529—734no—
289#529—1462no—
290#529—1462no—
291C2×#126—1461no—
292C2×#125—731no—
293C2×#124—731no—
294C2×#123—1461no—
295C2×C22⋊Q8—731no—
296C2×#121C2×D7311yescharacteristic
297C2×C4×Q8—731no—
298C2×C4×D4—731no—
299C2×C4×D4—1461no—
300C2×#117—1461no—
301C22×C4⋊C4—1461no—
302C22×C42—731no—
303#432—734no—
304#432—1462no—
305C2×C4⋊C8—1461no—
306C2×C22⋊C8—731no—
307C2×C22⋊C8C2×D7311yescharacteristic
308C2×#97—1461no—
309#382—734no—
310#382—1462no—
311C2×#95—731no—
312C2×#95—1461no—
313C2×#95C2×D7311yescharacteristic
314#328—734no—
315#328—734no—
316#327—734no—
317#327C2×D7314yes—
318C22×Q8—731no—
319C22×D4—21no—
320C22×D4C4×D7311yescharacteristic
321C23×C4—21no—
322C23×C4—731no—
323C23×C4—731no—
324C23×C4—1461no—
325C23×C4—1461no—
326C23×C4C22×D7311yescharacteristic
327C22×C8—21no—
328C22×C8—1461no—
329#126—1464no—
330#126—1464no—
331#125—734no—
332#125—1462no—
333#124—734no—
334#124—1462no—
335#123—1464no—
336#123—1464no—
337C22⋊Q8—732no—
338C22⋊Q8—732no—
339C22⋊Q8—1461no—
340C22⋊Q8—1461no—
341#121—21no—
342#121—21no—
343#121C4×D7312yes—
344#121C22×D7312yes—
345C4×Q8—734no—
346C4×Q8—1462no—
347C4×D4—734no—
348C4×D4—1462no—
349C4×D4—1464no—
350C4×D4—1464no—
351#117—1464no—
352#117—1464no—
353C2×C4⋊C4—2924no—
354C2×C4⋊C4—731no—
355C2×C4⋊C4—1464no—
356C2×C4⋊C4—1461no—
357C2×C4⋊C4—1461no—
358C2×C4⋊C4—1461no—
359C2×C4⋊C4—1461no—
360C2×C4⋊C4C4×D7311yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—1461no—
363C2×C22⋊C4—1461no—
364C2×C22⋊C4—1461no—
365C2×C22⋊C4—1461no—
366C2×C42—731no—
367C2×C42—731no—
368C2×C42—732no—
369C2×C42—731no—
370C2×C42—731no—
371C2×C42—732no—
372C2×C42—732no—
373C2×C42—732no—
374C2×C42—1461no—
375C4⋊C8—1464no—
376C22⋊C8—21no—
377C22⋊C8—732no—
378C22⋊C8—1461no—
379C22⋊C8C22×D7312yes—
380#97—1464no—
381#95—21no—
382#95—732no—
383#95—1464no—
384#95—1461no—
385#95C22×D7312yes—
386C24—21no—
387C24D4×D7311yescharacteristic
388C2×Q8—2922no—
389C2×Q8—732no—
390C2×Q8—1461no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4C2×C4×D7312yes—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—2924no—
405C22×C4—2922no—
406C22×C4—2922no—
407C22×C4—2922no—
408C22×C4—2922no—
409C22×C4—732no—
410C22×C4—732no—
411C22×C4—732no—
412C22×C4—731no—
413C22×C4—731no—
414C22×C4—731no—
415C22×C4—731no—
416C22×C4—732no—
417C22×C4—1462no—
418C22×C4—1464no—
419C22×C4—1461no—
420C22×C4—1461no—
421C22×C4—1462no—
422C22×C4—1462no—
423C22×C4C2×C4×D7311yescharacteristic
424C22×C4C2×C4×D7311yescharacteristic
425C22×C4D4×D7311yescharacteristic
426C22×C4D4×D7311yescharacteristic
427C22×C4D4×D7311yescharacteristic
428C22×C4C23×D7311yescharacteristic
429C2×C8—22no—
430C2×C8—42no—
431C2×C8—2922no—
432C2×C8—1462no—
433C4⋊C4—21no—
434C4⋊C4—2928no—
435C4⋊C4—732no—
436C4⋊C4—1464no—
437C4⋊C4—1464no—
438C4⋊C4—1464no—
439C4⋊C4—1462no—
440C4⋊C4—1461no—
441C4⋊C4—1462no—
442C4⋊C4C2×C4×D7312yes—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—1464no—
446C22⋊C4—1464no—
447C22⋊C4—1464no—
448C22⋊C4—1462no—
449C22⋊C4—1462no—
450C42—732no—
451C42—732no—
452C42—732no—
453C42—732no—
454C42—732no—
455C42—732no—
456C42—732no—
457C42—732no—
458C42—1464no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23C22⋊C4×D7311yescharacteristic
466C23C22⋊C4×D7311yescharacteristic
467C23#1455661512yes—
468C23#1455662012yes—
469C23C2×D4×D7311yescharacteristic
470Q8—2922no—
471Q8—2922no—
472D4—42no—
473D4—42no—
474D4—42no—
475D4—44no—
476D4—42no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4—2922no—
490C2×C4—2922no—
491C2×C4—2928no—
492C2×C4—2922no—
493C2×C4—2922no—
494C2×C4—2922no—
495C2×C4—2922no—
496C2×C4—2922no—
497C2×C4—5844no—
498C2×C4—732no—
499C2×C4—732no—
500C2×C4—732no—
501C2×C4—732no—
502C2×C4—1462no—
503C2×C4—1462no—
504C2×C4—1462no—
505C2×C4—1464no—
506C2×C4—1462no—
507C2×C4—1462no—
508C2×C4—1462no—
509C2×C4—1462no—
510C2×C4—1462no—
511C2×C4C22⋊C4×D7311yescharacteristic
512C2×C4C22⋊C4×D7311yescharacteristic
513C2×C4C22×C4×D7311yescharacteristic
514C2×C4C2×D4×D7311yescharacteristic
515C8—42no—
516C8—2922no—
517C22—21no—
518C22—21no—
519C22—24no—
520C22—24no—
521C22—21no—
522C22—21no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—84no—
527C22#1798855912yes—
528C22#1798858512yes—
529C22#1798858512yes—
530C22#1798860212yes—
531C22C2×C22⋊C4×D7311yescharacteristic
532C22C2×#1455661511yescharacteristic
533C22C2×#1455662011yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—42no—
539C4—82no—
540C4—2922no—
541C4—2922no—
542C4—5842no—
543C4—1462no—
544C4—1462no—
545C4—1462no—
546C4—1462no—
547C2—21no—
548C2—21no—
549C2—22no—
550C2—82no—
551C2#2260846614yesdirect product factor
552C2C2×#1798855911yescharacteristic
553C2C2×#1798858511yescharacteristic
554C2C2×#1798860211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#327×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC2×#121×C73C22
cosocleC22×C4×C73C24
hypercenterC2×#327D73
hypocenterC73C2×#1512
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#17988641C2semidirect
3. C2×#17988451C2semidirect
4. #22608466C2direct (N × H)
5. C2×#17988325C2semidirect
6. C2×#17988323C2semidirect
11. #17989118C4semidirect
14. C2×#14556582C4semidirect
15. C2×#14556578C4semidirect
18. C2×#14556556C4semidirect
20. C2×D4×Dic73C4semidirect
25. #17988641C22semidirect
30. #17988451C22semidirect
33. #17988325C22semidirect
34. #17988323C22semidirect
49. #14556582C2×C4semidirect
51. #14556578C2×C4semidirect
59. #14556556C2×C4semidirect
63. D4×Dic73C2×C4semidirect
274. C2×C73#1512semidirect
286. C73C2×#1512semidirect
551. C2#22608466direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891182
C2×#179886412
C2×#179884512
#226084662
C2×#179883252
C2×#179883232
C2×#179883212
C2×#327×C732
C2×#151273