Finite Group Databasebeta

← C2×#22608544 #33053912

Subgroups — C2×#22608544 #33053912

Order 18688.

1050 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989143C211yesmaximal, characteristic
2C2×#17988642C211yesmaximal, characteristic
3C2×#97×D73C211yesmaximal, characteristic
4#22608544C218yesmaximal, direct product factor
5C2×#17988329C211yesmaximal, characteristic, complemented
6C2×#17988328C211yesmaximal, characteristic, complemented
7C2×#17988328C211yesmaximal, characteristic, complemented
8C2×#330×C73C211yesmaximal, characteristic, complemented
9C22×C8×D73—21no—
10#17989143—22no—
11#17989143—22no—
12#17989143C414yes—
13#17989143C2214yes—
14C2×#14556590C411yescharacteristic
15C2×#14556590C411yescharacteristic
16C2×#14556583C2211yescharacteristic
17C2×#14556569—21no—
18C2×#14556569—21no—
19C2×#14556556—21no—
20C2×#14556556—21no—
21C2×#14556549C411yescharacteristic
22C2×#14556549C411yescharacteristic
23C2×C42×D73C2211yescharacteristic
24#17988642—22no—
25#17988642C2214yes—
26C2×#14556520—21no—
27C2×#14556503—21no—
28C2×#14556502C2211yescharacteristic
29C2×#14556502C2211yescharacteristic
30C2×#14556501—21no—
31#97×D73—22no—
32#97×D73C2214yes—
33#17988329C2214yescomplemented
34#17988328C2214yescomplemented
35#17988328C2214yescomplemented
36C2×#125×C73C2211yescharacteristic
37C2×#97×C73C2211yescharacteristic
38C2×#97×C73C2211yescharacteristic
39#330×C73C2214yescomplemented
40C22×Dic146—21no—
41C22×Dic146—21no—
42C22×C4×D73C2×C411yescharacteristic
43C22×C4×D73D411yescharacteristic
44C22×C4×D73D411yescharacteristic
45C22×#10596831—21no—
46C22×#10596831—21no—
47C2×C8×D73—28no—
48C2×C8×D73—24no—
49#14556590—22no—
50#14556590—22no—
51#14556590C2×C414yes—
52#14556590C2×C414yes—
53#14556583—21no—
54#14556583—21no—
55#14556583C2×C412yes—
56#14556583C2312yes—
57#14556569—24no—
58#14556569—24no—
59#14556569—24no—
60#14556569—24no—
61#14556556—24no—
62#14556556—24no—
63#14556556—24no—
64#14556556—24no—
65#14556549—22no—
66#14556549—22no—
67#14556549C2×C414yes—
68#14556549C2×C414yes—
69C2×C4⋊Dic73C2×C411yescharacteristic
70C2×C4⋊Dic73C2×C411yescharacteristic
71C2×#11924007—21no—
72C2×#11924007—21no—
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×#11924005—21no—
76C2×#11924005—21no—
77C2×C4×Dic73—21no—
78C2×C4×Dic73—21no—
79C2×C4×Dic73C2×C411yescharacteristic
80C2×C4×Dic73D411yescharacteristic
81C2×C4×Dic73D411yescharacteristic
82C42×D73C2×C412yes—
83C42×D73D412yes—
84C42×D73D412yes—
85C42×D73C2312yes—
86#14556520—24no—
87#14556503—24no—
88#14556502—21no—
89#14556502—21no—
90#14556502C2312yes—
91#14556502C2312yes—
92#14556501—24no—
93C22×C8×C73—21no—
94C22×C8×C73—21no—
95#125×C73—21no—
96#125×C73—21no—
97#125×C73C2×C412yes—
98#125×C73C2312yes—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73C2×C411yescharacteristic
102C2×C4⋊C4×C73C2×C411yescharacteristic
103C2×C42×C73C2311yescharacteristic
104#97×C73—21no—
105#97×C73—21no—
106#97×C73C2312yes—
107#97×C73C2312yes—
108C23×D73C22⋊C411yescharacteristic
109C2×Dic146—24no—
110C2×Dic146—24no—
111C2×Dic146—44no—
112C2×Dic146—44no—
113C22×Dic73—21no—
114C22×Dic73—21no—
115C22×Dic73C22⋊C411yescharacteristic
116C22×Dic73C22⋊C411yescharacteristic
117C22×Dic73C22⋊C411yescharacteristic
118C2×C4×D73—24no—
119C2×C4×D73—24no—
120C2×C4×D73—42no—
121C2×C4×D73C22⋊C412yes—
122C2×C4×D73C22⋊C412yes—
123C2×C4×D73C22⋊C412yes—
124C2×C4×D73C22×C412yes—
125C2×C4×D73C2×D412yes—
126C2×C4×D73C2×D412yes—
127C2×#10596831—24no—
128C2×#10596831—22no—
129C2×#10596831—22no—
130C2×#10596831—42no—
131C8×D73—216no—
132C4⋊Dic73—21no—
133C4⋊Dic73—21no—
134C4⋊Dic73C22×C412yes—
135C4⋊Dic73C22×C412yes—
136#11924007—22no—
137#11924007—22no—
138#11924007—22no—
139#11924007—22no—
140#11924007—24no—
141#11924007—24no—
142#11924005—24no—
143#11924005—24no—
144C4×Dic73—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—24no—
158C2×C8×C73—22no—
159C2×C8×C73—22no—
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#10114yes—
177C22×D73C2×C22⋊C412yes—
178C2×C4×C73—22no—
179C2×C4×C73—22no—
180C2×C4×C73—22no—
181C2×C4×C73—22no—
182C2×C4×C73—22no—
183C2×C4×C73—42no—
184C2×C4×C73—42no—
185C2×C4×C73C2×C22⋊C411yescharacteristic
186C2×C4×C73C2×C22⋊C411yescharacteristic
187C2×C4×C73C2×C22⋊C411yescharacteristic
188C2×C4×C73C23×C411yescharacteristic
189C2×C4×C73C22×D411yescharacteristic
190C2×C4×C73C22×D411yescharacteristic
191C2×Dic73—22no—
192C2×Dic73—22no—
193C2×Dic73—22no—
194C2×Dic73—22no—
195C2×Dic73—42no—
196C2×Dic73—42no—
197C2×Dic73#10414yes—
198C2×Dic73C2×C22⋊C412yes—
199C2×Dic73C2×C22⋊C412yes—
200C2×Dic73C2×C22⋊C412yes—
201C4×D73—24no—
202C4×D73—24no—
203C4×D73—24no—
204C4×D73—24no—
205C4×D73—42no—
206C4×D73—42no—
207Dic146—48no—
208Dic146—48no—
209C8×C73—24no—
210C8×C73—42no—
211#10596831—24no—
212#10596831—42no—
213C22×C73C2×#10112yes—
214C22×C73C2×#10412yes—
215C22×C73#42112yes—
216C22×C73C22×C22⋊C411yescharacteristic
217C2×D73—22no—
218C2×D73—22no—
219C2×D73—28no—
220C2×D73C2×#10114yes—
221C4×C73—21no—
222C4×C73—21no—
223C4×C73—21no—
224C4×C73—21no—
225C4×C73—21no—
226C4×C73—21no—
227C4×C73—42no—
228C4×C73—42no—
229Dic73—22no—
230Dic73—22no—
231Dic73—42no—
232Dic73—42no—
233Dic73C2×#10414yes—
234C2×#1531—731nomaximal, Sylow
235C2×C73#153114yescomplemented
236C2×C73C22×#10111yescharacteristic
237C2×C73C22×#10411yescharacteristic
238C2×C73C2×#42111yescharacteristic
239D73—24no—
240C2×#533—731no—
241C2×#432—731no—
242C22×#97—731no—
243#1531—738no—
244C2×#330—731no—
245C2×#330—731no—
246C2×#330—731no—
247C2×#330D7311yescharacteristic, complemented
248C73C2×#153111yescharacteristic, complemented, Sylow
249C23×C8—1461no—
250#533—734no—
251#533—734no—
252#533—1462no—
253#533—1462no—
254C2×C4⋊Q8—731no—
255C2×C4⋊Q8—731no—
256C2×#125—731no—
257C2×#125C2×D7311yescharacteristic
258C2×C22⋊Q8—1461no—
259C2×C22⋊Q8—1461no—
260C2×C4×Q8—1461no—
261C2×C4×Q8—1461no—
262C2×#117—731no—
263C2×#117—731no—
264C22×C42—731no—
265#432—734no—
266#432—1462no—
267C2×C4⋊C8—1461no—
268C2×C22⋊C8—1461no—
269C2×#97—731no—
270C2×#97—731no—
271C2×#97—734no—
272C2×#97—1462no—
273C2×#97—1461no—
274C2×#97C2×D7311yescharacteristic
275C2×#97C2×D7311yescharacteristic
276#330—734no—
277#330—734no—
278#330—734no—
279#330C2×D7314yescomplemented
280C22×Q8—1461no—
281C22×Q8—1461no—
282C23×C4—731no—
283C23×C4—731no—
284C23×C4—731no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—1464no—
288C22×C8—1468no—
289C22×C8—1461no—
290C22×C8—1461no—
291C4⋊Q8—734no—
292C4⋊Q8—734no—
293C4⋊Q8—1462no—
294C4⋊Q8—1462no—
295#125—21no—
296#125—21no—
297#125—732no—
298#125—732no—
299#125—1461no—
300#125—1461no—
301#125C4×D7312yes—
302#125C22×D7312yes—
303C22⋊Q8—1464no—
304C22⋊Q8—1464no—
305C22⋊Q8—1464no—
306C22⋊Q8—1464no—
307C4×Q8—1464no—
308C4×Q8—1464no—
309C4×Q8—1464no—
310C4×Q8—1464no—
311#117—734no—
312#117—734no—
313#117—1462no—
314#117—1462no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—731no—
318C2×C4⋊C4—731no—
319C2×C4⋊C4—1461no—
320C2×C4⋊C4—1461no—
321C2×C4⋊C4—1461no—
322C2×C4⋊C4—1461no—
323C2×C4⋊C4C4×D7311yescharacteristic
324C2×C4⋊C4C4×D7311yescharacteristic
325C2×C22⋊C4—1461no—
326C2×C22⋊C4—1461no—
327C2×C42—731no—
328C2×C42—731no—
329C2×C42—731no—
330C2×C42—732no—
331C2×C42—732no—
332C2×C42—732no—
333C2×C42—732no—
334C2×C42—1461no—
335C2×C42—1461no—
336C2×C42C22×D7311yescharacteristic
337C4⋊C8—1464no—
338C22⋊C8—1464no—
339#97—21no—
340#97—21no—
341#97—732no—
342#97—732no—
343#97—1464no—
344#97—1461no—
345#97—1461no—
346#97C22×D7312yes—
347#97C22×D7312yes—
348C24—731no—
349C2×Q8—2924no—
350C2×Q8—2924no—
351C2×Q8—1464no—
352C2×Q8—1464no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—2922no—
356C22×C4—732no—
357C22×C4—732no—
358C22×C4—731no—
359C22×C4—731no—
360C22×C4—731no—
361C22×C4—732no—
362C22×C4—732no—
363C22×C4—732no—
364C22×C4—732no—
365C22×C4—1464no—
366C22×C4—1464no—
367C22×C4—1461no—
368C22×C4—1461no—
369C22×C4C2×C4×D7311yescharacteristic
370C22×C4D4×D7311yescharacteristic
371C22×C4D4×D7311yescharacteristic
372C2×C8—24no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—42no—
376C2×C8—2922no—
377C2×C8—14616no—
378C2×C8—1462no—
379C2×C8—1464no—
380C2×C8—1462no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—732no—
388C4⋊C4—732no—
389C4⋊C4—1464no—
390C4⋊C4—1464no—
391C4⋊C4—1462no—
392C4⋊C4—1462no—
393C4⋊C4—1461no—
394C4⋊C4—1461no—
395C4⋊C4—1462no—
396C4⋊C4—1462no—
397C4⋊C4C2×C4×D7312yes—
398C4⋊C4C2×C4×D7312yes—
399C22⋊C4—1464no—
400C22⋊C4—1464no—
401C42—732no—
402C42—732no—
403C42—732no—
404C42—732no—
405C42—732no—
406C42—732no—
407C42—1464no—
408C42—1464no—
409C42C2×C4×D7311yescharacteristic
410C42D4×D7311yescharacteristic
411C42D4×D7311yescharacteristic
412C42C23×D7311yescharacteristic
413C23—732no—
414C23—734no—
415C23—1462no—
416C23—1462no—
417C23C22⋊C4×D7311yescharacteristic
418Q8—2928no—
419Q8—2928no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—2922no—
428C2×C4—2922no—
429C2×C4—2922no—
430C2×C4—2922no—
431C2×C4—732no—
432C2×C4—734no—
433C2×C4—732no—
434C2×C4—732no—
435C2×C4—1464no—
436C2×C4—1464no—
437C2×C4—1464no—
438C2×C4—1464no—
439C2×C4—1462no—
440C2×C4—1462no—
441C2×C4—1462no—
442C2×C4—1462no—
443C2×C4C22⋊C4×D7311yescharacteristic
444C2×C4C22⋊C4×D7311yescharacteristic
445C2×C4C22⋊C4×D7311yescharacteristic
446C2×C4C22×C4×D7311yescharacteristic
447C2×C4C2×D4×D7311yescharacteristic
448C2×C4C2×D4×D7311yescharacteristic
449C8—24no—
450C8—42no—
451C8—2922no—
452C8—1464no—
453C22—734no—
454C22—1462no—
455C22—1462no—
456C22—1468no—
457C22#101×D7312yes—
458C22#104×D7312yes—
459C22#1798860212yes—
460C22C2×C22⋊C4×D7311yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—42no—
468C4—42no—
469C4—2922no—
470C4—2922no—
471C4—734no—
472C4—1462no—
473C4—1462no—
474C2—1464no—
475C2#2260854414yesdirect product factor
476C2C2×#101×D7311yescharacteristic
477C2C2×#104×D7311yescharacteristic
478C2C2×#1798860211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC2×#330×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC42×C73C24
hypercenterC2×#330D73
hypocenterC73C2×#1531
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
4. #22608544C2direct (N × H)
5. C2×#17988329C2semidirect
6. C2×#17988328C2semidirect
7. C2×#17988328C2semidirect
8. C2×#330×C73C2semidirect
33. #17988329C22semidirect
34. #17988328C22semidirect
35. #17988328C22semidirect
39. #330×C73C22semidirect
235. C2×C73#1531semidirect
247. C2×#330D73semidirect
248. C73C2×#1531semidirect
279. #330C2×D73semidirect
475. C2#22608544direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891432
C2×#179886422
C2×#97×D732
#226085442
C2×#179883292
C2×#179883282
C2×#330×C732
C2×#153173