Finite Group Databasebeta

← C2×#11739349 #14234240

Subgroups — C2×#11739349 #14234240

Order 1792.

1842 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90421C211yesmaximal, characteristic
2C2×#90412C211yesmaximal, characteristic, complemented
3C2×C7×#498C211yesmaximal, characteristic, complemented
4C2×#89863C211yesmaximal, characteristic, complemented
5C2×#89859C211yesmaximal, characteristic
6#11739349C2116yesmaximal, direct product factor
7C2×#89629C212yesmaximal, complemented
8C2×#89643C212yesmaximal
9C2×#89630C212yesmaximal, complemented
10C2×#89624C212yesmaximal
11C2×C4×#1132C211yesmaximal, characteristic
12C2×C8×Dic14C211yesmaximal, characteristic, complemented
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×#6509—22no—
16C2×Q8×Dic7—21no—
17C2×#6507—21no—
18C22×#1132C2211yescharacteristic
19#90421—24no—
20#90421C2218yes—
21#90412—24no—
22#90412C2218yescomplemented
23C2×#6460—21no—
24C2×#6456C2212yes—
25C2×D7×C4⋊C4—21no—
26C2×#6453C2212yes—
27C2×#6453C2212yes—
28C2×#6452—22no—
29C2×#6450C2212yes—
30C2×C4×D28C2211yescharacteristic
31C2×C4×Dic14C2211yescharacteristic
32C2×C4×Dic14C2211yescharacteristic
33C7×#498C2218yescomplemented
34C2×C7×#106C2212yes—
35C2×C7×#106C2212yes—
36C2×C4×C7×C8C2211yescharacteristic
37C2×#6395C2211yescharacteristic
38C2×#6391C2211yescharacteristic
39C2×#6390C2211yescharacteristic
40C2×Dic7⋊C8C2212yes—
41C2×C8×Dic7C2212yes—
42#89863C2218yescomplemented
43#89859C2218yes—
44C2×#6384C2212yes—
45C2×#6383C2212yes—
46C2×#6381C2212yes—
47C2×#6381C2212yes—
48C2×C4⋊(C7⋊C8)C2211yescharacteristic
49#89643C22116yes—
50#89630C22116yescomplemented
51#89629C22116yescomplemented
52#89624C22116yes—
53C4×#1132C2218yes—
54C8×Dic14C2218yescomplemented
55C2×#3381—71nomaximal, Sylow
56C22×C7×Q8—21no—
57C22×C7×Q8—21no—
58C22×D28C2311yescharacteristic
59C22×C4×D7—21no—
60C22×C4×D7—22no—
61C22×Dic14D411yescharacteristic
62C22×Dic14C2311yescharacteristic
63C22×C7×C8C2311yescharacteristic
64C22×C7×C8C2311yescharacteristic
65C7×C4⋊Q8—22no—
66C7×C4⋊Q8—22no—
67C7×C4⋊Q8C2314yes—
68C7×C4⋊Q8C2314yes—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4C2312yes—
72C2×C7×C4⋊C4C2312yes—
73C2×C42×C7C2311yescharacteristic
74#6509—216no—
75Q8×Dic7—28no—
76#6507—28no—
77C2×(C2×D7)⋊C4—21no—
78C2×(C2×D7)⋊C4—22no—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7D411yescharacteristic
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4⋊Dic7C2311yescharacteristic
84C2×Dic7⋊C4—21no—
85C2×Dic7⋊C4—22no—
86C2×Dic7⋊C4—22no—
87C2×Dic7⋊C4—22no—
88C2×Dic7⋊C4D412yes—
89C2×C4×Dic7—21no—
90C2×C4×Dic7—22no—
91C2×C4×Dic7C2312yes—
92C22×C7⋊C8C2312yes—
93C2×#1132Q818yescomplemented
94C2×#1132C2314yes—
95#6460—28no—
96#6456—24no—
97#6456C2318yes—
98D7×C4⋊C4—28no—
99#6453—24no—
100#6453—24no—
101#6453C2318yes—
102#6453C2318yes—
103#6452—216no—
104#6450—24no—
105#6450C2318yes—
106C4×D28—22no—
107C4×D28C2314yes—
108C4×Dic14—22no—
109C4×Dic14D414yes—
110C4×Dic14C2314yes—
111C4×Dic14C2314yes—
112C7×#106C2318yes—
113C7×#106C2318yes—
114C4×C7×C8C2314yes—
115#6395C2314yes—
116#6391C2314yes—
117#6390C2314yes—
118Dic7⋊C8C2318yes—
119C8×Dic7C2318yes—
120#6384C2318yes—
121#6383C2318yes—
122#6381C2318yes—
123#6381C2318yes—
124C4⋊(C7⋊C8)C2314yes—
125C2×#557—71no—
126C2×#554—71no—
127#3381—716no—
128C2×#499—72no—
129C2×#498D711yescharacteristic, complemented
130C2×#479—72no—
131C2×#477—71no—
132C2×#478—72no—
133C2×#474—71no—
134C2×C8×Q8—71no—
135C2×C4×SD16—72no—
136C2×C4×SD16—71no—
137C23×D7—21no—
138C2×C7×Q8—24no—
139C2×C7×Q8—24no—
140C2×C7×Q8—44no—
141C2×C7×Q8—82no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2411yescharacteristic
147C22×Dic7—21no—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7C2×D412yes—
151C22×Dic7C2×D412yes—
152C2×D28—21no—
153C2×D28—22no—
154C2×D28C2×Q814yes—
155C2×D28C2412yes—
156C2×C4×D7—24no—
157C2×C4×D7—28no—
158C2×C4×D7—44no—
159C2×C4×D7—84no—
160C2×Dic14—24no—
161C2×Dic14—21no—
162C2×Dic14—22no—
163C2×Dic14C2×D414yes—
164C2×Dic14C2×Q814yes—
165C2×Dic14C2412yes—
166C2×C7×C8—22no—
167C2×C7×C8C2×Q814yes—
168C2×C7×C8C2412yes—
169C2×C7×C8C2412yes—
170C7×C4⋊C4—22no—
171C7×C4⋊C4—24no—
172C7×C4⋊C4—22no—
173C7×C4⋊C4—24no—
174C7×C4⋊C4C2414yes—
175C7×C4⋊C4C2414yes—
176C42×C7C2×D412yes—
177C42×C7C2412yes—
178(C2×D7)⋊C4—24no—
179(C2×D7)⋊C4—28no—
180C4⋊Dic7—21no—
181C4⋊Dic7—21no—
182C4⋊Dic7—28no—
183C4⋊Dic7—28no—
184C4⋊Dic7C2×D414yes—
185C4⋊Dic7C2412yes—
186C4⋊Dic7C2412yes—
187Dic7⋊C4—24no—
188Dic7⋊C4—28no—
189Dic7⋊C4—28no—
190Dic7⋊C4—28no—
191Dic7⋊C4C2×D418yes—
192C4×Dic7—24no—
193C4×Dic7—28no—
194C4×Dic7C2×D414yes—
195C4×Dic7C2414yes—
196C2×C7⋊C8—24no—
197C2×C7⋊C8C2414yes—
198#1132C2×Q8116yescomplemented
199C22×SD16—71no—
200#557—78no—
201#557—144no—
202#554—78no—
203#554—144no—
204C2×C4⋊Q8—141no—
205C2×C4⋊Q8C2×D711yescharacteristic
206C2×C4⋊Q8C2×D711yescharacteristic
207C2×#125—72no—
208C2×#125—72no—
209C2×#125—142no—
210C2×C22⋊Q8—141no—
211C2×C22⋊Q8—142no—
212C2×C4×Q8—71no—
213C2×C4×Q8—72no—
214C2×C4×Q8—71no—
215C2×C4×Q8—141no—
216C2×C4×D4—72no—
217C2×C4×D4—71no—
218C22×C4⋊C4—141no—
219#499—716no—
220#498C2×D718yescomplemented
221#479—716no—
222#478—716no—
223#477—78no—
224#474—78no—
225C8×Q8—78no—
226C4×SD16—716no—
227C4×SD16—78no—
228C2×#107—72no—
229C2×#107—72no—
230C2×#106—71no—
231C2×#106C2×D712yes—
232C2×#106C2×D712yes—
233C2×C4⋊C8—72no—
234C2×C4⋊C8—71no—
235C2×#103—71no—
236C2×#103—72no—
237C2×#102—71no—
238C2×#102—72no—
239C2×C4×C8—72no—
240C2×C4×C8C2×D711yescharacteristic
241C23×C7C22×D411yescharacteristic
242C22×D7—24no—
243C22×D7—22no—
244C22×D7—42no—
245C22×D7—42no—
246C7×Q8—48no—
247C7×Q8—84no—
248C2×C4×C7—22no—
249C2×C4×C7—24no—
250C2×C4×C7—24no—
251C2×C4×C7—44no—
252C2×C4×C7—44no—
253C2×C4×C7#13514yes—
254C2×C4×C7C22×D412yes—
255C2×C4×C7C22×D411yescharacteristic
256C2×C4×C7C22×D412yes—
257C2×C4×C7C22×Q812yes—
258C2×C4×C72−1+412yes—
259C2×C4×C7C2511yescharacteristic
260C2×Dic7—24no—
261C2×Dic7—24no—
262C2×Dic7—24no—
263C2×Dic7—22no—
264C2×Dic7—22no—
265C2×Dic7—22no—
266C2×Dic7—42no—
267C2×Dic7—42no—
268C2×Dic7C22×D414yes—
269C2×Dic7C22×D414yes—
270D28—24no—
271D28—22no—
272D28C22×Q814yes—
273C4×D7—48no—
274C4×D7—88no—
275Dic14—24no—
276Dic14—28no—
277Dic14—22no—
278Dic14C22×Q814yes—
279C7×C8—22no—
280C7×C8C22×Q814yes—
281C7⋊C8—24no—
282C22×Q8—21no—
283C22×Q8—21no—
284C22×Q8—71no—
285C22×Q8—71no—
286C22×D4—71no—
287C23×C4—142no—
288C23×C4—141no—
289C2×SD16—78no—
290C2×SD16—74no—
291C22×C8—72no—
292C22×C8C22×D711yescharacteristic
293C22×C8C22×D711yescharacteristic
294C4⋊Q8—22no—
295C4⋊Q8—22no—
296C4⋊Q8—148no—
297C4⋊Q8C22×D714yes—
298C4⋊Q8C22×D714yes—
299#125—78no—
300#125—78no—
301#125—144no—
302#125—144no—
303#125—1416no—
304C22⋊Q8—148no—
305C22⋊Q8—1416no—
306C4×Q8—74no—
307C4×Q8—74no—
308C4×Q8—78no—
309C4×Q8—74no—
310C4×Q8—144no—
311C4×Q8—148no—
312C4×Q8—142no—
313C4×D4—78no—
314C4×D4—74no—
315C4×D4—144no—
316C4×D4—142no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—71no—
320C2×C4⋊C4—72no—
321C2×C4⋊C4—71no—
322C2×C4⋊C4—71no—
323C2×C4⋊C4—148no—
324C2×C4⋊C4—142no—
325C2×C4⋊C4—142no—
326C2×C4⋊C4—142no—
327C2×C4⋊C4—142no—
328C2×C4⋊C4—142no—
329C2×C4⋊C4—141no—
330C2×C4⋊C4C22×D712yes—
331C2×C4⋊C4C22×D712yes—
332C2×C22⋊C4—142no—
333C2×C22⋊C4—141no—
334C2×C42—72no—
335C2×C42—142no—
336C2×C42—141no—
337C2×C42C22×D711yescharacteristic
338#107—78no—
339#107—78no—
340#106—74no—
341#106C22×D718yes—
342#106C22×D718yes—
343C4⋊C8—78no—
344C4⋊C8—74no—
345#103—74no—
346#103—78no—
347#102—74no—
348#102—78no—
349C4×C8—78no—
350C4×C8C22×D714yes—
351C22×C7D4×Q812yes—
352C22×C7C2×#13512yes—
353C22×C7#57712yes—
354C22×C7C23×D411yescharacteristic
355C2×D7—24no—
356C2×D7—48no—
357C2×D7—42no—
358C2×D7—42no—
359C4×C7—22no—
360C4×C7—44no—
361C4×C7—44no—
362C4×C7D4×Q812yes—
363C4×C7C2×#13514yes—
364C4×C7C23×Q811yescharacteristic
365C4×C7C2×2−1+411yescharacteristic
366Dic7—24no—
367Dic7—24no—
368Dic7—24no—
369Dic7—42no—
370Dic7—42no—
371C24—141no—
372C2×Q8—24no—
373C2×Q8—24no—
374C2×Q8—44no—
375C2×Q8—74no—
376C2×Q8—74no—
377C2×Q8—72no—
378C2×Q8—82no—
379C2×Q8—144no—
380C2×Q8—141no—
381C2×Q8—142no—
382C2×D4—74no—
383C2×D4—72no—
384C2×D4—141no—
385C2×D4—142no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—72no—
389C22×C4—72no—
390C22×C4—148no—
391C22×C4—141no—
392C22×C4—141no—
393C22×C4—141no—
394C22×C4—144no—
395C22×C4—284no—
396C22×C4—564no—
397C22×C4D4×D711yescharacteristic
398C22×C4D4×D711yescharacteristic
399C22×C4C23×D711yescharacteristic
400SD16—716no—
401C2×C8—22no—
402C2×C8—74no—
403C2×C8—144no—
404C2×C8Q8×D714yes—
405C2×C8C23×D712yes—
406C2×C8C23×D712yes—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—78no—
412C4⋊C4—74no—
413C4⋊C4—72no—
414C4⋊C4—72no—
415C4⋊C4—148no—
416C4⋊C4—148no—
417C4⋊C4—148no—
418C4⋊C4—148no—
419C4⋊C4—148no—
420C4⋊C4—144no—
421C4⋊C4—141no—
422C4⋊C4—141no—
423C4⋊C4C23×D714yes—
424C4⋊C4C23×D714yes—
425C22⋊C4—148no—
426C22⋊C4—144no—
427C42—74no—
428C42—74no—
429C42—148no—
430C42—144no—
431C42D4×D712yes—
432C42C23×D712yes—
433C2×C7#338114yescomplemented
434C2×C7C2×D4×Q811yescharacteristic
435C2×C7C22×#13511yescharacteristic
436C2×C7C2×#57711yescharacteristic
437D7—44no—
438C23—144no—
439C23—142no—
440C23—282no—
441C23—282no—
442C23C2×D4×D711yescharacteristic
443Q8—48no—
444Q8—74no—
445Q8—84no—
446Q8—144no—
447Q8—148no—
448Q8—142no—
449D4—74no—
450D4—144no—
451D4—142no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—44no—
456C2×C4—44no—
457C2×C4—74no—
458C2×C4—74no—
459C2×C4—144no—
460C2×C4—144no—
461C2×C4—144no—
462C2×C4—142no—
463C2×C4—142no—
464C2×C4—142no—
465C2×C4—282no—
466C2×C4—282no—
467C2×C4—288no—
468C2×C4—568no—
469C2×C4#647914yes—
470C2×C4C2×D4×D712yes—
471C2×C4C2×D4×D711yescharacteristic
472C2×C4C2×D4×D712yes—
473C2×C4C2×Q8×D712yes—
474C2×C4#655112yes—
475C2×C4C24×D711yescharacteristic
476C8—22no—
477C8—144no—
478C8C2×Q8×D714yes—
479C7C2×#338111yescharacteristic, complemented, Sylow
480C22—144no—
481C22—288no—
482C22—282no—
483C22—282no—
484C22#9041812yes—
485C22C2×#647912yes—
486C22#9045312yes—
487C22C22×D4×D711yescharacteristic
488C4—22no—
489C4—44no—
490C4—44no—
491C4—144no—
492C4—144no—
493C4—144no—
494C4—282no—
495C4—282no—
496C4#9041812yes—
497C4C2×#647914yes—
498C4C22×Q8×D711yescharacteristic
499C4C2×#655111yescharacteristic
500C2—284no—
501C2#1173934914yesdirect product factor
502C2C2×#9041811yescharacteristic
503C2C22×#647911yescharacteristic
504C2C2×#9045311yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#498C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×#498D7
hypocenterC7C2×#3381
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
2. C2×#90412C2semidirect
3. C2×C7×#498C2semidirect
4. C2×#89863C2semidirect
6. #11739349C2direct (N × H)
7. C2×#89629C2semidirect
9. C2×#89630C2semidirect
12. C2×C8×Dic14C2semidirect
22. #90412C22semidirect
33. C7×#498C22semidirect
42. #89863C22semidirect
50. #89630C22semidirect
51. #89629C22semidirect
54. C8×Dic14C22semidirect
93. C2×#1132Q8semidirect
129. C2×#498D7semidirect
198. #1132C2×Q8semidirect
220. #498C2×D7semidirect
433. C2×C7#3381semidirect
479. C7C2×#3381semidirect
501. C2#11739349direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904212
C2×#904122
C2×C7×#4982
C2×#898632
C2×#898592
#117393492
C2×#896292
C2×#896432
C2×#896302
C2×#896242
C2×C4×#11322
C2×C8×Dic142
C2×#33817