Finite Group Databasebeta

← C2×#11738403 #14234239

Subgroups — C2×#11738403 #14234239

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×#90412C211yesmaximal, characteristic, complemented
2C2×#90234C211yesmaximal, characteristic
3C2×C7×#474C211yesmaximal, characteristic
4C2×#89851C211yesmaximal, characteristic, complemented
5C2×C4×#1142C211yesmaximal, characteristic
6#11738403C2116yesmaximal, direct product factor
7C2×#89649C212yesmaximal, complemented
8C2×#89650C212yesmaximal, complemented
9C2×#89622C211yesmaximal, characteristic, complemented
10C2×#89602C211yesmaximal, characteristic, complemented
11C2×#89538C212yesmaximal
12C2×#89530C212yesmaximal
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C4×C7×D4C2211yescharacteristic
15C2×Q8×Dic7—21no—
16C2×#6507—21no—
17C2×D4×Dic7C2212yes—
18C22×#1142C2211yescharacteristic
19C22×C4⋊Dic7—21no—
20C2×#6487—21no—
21#90412—24no—
22#90412C2218yescomplemented
23#90234—24no—
24#90234C2218yes—
25C2×#6453C2212yes—
26C2×#6453C2212yes—
27C2×#6452—22no—
28C2×#6450C2212yes—
29C2×#6441—22no—
30C2×#6432C2211yescharacteristic
31C2×C4×Dic14C2211yescharacteristic
32C2×C4×Dic14C2211yescharacteristic
33C7×#474C2218yes—
34C2×C7×#107C2212yes—
35C2×C7×C4⋊C8C2211yescharacteristic
36C2×C7×#102C2212yes—
37C2×#6406C2211yescharacteristic
38C2×#6392C2212yes—
39C2×#6390C2212yes—
40C2×Dic7⋊C8C2212yes—
41C2×C8×Dic7C2212yes—
42#89851C2218yescomplemented
43C4×#1142C2218yes—
44C2×#6384C2211yescharacteristic
45C2×#6382C2211yescharacteristic
46C2×#6382C2212yes—
47C2×#6382C2212yes—
48C2×C4×C7⋊C8C2211yescharacteristic
49#89650C22116yescomplemented
50#89649C22116yescomplemented
51#89622C2218yescomplemented
52#89602C2218yescomplemented
53#89538C22116yes—
54#89530C22116yes—
55C2×#3381—71nomaximal, Sylow
56C22×C7×Q8—21no—
57C22×C7×D4C2311yescharacteristic
58C23×C4×C7—21no—
59C23×Dic7—22no—
60C22×Dic14—21no—
61C22×Dic14D411yescharacteristic
62C22×Dic14C2311yescharacteristic
63C22×C7×C8C2312yes—
64C7×C4⋊Q8—22no—
65C7×C4⋊Q8C2314yes—
66C4×C7×D4—22no—
67C4×C7×D4C2314yes—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4C2312yes—
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C22⋊C4—21no—
72C2×C42×C7C2311yescharacteristic
73C2×C22⋊Dic7—22no—
74Q8×Dic7—28no—
75#6507—28no—
76D4×Dic7—24no—
77D4×Dic7C2318yes—
78C2×#1142Q818yescomplemented
79C2×#1142C2314yes—
80C2×C4⋊Dic7—21no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—28no—
84C2×C4⋊Dic7D411yescharacteristic
85C2×C4⋊Dic7C2312yes—
86C2×C4⋊Dic7C2311yescharacteristic
87#6487—28no—
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—22no—
90C2×Dic7⋊C4—22no—
91C2×Dic7⋊C4—22no—
92C2×Dic7⋊C4D412yes—
93C2×C4×Dic7—21no—
94C2×C4×Dic7—22no—
95C2×C4×Dic7C2312yes—
96C22×C7⋊C8C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98#6453—24no—
99#6453—24no—
100#6453C2318yes—
101#6453C2318yes—
102#6452—216no—
103#6450—24no—
104#6450C2318yes—
105#6441—216no—
106#6432—22no—
107#6432C2314yes—
108C4×Dic14—22no—
109C4×Dic14D414yes—
110C4×Dic14C2314yes—
111C4×Dic14C2314yes—
112C7×#107C2318yes—
113C7×C4⋊C8C2314yes—
114C7×#102C2318yes—
115#6406C2314yes—
116#6392C2318yes—
117#6390C2318yes—
118Dic7⋊C8C2318yes—
119C8×Dic7C2318yes—
120#6384C2314yes—
121#6382C2318yes—
122#6382C2314yes—
123#6382C2318yes—
124C4×C7⋊C8C2314yes—
125C2×#557—71no—
126C2×#554—71no—
127#3381—716no—
128C2×#499—72no—
129C2×#498—71no—
130C2×#479—72no—
131C2×#477—71no—
132C2×#478—72no—
133C2×#474D711yescharacteristic
134C2×C8×Q8—71no—
135C2×C4×SD16—72no—
136C2×C4×SD16—71no—
137C24×C7—21no—
138C2×C7×Q8—24no—
139C2×C7×Q8—44no—
140C2×C7×D4—21no—
141C2×C7×D4—22no—
142C2×C7×D4C2×Q814yes—
143C2×C7×D4C2412yes—
144C22×C4×C7—22no—
145C22×C4×C7—21no—
146C22×C4×C7—24no—
147C22×C4×C7—44no—
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2411yescharacteristic
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—22no—
154C22×Dic7—28no—
155C22×Dic7—84no—
156C22×Dic7C2×D412yes—
157C22×Dic7C2×D412yes—
158C2×Dic14—24no—
159C2×Dic14—21no—
160C2×Dic14—22no—
161C2×Dic14—24no—
162C2×Dic14—82no—
163C2×Dic14C2×D414yes—
164C2×Dic14C2×Q814yes—
165C2×Dic14C2412yes—
166C2×C7×C8—24no—
167C2×C7×C8C2414yes—
168C7×C4⋊C4—22no—
169C7×C4⋊C4—24no—
170C7×C4⋊C4—21no—
171C7×C4⋊C4C2414yes—
172C7×C4⋊C4C2412yes—
173C7×C22⋊C4—24no—
174C42×C7C2×D412yes—
175C42×C7C2412yes—
176C22⋊Dic7—28no—
177#1142C2×Q8116yescomplemented
178C4⋊Dic7—21no—
179C4⋊Dic7—22no—
180C4⋊Dic7—24no—
181C4⋊Dic7—28no—
182C4⋊Dic7—28no—
183C4⋊Dic7C2×D414yes—
184C4⋊Dic7C2412yes—
185C4⋊Dic7C2414yes—
186Dic7⋊C4—24no—
187Dic7⋊C4—28no—
188Dic7⋊C4—28no—
189Dic7⋊C4—28no—
190Dic7⋊C4C2×D418yes—
191C4×Dic7—24no—
192C4×Dic7—28no—
193C4×Dic7C2×D414yes—
194C4×Dic7C2414yes—
195C2×C7⋊C8—22no—
196C2×C7⋊C8C2×Q814yes—
197C2×C7⋊C8C2412yes—
198C2×C7⋊C8C2412yes—
199C22×SD16—71no—
200#557—78no—
201#557—144no—
202#554—78no—
203#554—144no—
204C2×C4⋊Q8—71no—
205C2×C4⋊Q8—141no—
206C2×C4⋊Q8C2×D711yescharacteristic
207C2×#125—72no—
208C2×#125—72no—
209C2×#125—142no—
210C2×C22⋊Q8—142no—
211C2×C22⋊Q8—141no—
212C2×C4×Q8—71no—
213C2×C4×Q8—72no—
214C2×C4×Q8—71no—
215C2×C4×Q8—141no—
216C2×C4×D4—72no—
217C2×C4×D4C2×D711yescharacteristic
218C22×C4⋊C4—141no—
219#499—716no—
220#498—78no—
221#479—716no—
222#478—716no—
223#477—78no—
224#474C2×D718yes—
225C8×Q8—78no—
226C4×SD16—78no—
227C4×SD16—716no—
228C2×#107—72no—
229C2×#107C2×D712yes—
230C2×#106—72no—
231C2×#106—72no—
232C2×#106—71no—
233C2×C4⋊C8—72no—
234C2×C4⋊C8C2×D711yescharacteristic
235C2×#103—72no—
236C2×#103—71no—
237C2×#102—71no—
238C2×#102C2×D712yes—
239C2×C4×C8—72no—
240C2×C4×C8—71no—
241C23×C7—24no—
242C23×C7—22no—
243C23×C7—42no—
244C23×C7—42no—
245C23×C7C22×D411yescharacteristic
246C7×Q8—48no—
247C7×D4—24no—
248C7×D4—22no—
249C7×D4C22×Q814yes—
250C2×C4×C7—22no—
251C2×C4×C7—24no—
252C2×C4×C7—22no—
253C2×C4×C7—42no—
254C2×C4×C7—44no—
255C2×C4×C7—48no—
256C2×C4×C7#13514yes—
257C2×C4×C7C22×D412yes—
258C2×C4×C7C22×D411yescharacteristic
259C2×C4×C7C22×D412yes—
260C2×C4×C7C22×Q812yes—
261C2×C4×C72−1+412yes—
262C2×C4×C7C2511yescharacteristic
263C2×Dic7—24no—
264C2×Dic7—24no—
265C2×Dic7—24no—
266C2×Dic7—22no—
267C2×Dic7—22no—
268C2×Dic7—24no—
269C2×Dic7—44no—
270C2×Dic7—42no—
271C2×Dic7—88no—
272C2×Dic7C22×D414yes—
273C2×Dic7C22×D414yes—
274Dic14—24no—
275Dic14—28no—
276Dic14—22no—
277Dic14—84no—
278Dic14C22×Q814yes—
279C7×C8—24no—
280C7⋊C8—22no—
281C7⋊C8C22×Q814yes—
282C22×Q8—21no—
283C22×Q8—71no—
284C22×Q8—71no—
285C22×Q8—141no—
286C22×D4C22×D711yescharacteristic
287C23×C4—21no—
288C23×C4—142no—
289C2×SD16—78no—
290C2×SD16—74no—
291C22×C8—71no—
292C22×C8—71no—
293C22×C8C22×D712yes—
294C4⋊Q8—22no—
295C4⋊Q8—74no—
296C4⋊Q8—148no—
297C4⋊Q8—142no—
298C4⋊Q8C22×D714yes—
299#125—78no—
300#125—78no—
301#125—144no—
302#125—144no—
303#125—1416no—
304C22⋊Q8—1416no—
305C22⋊Q8—148no—
306C4×Q8—74no—
307C4×Q8—74no—
308C4×Q8—78no—
309C4×Q8—74no—
310C4×Q8—144no—
311C4×Q8—148no—
312C4×Q8—142no—
313C4×D4—22no—
314C4×D4—78no—
315C4×D4—144no—
316C4×D4C22×D714yes—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—71no—
319C2×C4⋊C4—72no—
320C2×C4⋊C4—72no—
321C2×C4⋊C4—71no—
322C2×C4⋊C4—148no—
323C2×C4⋊C4—142no—
324C2×C4⋊C4—142no—
325C2×C4⋊C4—142no—
326C2×C4⋊C4—142no—
327C2×C4⋊C4—142no—
328C2×C4⋊C4—141no—
329C2×C4⋊C4—141no—
330C2×C4⋊C4C22×D711yescharacteristic
331C2×C4⋊C4C22×D712yes—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—142no—
334C2×C42—72no—
335C2×C42—142no—
336C2×C42—141no—
337C2×C42C22×D711yescharacteristic
338#107—78no—
339#107C22×D718yes—
340#106—78no—
341#106—74no—
342#106—78no—
343C4⋊C8—78no—
344C4⋊C8C22×D714yes—
345#103—78no—
346#103—74no—
347#102—74no—
348#102C22×D718yes—
349C4×C8—78no—
350C4×C8—74no—
351C22×C7—24no—
352C22×C7—48no—
353C22×C7—42no—
354C22×C7—42no—
355C22×C7D4×Q812yes—
356C22×C7C2×#13512yes—
357C22×C7#57712yes—
358C22×C7C23×D411yescharacteristic
359C4×C7—22no—
360C4×C7—42no—
361C4×C7—44no—
362C4×C7D4×Q812yes—
363C4×C7C2×#13514yes—
364C4×C7C23×Q811yescharacteristic
365C4×C7C2×2−1+411yescharacteristic
366Dic7—24no—
367Dic7—24no—
368Dic7—24no—
369Dic7—44no—
370Dic7—42no—
371C24—21no—
372C2×Q8—24no—
373C2×Q8—44no—
374C2×Q8—74no—
375C2×Q8—74no—
376C2×Q8—72no—
377C2×Q8—144no—
378C2×Q8—141no—
379C2×Q8—144no—
380C2×Q8—142no—
381C2×Q8—562no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4Q8×D714yes—
385C2×D4C23×D712yes—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—24no—
389C22×C4—44no—
390C22×C4—72no—
391C22×C4—72no—
392C22×C4—148no—
393C22×C4—141no—
394C22×C4—141no—
395C22×C4—142no—
396C22×C4—564no—
397C22×C4D4×D711yescharacteristic
398C22×C4D4×D711yescharacteristic
399C22×C4C23×D711yescharacteristic
400SD16—716no—
401C2×C8—24no—
402C2×C8—74no—
403C2×C8—72no—
404C2×C8—72no—
405C2×C8—142no—
406C2×C8C23×D714yes—
407C4⋊C4—24no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—78no—
411C4⋊C4—74no—
412C4⋊C4—72no—
413C4⋊C4—74no—
414C4⋊C4—148no—
415C4⋊C4—148no—
416C4⋊C4—148no—
417C4⋊C4—148no—
418C4⋊C4—148no—
419C4⋊C4—144no—
420C4⋊C4—142no—
421C4⋊C4—141no—
422C4⋊C4—144no—
423C4⋊C4C23×D714yes—
424C4⋊C4C23×D712yes—
425C22⋊C4—24no—
426C22⋊C4—148no—
427C42—74no—
428C42—74no—
429C42—148no—
430C42—144no—
431C42D4×D712yes—
432C42C23×D712yes—
433C2×C7—44no—
434C2×C7#338114yescomplemented
435C2×C7C2×D4×Q811yescharacteristic
436C2×C7C22×#13511yescharacteristic
437C2×C7C2×#57711yescharacteristic
438C23—24no—
439C23—22no—
440C23—42no—
441C23—42no—
442C23C2×D4×D711yescharacteristic
443Q8—48no—
444Q8—74no—
445Q8—148no—
446Q8—144no—
447Q8—142no—
448Q8—564no—
449D4—24no—
450D4—22no—
451D4C2×Q8×D714yes—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—48no—
458C2×C4—74no—
459C2×C4—74no—
460C2×C4—144no—
461C2×C4—144no—
462C2×C4—144no—
463C2×C4—142no—
464C2×C4—142no—
465C2×C4—144no—
466C2×C4—282no—
467C2×C4—284no—
468C2×C4—568no—
469C2×C4#647514yes—
470C2×C4C2×D4×D712yes—
471C2×C4C2×D4×D712yes—
472C2×C4C2×D4×D711yescharacteristic
473C2×C4C2×Q8×D712yes—
474C2×C4#655412yes—
475C2×C4C24×D711yescharacteristic
476C8—24no—
477C8—74no—
478C8—142no—
479C7C2×#338111yescharacteristic, complemented, Sylow
480C22—24no—
481C22—42no—
482C22—48no—
483C22—42no—
484C22#9032312yes—
485C22C2×#647512yes—
486C22#9046912yes—
487C22C22×D4×D711yescharacteristic
488C4—22no—
489C4—42no—
490C4—44no—
491C4—144no—
492C4—144no—
493C4—144no—
494C4—284no—
495C4—282no—
496C4#9032312yes—
497C4C2×#647514yes—
498C4C22×Q8×D711yescharacteristic
499C4C2×#655411yescharacteristic
500C2—44no—
501C2#1173840314yesdirect product factor
502C2C2×#9032311yescharacteristic
503C2C22×#647511yescharacteristic
504C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#474C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
hypercenterC2×#474D7
hypocenterC7C2×#3381
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#90412C2semidirect
4. C2×#89851C2semidirect
6. #11738403C2direct (N × H)
7. C2×#89649C2semidirect
8. C2×#89650C2semidirect
9. C2×#89622C2semidirect
10. C2×#89602C2semidirect
22. #90412C22semidirect
42. #89851C22semidirect
49. #89650C22semidirect
50. #89649C22semidirect
51. #89622C22semidirect
52. #89602C22semidirect
78. C2×#1142Q8semidirect
177. #1142C2×Q8semidirect
434. C2×C7#3381semidirect
479. C7C2×#3381semidirect
501. C2#11738403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904122
C2×#902342
C2×C7×#4742
C2×#898512
C2×C4×#11422
#117384032
C2×#896492
C2×#896502
C2×#896222
C2×#896022
C2×#895382
C2×#895302
C2×#33817