Finite Group Databasebeta

← C2×#11725882 #13319748

Subgroups — C2×#11725882 #13319748

Order 1792.

1002 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6452C211yesmaximal, characteristic
2C2×#89491C211yesmaximal, characteristic
3C2×#89490C211yesmaximal, characteristic
4C2×C7×#324C211yesmaximal, characteristic
5C2×#89323C211yesmaximal, characteristic
6C2×#89264C211yesmaximal, characteristic
7C2×#89264C211yesmaximal, characteristic
8#11725882C218yesmaximal, direct product factor
9C22×C7×C4⋊C4C2211yescharacteristic
10C22×C4⋊Dic7C411yescharacteristic
11C22×Dic7⋊C4C411yescharacteristic
12C22×Dic7⋊C4C411yescharacteristic
13C22×Dic7⋊C4C411yescharacteristic
14C22×Dic7⋊C4C2211yescharacteristic
15C22×C4×Dic7C2211yescharacteristic
16C2×#6452—21no—
17C2×#6452—21no—
18C2×#6452—21no—
19C2×#6452—21no—
20C2×#6452—22no—
21C2×#6452—22no—
22C2×#6452C414yes—
23C2×#6452C2214yes—
24C2×C7×C22⋊C8C2211yescharacteristic
25C2×C7×C22⋊C8C2211yescharacteristic
26C2×C22⋊(C7⋊C8)C2211yescharacteristic
27C2×C22⋊(C7⋊C8)C2211yescharacteristic
28C2×#6389—21no—
29C2×Dic7⋊C8—21no—
30C2×Dic7⋊C8—21no—
31C2×C8×Dic7—21no—
32#89491—22no—
33#89491C2214yes—
34#89490—22no—
35#89490C2214yes—
36C7×#324C2214yes—
37#89323C2214yes—
38#89264C2214yes—
39#89264C2214yes—
40C2×#1470—71nomaximal, Sylow
41C23×C4×C7C2×C411yescharacteristic
42C23×C4×C7C2×C411yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×Dic7C2×C411yescharacteristic
45C23×Dic7C2×C411yescharacteristic
46C23×Dic7C2×C411yescharacteristic
47C23×Dic7C2×C411yescharacteristic
48C22×C7×C8—21no—
49C22×C7×C8—21no—
50C2×C7×C4⋊C4—21no—
51C2×C7×C4⋊C4—21no—
52C2×C7×C4⋊C4—21no—
53C2×C7×C4⋊C4—21no—
54C2×C7×C4⋊C4C2×C412yes—
55C2×C7×C4⋊C4C2312yes—
56C2×C4⋊Dic7—22no—
57C2×C4⋊Dic7—21no—
58C2×C4⋊Dic7—21no—
59C2×C4⋊Dic7C2×C414yes—
60C2×Dic7⋊C4—21no—
61C2×Dic7⋊C4—21no—
62C2×Dic7⋊C4—21no—
63C2×Dic7⋊C4—21no—
64C2×Dic7⋊C4—21no—
65C2×Dic7⋊C4—22no—
66C2×Dic7⋊C4—22no—
67C2×Dic7⋊C4—21no—
68C2×Dic7⋊C4—21no—
69C2×Dic7⋊C4—21no—
70C2×Dic7⋊C4—21no—
71C2×Dic7⋊C4—22no—
72C2×Dic7⋊C4—21no—
73C2×Dic7⋊C4C2×C412yes—
74C2×Dic7⋊C4C2×C414yes—
75C2×Dic7⋊C4C2×C414yes—
76C2×Dic7⋊C4C2×C414yes—
77C2×Dic7⋊C4C2312yes—
78C2×C4×Dic7C2×C412yes—
79C2×C4×Dic7D411yescharacteristic
80C2×C4×Dic7D411yescharacteristic
81C2×C4×Dic7D411yescharacteristic
82C2×C4×Dic7D411yescharacteristic
83C2×C4×Dic7D412yes—
84C2×C4×Dic7D412yes—
85C2×C4×Dic7C2312yes—
86C22×C7⋊C8—21no—
87C22×C7⋊C8—21no—
88#6452—24no—
89#6452—24no—
90#6452—24no—
91#6452—24no—
92#6452—24no—
93#6452—24no—
94#6452—24no—
95#6452—24no—
96C7×C22⋊C8—21no—
97C7×C22⋊C8—21no—
98C7×C22⋊C8C2312yes—
99C7×C22⋊C8C2312yes—
100C22⋊(C7⋊C8)—21no—
101C22⋊(C7⋊C8)—21no—
102C22⋊(C7⋊C8)C2312yes—
103C22⋊(C7⋊C8)C2312yes—
104#6389—24no—
105Dic7⋊C8—24no—
106Dic7⋊C8—24no—
107C8×Dic7—24no—
108C22×#125—71no—
109C2×#432—71no—
110C2×#431—71no—
111#1470—78no—
112C2×#324—71no—
113C2×#324—71no—
114C2×#324—71no—
115C2×#324D711yescharacteristic
116C24×C7C22×C411yescharacteristic
117C22×C4×C7—21no—
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—42no—
124C22×C4×C7—42no—
125C22×C4×C7C22×C412yes—
126C22×C4×C7C22×C412yes—
127C22×C4×C7C22×C411yescharacteristic
128C22×C4×C7C2×D411yescharacteristic
129C22×C4×C7C2×D411yescharacteristic
130C22×C4×C7C2×D411yescharacteristic
131C22×C4×C7C2×D411yescharacteristic
132C22×C4×C7C2411yescharacteristic
133C22×Dic7—22no—
134C22×Dic7—22no—
135C22×Dic7—24no—
136C22×Dic7—21no—
137C22×Dic7—21no—
138C22×Dic7—21no—
139C22×Dic7—21no—
140C22×Dic7—22no—
141C22×Dic7—22no—
142C22×Dic7—42no—
143C22×Dic7C22⋊C411yescharacteristic
144C22×Dic7C22⋊C412yes—
145C22×Dic7C22⋊C412yes—
146C22×Dic7C22⋊C411yescharacteristic
147C22×Dic7C22⋊C411yescharacteristic
148C22×Dic7C22⋊C411yescharacteristic
149C22×Dic7C22×C412yes—
150C22×Dic7C22×C412yes—
151C22×Dic7C22×C412yes—
152C22×Dic7C22×C412yes—
153C2×C7×C8—22no—
154C2×C7×C8—22no—
155C2×C7×C8—42no—
156C2×C7×C8—42no—
157C7×C4⋊C4—22no—
158C7×C4⋊C4—22no—
159C7×C4⋊C4—22no—
160C7×C4⋊C4—22no—
161C4⋊Dic7—24no—
162C4⋊Dic7—24no—
163Dic7⋊C4—22no—
164Dic7⋊C4—22no—
165Dic7⋊C4—22no—
166Dic7⋊C4—22no—
167Dic7⋊C4—24no—
168Dic7⋊C4—24no—
169Dic7⋊C4—24no—
170Dic7⋊C4—24no—
171Dic7⋊C4—24no—
172Dic7⋊C4—24no—
173C4×Dic7C22⋊C412yes—
174C4×Dic7C22⋊C412yes—
175C4×Dic7C22⋊C412yes—
176C4×Dic7C22⋊C412yes—
177C4×Dic7C2×D412yes—
178C4×Dic7C2×D412yes—
179C4×Dic7C2×D412yes—
180C4×Dic7C2×D412yes—
181C2×C7⋊C8—22no—
182C2×C7⋊C8—22no—
183C2×C7⋊C8—42no—
184C2×C7⋊C8—42no—
185C2×#125—74no—
186C2×#125—74no—
187C2×#125—141no—
188C2×#125—141no—
189C2×#125—141no—
190C2×#125—141no—
191C2×#125—142no—
192C2×#125—142no—
193C22×C4⋊C4—71no—
194C22×C4⋊C4—71no—
195C22×C4⋊C4—71no—
196C22×C4⋊C4—71no—
197C22×C4⋊C4—71no—
198C22×C4⋊C4C2×D711yescharacteristic
199C22×C42—71no—
200#432—74no—
201#432—142no—
202#431—74no—
203#431—142no—
204C2×C4⋊C8—141no—
205C2×C4⋊C8—141no—
206C2×C22⋊C8—71no—
207C2×C22⋊C8—71no—
208C2×C22⋊C8C2×D711yescharacteristic
209C2×C22⋊C8C2×D711yescharacteristic
210C2×#97—141no—
211C2×C4×C8—141no—
212#324—74no—
213#324—74no—
214#324—74no—
215#324C2×D714yes—
216C23×C7—22no—
217C23×C7—22no—
218C23×C7C2×C22⋊C411yescharacteristic
219C23×C7C2×C22⋊C411yescharacteristic
220C23×C7#13112yes—
221C23×C7#13112yes—
222C23×C7C23×C411yescharacteristic
223C2×C4×C7—22no—
224C2×C4×C7—22no—
225C2×C4×C7—22no—
226C2×C4×C7—22no—
227C2×C4×C7—22no—
228C2×C4×C7—22no—
229C2×C4×C7—41no—
230C2×C4×C7—41no—
231C2×C4×C7—41no—
232C2×C4×C7—41no—
233C2×C4×C7—42no—
234C2×C4×C7—42no—
235C2×C4×C7—42no—
236C2×C4×C7—42no—
237C2×C4×C7—42no—
238C2×C4×C7C2×C22⋊C411yescharacteristic
239C2×C4×C7C2×C22⋊C411yescharacteristic
240C2×C4×C7C22×D411yescharacteristic
241C2×C4×C7C22×D411yescharacteristic
242C2×Dic7—22no—
243C2×Dic7—22no—
244C2×Dic7—24no—
245C2×Dic7—22no—
246C2×Dic7—22no—
247C2×Dic7—22no—
248C2×Dic7—24no—
249C2×Dic7—24no—
250C2×Dic7—22no—
251C2×Dic7—22no—
252C2×Dic7—22no—
253C2×Dic7—22no—
254C2×Dic7—42no—
255C2×Dic7—42no—
256C2×Dic7—42no—
257C2×Dic7—42no—
258C2×Dic7—42no—
259C2×Dic7#10114yes—
260C2×Dic7C2×C22⋊C412yes—
261C2×Dic7C2×C22⋊C412yes—
262C2×Dic7C2×C22⋊C412yes—
263C2×Dic7C2×C22⋊C412yes—
264C7×C8—42no—
265C7×C8—42no—
266C7⋊C8—42no—
267C7⋊C8—42no—
268C23×C4—71no—
269C23×C4—71no—
270C23×C4—71no—
271C23×C4—71no—
272C23×C4C4×D711yescharacteristic
273C23×C4C4×D711yescharacteristic
274C23×C4C22×D711yescharacteristic
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—141no—
278C22×C8—141no—
279#125—144no—
280#125—144no—
281#125—144no—
282#125—144no—
283#125—144no—
284#125—144no—
285#125—144no—
286#125—144no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—74no—
292C2×C4⋊C4—74no—
293C2×C4⋊C4—74no—
294C2×C4⋊C4—72no—
295C2×C4⋊C4—74no—
296C2×C4⋊C4—72no—
297C2×C4⋊C4—142no—
298C2×C4⋊C4—142no—
299C2×C4⋊C4—142no—
300C2×C4⋊C4—141no—
301C2×C4⋊C4—141no—
302C2×C4⋊C4—141no—
303C2×C4⋊C4—141no—
304C2×C4⋊C4—141no—
305C2×C4⋊C4—141no—
306C2×C4⋊C4—142no—
307C2×C4⋊C4—141no—
308C2×C4⋊C4—141no—
309C2×C4⋊C4—141no—
310C2×C4⋊C4—141no—
311C2×C4⋊C4—141no—
312C2×C4⋊C4—141no—
313C2×C4⋊C4C4×D712yes—
314C2×C4⋊C4C22×D712yes—
315C2×C42—72no—
316C2×C42—71no—
317C2×C42—71no—
318C2×C42—71no—
319C2×C42—71no—
320C2×C42—72no—
321C2×C42—72no—
322C2×C42—72no—
323C4⋊C8—144no—
324C4⋊C8—144no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327C22⋊C8—72no—
328C22⋊C8—72no—
329C22⋊C8—141no—
330C22⋊C8—141no—
331C22⋊C8C22×D712yes—
332C22⋊C8C22×D712yes—
333#97—144no—
334C4×C8—144no—
335C22×C7—21no—
336C22×C7—21no—
337C22×C7—21no—
338C22×C7—21no—
339C22×C7—24no—
340C22×C7—24no—
341C22×C7#40812yes—
342C22×C7#40812yes—
343C22×C7#41012yes—
344C22×C7C2×#10112yes—
345C22×C7C22×C22⋊C411yescharacteristic
346C22×C7C2×#13111yescharacteristic
347C22×C7C2×#13111yescharacteristic
348C4×C7—21no—
349C4×C7—21no—
350C4×C7—21no—
351C4×C7—21no—
352C4×C7—42no—
353C4×C7—42no—
354Dic7—22no—
355Dic7—22no—
356Dic7—22no—
357Dic7—42no—
358Dic7—42no—
359Dic7C2×#10114yes—
360C24C2×C4×D711yescharacteristic
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—71no—
370C22×C4—72no—
371C22×C4—72no—
372C22×C4—71no—
373C22×C4—71no—
374C22×C4—71no—
375C22×C4—72no—
376C22×C4—72no—
377C22×C4—72no—
378C22×C4—72no—
379C22×C4—144no—
380C22×C4—142no—
381C22×C4—142no—
382C22×C4—141no—
383C22×C4—141no—
384C22×C4—141no—
385C22×C4—141no—
386C22×C4—142no—
387C22×C4—142no—
388C22×C4—282no—
389C22×C4C2×C4×D712yes—
390C22×C4C2×C4×D712yes—
391C22×C4C2×C4×D711yescharacteristic
392C22×C4D4×D711yescharacteristic
393C22×C4D4×D711yescharacteristic
394C22×C4D4×D711yescharacteristic
395C22×C4D4×D711yescharacteristic
396C22×C4C23×D711yescharacteristic
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—42no—
400C2×C8—42no—
401C2×C8—142no—
402C2×C8—142no—
403C2×C8—282no—
404C2×C8—282no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—144no—
410C4⋊C4—144no—
411C4⋊C4—144no—
412C4⋊C4—144no—
413C4⋊C4—144no—
414C4⋊C4—144no—
415C4⋊C4—144no—
416C4⋊C4—144no—
417C4⋊C4—142no—
418C4⋊C4—142no—
419C4⋊C4—142no—
420C4⋊C4—142no—
421C42—72no—
422C42—72no—
423C42—72no—
424C42—72no—
425C42—72no—
426C42—72no—
427C42—72no—
428C42—72no—
429C2×C7—21no—
430C2×C7—21no—
431C2×C7—22no—
432C2×C7#147014yescomplemented
433C2×C7C2×#40811yescharacteristic
434C2×C7C2×#41011yescharacteristic
435C2×C7C22×#10111yescharacteristic
436C23—22no—
437C23—22no—
438C23D7×C22⋊C411yescharacteristic
439C23D7×C22⋊C411yescharacteristic
440C23#646412yes—
441C23#647012yes—
442C23C22×C4×D711yescharacteristic
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—72no—
459C2×C4—74no—
460C2×C4—72no—
461C2×C4—72no—
462C2×C4—72no—
463C2×C4—144no—
464C2×C4—144no—
465C2×C4—142no—
466C2×C4—142no—
467C2×C4—144no—
468C2×C4—142no—
469C2×C4—142no—
470C2×C4—142no—
471C2×C4—142no—
472C2×C4—142no—
473C2×C4—142no—
474C2×C4—142no—
475C2×C4—282no—
476C2×C4—282no—
477C2×C4—282no—
478C2×C4—282no—
479C2×C4—282no—
480C2×C4D7×C22⋊C411yescharacteristic
481C2×C4D7×C22⋊C411yescharacteristic
482C2×C4C2×D4×D711yescharacteristic
483C2×C4C2×D4×D711yescharacteristic
484C8—42no—
485C8—42no—
486C8—282no—
487C8—282no—
488C7C2×#147011yescharacteristic, complemented, Sylow
489C22—24no—
490C22—24no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22#8949912yes—
496C22#8949912yes—
497C22#8951212yes—
498C22D7×#10112yes—
499C22C2×D7×C22⋊C411yescharacteristic
500C22C2×#646411yescharacteristic
501C22C2×#647011yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—42no—
507C4—42no—
508C4—74no—
509C4—142no—
510C4—142no—
511C4—142no—
512C4—282no—
513C4—282no—
514C2—21no—
515C2—21no—
516C2—22no—
517C2#1172588214yesdirect product factor
518C2C2×#8949911yescharacteristic
519C2C2×#8951211yescharacteristic
520C2C2×D7×#10111yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#324C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22×C4
cosocleC22×C4×C7C24
hypercenterC2×#324D7
hypocenterC7C2×#1470
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
8. #11725882C2direct (N × H)
432. C2×C7#1470semidirect
488. C7C2×#1470semidirect
517. C2#11725882direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64522
C2×#894912
C2×#894902
C2×C7×#3242
C2×#893232
C2×#892642
#117258822
C2×#14707