Finite Group Databasebeta

← #13244347

Subgroups — #13244347

Order 1792.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#435C211yesmaximal, characteristic
2#11729721C211yesmaximal, characteristic, complemented
3C8×C22⋊Dic7C211yesmaximal, characteristic, complemented
4C4×#6408C211yesmaximal, characteristic
5#11729354C211yesmaximal, characteristic
6#11725483C211yesmaximal, characteristic, complemented
7#11725483C211yesmaximal, characteristic, complemented
8C22×C7×M16C411yescharacteristic, complemented
9C23×C7×C8C2211yescharacteristic
10C2×C4×C7×D4C2211yescharacteristic
11C7×#435—21no—
12C7×#435—21no—
13C7×#435—21no—
14C7×#435—21no—
15C2×C7×C4⋊C8C411yescharacteristic, complemented
16C2×C7×C22⋊C8C411yescharacteristic, complemented
17C2×C7×C22⋊C8C2211yescharacteristic
18C2×C7×#97C411yescharacteristic, complemented
19C2×#6408C412yes—
20C4×C22⋊Dic7C2211yescharacteristic
21C4×C22⋊Dic7C2211yescharacteristic
22C2×C22⋊(C7⋊C8)C2211yescharacteristic
23C2×C22⋊(C7⋊C8)C2211yescharacteristic
24C2×#6389—21no—
25C2×C8×Dic7—21no—
26#89345—21no—
27#89345—21no—
28#89323C412yescomplemented
29#89321C412yes—
30#89320C412yescomplemented
31#8161—71nomaximal, Sylow
32C22×C7×D4C2×C411yescharacteristic
33C23×C4×C7C2×C411yescharacteristic
34C23×C4×C7C2311yescharacteristic
35C2×C7×M16—21no—
36C2×C7×M16—21no—
37C2×C7×M16—42no—
38C22×C7×C8—42no—
39C22×C7×C8C2×C411yescharacteristic
40C22×C7×C8C2×C411yescharacteristic
41C22×C7×C8C2×C411yescharacteristic
42C22×C7×C8C2×C411yescharacteristic
43C22×C7×C8D411yescharacteristic
44C22×C7×C8D411yescharacteristic
45C22×C7×C8D411yescharacteristic
46C22×C7×C8D411yescharacteristic
47C4×C7×D4—21no—
48C4×C7×D4—21no—
49C4×C7×D4—21no—
50C4×C7×D4—21no—
51C2×C7×C4⋊C4C2×C411yescharacteristic
52C2×C7×C22⋊C4C2×C411yescharacteristic
53C2×C7×C22⋊C4C2×C411yescharacteristic
54C2×C42×C7C2×C411yescharacteristic
55C2×C22⋊Dic7C2×C412yes—
56C2×C22⋊Dic7C2×C412yes—
57C2×C4×Dic7—21no—
58C2×C4×Dic7—21no—
59C22×C7⋊C8—21no—
60C22×C7⋊C8—21no—
61C7×C4⋊C8—21no—
62C7×C4⋊C8—21no—
63C7×C22⋊C8—21no—
64C7×C22⋊C8—21no—
65C7×C22⋊C8—21no—
66C7×C22⋊C8—21no—
67C7×#97—21no—
68C7×#97—21no—
69#6408—24no—
70C7⋊#95—21no—
71C7⋊#95—21no—
72C22⋊(C7⋊C8)—21no—
73C22⋊(C7⋊C8)—21no—
74C22⋊(C7⋊C8)C2×C412yes—
75C22⋊(C7⋊C8)C2×C412yes—
76#6389—42no—
77C8×Dic7—42no—
78C2×#435D711yescharacteristic
79C4×#99—71no—
80#1752—71no—
81C8×C22⋊C4—71no—
82#1459—71no—
83#1282—71no—
84#1282—71no—
85C24×C7C4211yescharacteristic
86C24×C7C22×C411yescharacteristic
87C2×C7×D4—21no—
88C2×C7×D4—21no—
89C2×C7×D4—22no—
90C2×C7×D4—22no—
91C22×C4×C7—21no—
92C22×C4×C7—21no—
93C22×C4×C7—41no—
94C22×C4×C7—41no—
95C22×C4×C7—41no—
96C22×C4×C7—41no—
97C22×C4×C7C4211yescharacteristic
98C22×C4×C7C4211yescharacteristic
99C22×C4×C7C4211yescharacteristic
100C22×C4×C7C22×C411yescharacteristic
101C22×C4×C7C22×C411yescharacteristic
102C22×C4×C7C2×D411yescharacteristic
103C22×C4×C7C2×D411yescharacteristic
104C22×C4×C7#4111yescharacteristic
105C22×C4×C7#4111yescharacteristic
106C22×Dic7—22no—
107C22×Dic7—22no—
108C7×M16—42no—
109C7×M16—42no—
110C2×C7×C8—22no—
111C2×C7×C8—22no—
112C2×C7×C8—22no—
113C2×C7×C8—21no—
114C2×C7×C8—21no—
115C2×C7×C8—41no—
116C2×C7×C8—41no—
117C2×C7×C8—41no—
118C2×C7×C8—41no—
119C2×C7×C8—41no—
120C2×C7×C8C22⋊C411yescharacteristic
121C2×C7×C8C22⋊C411yescharacteristic
122C2×C7×C8C22⋊C411yescharacteristic
123C2×C7×C8C22⋊C411yescharacteristic
124C7×C4⋊C4—21no—
125C7×C4⋊C4—21no—
126C7×C22⋊C4—21no—
127C7×C22⋊C4—21no—
128C7×C22⋊C4—21no—
129C7×C22⋊C4—21no—
130C42×C7—21no—
131C42×C7—21no—
132C22⋊Dic7—22no—
133C22⋊Dic7—22no—
134C22⋊Dic7—22no—
135C22⋊Dic7M1614yescomplemented
136C4×Dic7—41no—
137C4×Dic7—41no—
138C4×Dic7—41no—
139C4×Dic7—41no—
140C2×C7⋊C8—22no—
141C2×C7⋊C8—22no—
142C2×C7⋊C8—41no—
143C2×C7⋊C8—41no—
144C2×C7⋊C8—41no—
145C2×C7⋊C8—41no—
146C22×M16Dic711yescharacteristic, complemented
147C23×C8C2×D711yescharacteristic
148C2×C4×D4C2×D711yescharacteristic
149#435—21no—
150#435—21no—
151#435—21no—
152#435—21no—
153C2×C4⋊C8Dic711yescharacteristic, complemented
154C2×#99—72no—
155C2×C22⋊C8—71no—
156C2×C22⋊C8—71no—
157C2×C22⋊C8Dic711yescharacteristic, complemented
158C2×C22⋊C8C2×D711yescharacteristic
159C2×#97—141no—
160C2×#97Dic711yescharacteristic, complemented
161C2×C4×C8—141no—
162C4×C22⋊C4—71no—
163C4×C22⋊C4—71no—
164#342—72no—
165#336—141no—
166#336—141no—
167#324—72no—
168#323—72no—
169C23×C7—21no—
170C23×C7—21no—
171C23×C7—21no—
172C23×C7—41no—
173C23×C7—41no—
174C23×C7—41no—
175C23×C7—41no—
176C23×C7C2×C4211yescharacteristic
177C23×C7C4×D411yescharacteristic
178C23×C7C4×D411yescharacteristic
179C23×C7C2×M1612yes—
180C23×C7#13112yes—
181C7×D4—42no—
182C7×D4—42no—
183C2×C4×C7—21no—
184C2×C4×C7—21no—
185C2×C4×C7—21no—
186C2×C4×C7—21no—
187C2×C4×C7—21no—
188C2×C4×C7—21no—
189C2×C4×C7—21no—
190C2×C4×C7—21no—
191C2×C4×C7—21no—
192C2×C4×C7—21no—
193C2×C4×C7—21no—
194C2×C4×C7—41no—
195C2×C4×C7—41no—
196C2×C4×C7—41no—
197C2×C4×C7—42no—
198C2×C4×C7—41no—
199C2×C4×C7—41no—
200C2×C4×C7—41no—
201C2×C4×C7—41no—
202C2×C4×C7C2×C22⋊C411yescharacteristic
203C2×C4×C7#11711yescharacteristic
204C2×C4×C7C4×D411yescharacteristic
205C2×C4×C7C4×D411yescharacteristic
206C2×Dic7—24no—
207C2×Dic7—42no—
208C2×Dic7—42no—
209C2×Dic7—42no—
210C2×Dic7—42no—
211C2×Dic7—42no—
212C7×C8—21no—
213C7×C8—21no—
214C7×C8—21no—
215C7×C8—41no—
216C7×C8—41no—
217C7×C8#9912yescomplemented
218C7⋊C8—42no—
219C7⋊C8—42no—
220C22×D4C4×D711yescharacteristic
221C23×C4C2×Dic711yescharacteristic
222C23×C4C22×D711yescharacteristic
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—42no—
226C22×C8—42no—
227C22×C8—141no—
228C22×C8—141no—
229C22×C8C2×Dic711yescharacteristic
230C22×C8C2×Dic711yescharacteristic
231C22×C8C2×Dic711yescharacteristic
232C22×C8C2×Dic711yescharacteristic
233C22×C8C22⋊D711yescharacteristic
234C22×C8C22⋊D711yescharacteristic
235C22×C8C22⋊D711yescharacteristic
236C22×C8C22⋊D711yescharacteristic
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240C4×D4—21no—
241C2×C4⋊C4C4×D711yescharacteristic
242C2×C22⋊C4—72no—
243C2×C22⋊C4—72no—
244C2×C22⋊C4C4×D711yescharacteristic
245C2×C22⋊C4C4×D711yescharacteristic
246C2×C42—141no—
247C2×C42—141no—
248C2×C42C2×Dic711yescharacteristic
249C4⋊C8—21no—
250C4⋊C8—21no—
251#99—144no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—72no—
257C22⋊C8—72no—
258C22⋊C8—141no—
259C22⋊C8—141no—
260#97—21no—
261#97—21no—
262#97—282no—
263C4×C8—282no—
264#95—141no—
265#95—141no—
266C22×C7—21no—
267C22×C7—21no—
268C22×C7—21no—
269C22×C7—21no—
270C22×C7—21no—
271C22×C7—21no—
272C22×C7—42no—
273C22×C7—42no—
274C22×C7—41no—
275C22×C7—41no—
276C22×C7—41no—
277C22×C7—81no—
278C22×C7—81no—
279C22×C7C4×C22⋊C411yescharacteristic
280C22×C7C4×M1611yescharacteristic
281C22×C7#40511yescharacteristic
282C22×C7#43512yes—
283C22×C7#43612yes—
284C4×C7—21no—
285C4×C7—21no—
286C4×C7—21no—
287C4×C7—41no—
288C4×C7—41no—
289C4×C7—41no—
290C4×C7C2×#9911yescharacteristic
291C4×C7#41011yescharacteristic
292Dic7—44no—
293Dic7—82no—
294C24C4×Dic711yescharacteristic
295C24C2×C4×D711yescharacteristic
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—21no—
299C2×D4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—142no—
307C22×C4—142no—
308C22×C4C4×Dic711yescharacteristic
309C22×C4C4×Dic711yescharacteristic
310C22×C4C4×Dic711yescharacteristic
311C22×C4C2×C4×D711yescharacteristic
312C22×C4#115711yescharacteristic
313C22×C4#115711yescharacteristic
314C22×C4C22×Dic711yescharacteristic
315C22×C4C2×C22⋊D711yescharacteristic
316C22×C4C2×C22⋊D711yescharacteristic
317M16—42no—
318M16—42no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—142no—
330C2×C8—142no—
331C2×C8—281no—
332C2×C8—281no—
333C2×C8—281no—
334C2×C8—281no—
335C2×C8C22⋊Dic711yescharacteristic
336C2×C8C22⋊Dic711yescharacteristic
337C2×C8C22⋊Dic711yescharacteristic
338C2×C8C22⋊Dic711yescharacteristic
339C4⋊C4—21no—
340C4⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C22⋊C4—74no—
346C22⋊C4—142no—
347C22⋊C4—142no—
348C22⋊C4—142no—
349C42—21no—
350C42—21no—
351C42—281no—
352C42—281no—
353C42—281no—
354C42—281no—
355C2×C7—22no—
356C2×C7—22no—
357C2×C7—21no—
358C2×C7—21no—
359C2×C7—81no—
360C2×C7#175311yescharacteristic
361C2×C7C4×#9911yescharacteristic
362C2×C7#175711yescharacteristic
363C23—21no—
364C23—21no—
365C23—21no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23D7×M1612yes—
371C23#647012yes—
372C23C2×C4×Dic711yescharacteristic
373C23C4×C22⋊D711yescharacteristic
374C23C4×C22⋊D711yescharacteristic
375D4—42no—
376D4—42no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—144no—
397C2×C4—282no—
398C2×C4—282no—
399C2×C4—282no—
400C2×C4—282no—
401C2×C4—282no—
402C2×C4#648911yescharacteristic
403C2×C4C4×C22⋊D711yescharacteristic
404C2×C4C4×C22⋊D711yescharacteristic
405C2×C4C2×C22⋊Dic711yescharacteristic
406C8—21no—
407C8—21no—
408C8—21no—
409C8—41no—
410C8—41no—
411C8—282no—
412C8—282no—
413C8#640812yescomplemented
414C7#816111yescharacteristic, complemented, Sylow
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—81no—
427C22—81no—
428C22M16×Dic711yescharacteristic
429C22#8989411yescharacteristic
430C22#8989912yes—
431C22#8990012yes—
432C22C4×C22⋊Dic711yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—284no—
440C4—562no—
441C4C2×#640811yescharacteristic
442C4#9001211yescharacteristic
443C2—22no—
444C2—22no—
445C2—21no—
446C2—21no—
447C2—81no—
448C2C4×#640811yescharacteristic
449C2#1172973711yescharacteristic
450C2#1172976511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic7
commutatorC23×C7C2×C42
FrattiniC23×C4C22×D7
FittingC2×C7×#435C2
socleC22×C7C4×C22⋊C4
prime radicalC22×C7×D4C2×C4
cosocleC23×C4×C7C23
hypercenterC2×#435D7
hypocenterC7#8161
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #11729721C2semidirect
3. C8×C22⋊Dic7C2semidirect
6. #11725483C2semidirect
7. #11725483C2semidirect
8. C22×C7×M16C4semidirect
15. C2×C7×C4⋊C8C4semidirect
16. C2×C7×C22⋊C8C4semidirect
18. C2×C7×#97C4semidirect
28. #89323C4semidirect
30. #89320C4semidirect
135. C22⋊Dic7M16semidirect
146. C22×M16Dic7semidirect
153. C2×C4⋊C8Dic7semidirect
157. C2×C22⋊C8Dic7semidirect
160. C2×#97Dic7semidirect
217. C7×C8#99semidirect
413. C8#6408semidirect
414. C7#8161semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4352
#117297212
C8×C22⋊Dic72
C4×#64082
#117293542
#117254832
#81617