Finite Group Databasebeta

← #13252938

Subgroups — #13252938

Order 1792.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739522C211yesmaximal, characteristic
2C7×#1797C211yesmaximal, characteristic, complemented
3#11729288C211yesmaximal, characteristic, complemented
4C2×#89262C212yesmaximal, complemented
5C2×#89265C212yesmaximal
6C22×C42×C7C2211yescharacteristic
7C2×#6493C2211yescharacteristic
8C2×#6487C2211yescharacteristic
9C2×#6438C411yescharacteristic, complemented
10C2×C7×C4⋊C8—21no—
11C2×C7×C22⋊C8C2212yes—
12#89985—21no—
13#89985—21no—
14C2×C7⋊#95—21no—
15C2×C7⋊#95—21no—
16C2×C7⋊#95C2212yes—
17#89712—21no—
18#89712—21no—
19#89711C411yescharacteristic, complemented
20#89708C411yescharacteristic, complemented
21#89701C411yescharacteristic, complemented
22C7×#336—21no—
23#89265—24no—
24#89262—24no—
25#9716—71nomaximal, Sylow
26C23×C4×C7D411yescharacteristic
27C23×C4×C7D411yescharacteristic
28C23×C4×C7C2311yescharacteristic
29C22×C22⋊D7—21no—
30C23×Dic7—22no—
31C22×D28C2×C411yescharacteristic
32C22×Dic14C2×C411yescharacteristic
33C22×C7×C8—22no—
34C2×C42×C7—42no—
35C2×C42×C7C2×C411yescharacteristic
36C2×C42×C7C2×C411yescharacteristic
37C2×C42×C7D411yescharacteristic
38C2×C42×C7D411yescharacteristic
39C2×C22⋊Dic7—21no—
40#6493—22no—
41#6493—22no—
42C2×(C2×D7)⋊C4—21no—
43C2×(C2×D7)⋊C4—21no—
44C2×(C2×D7)⋊C4—21no—
45C2×(C2×D7)⋊C4—21no—
46C2×(C2×D7)⋊C4—21no—
47C2×C4⋊Dic7C2×C411yescharacteristic
48C2×C4⋊Dic7C2×C411yescharacteristic
49#6487—22no—
50#6487—22no—
51C2×Dic7⋊C4—21no—
52#6438—42no—
53C7×C4⋊C8—42no—
54C7×C22⋊C8—22no—
55C7×C22⋊C8—22no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C7⋊#95—21no—
59C7⋊#95—21no—
60C7⋊#95—22no—
61C7⋊#95—42no—
62C7⋊#95—42no—
63C7⋊#95D414yes—
64#2850—71no—
65#1797D711yescharacteristic, complemented
66C2×#328—72no—
67C2×#327—72no—
68#1434—71no—
69C24×C7C2×D411yescharacteristic
70C23×D7—21no—
71C22×C4×C7—22no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—22no—
75C22×C4×C7—41no—
76C22×C4×C7—41no—
77C22×C4×C7—41no—
78C22×C4×C7—41no—
79C22×C4×C7—41no—
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C22⋊C411yescharacteristic
83C22×C4×C7C22⋊C411yescharacteristic
84C22×C4×C7C22×C411yescharacteristic
85C22×C4×C7C2×D411yescharacteristic
86C22×C4×C7C2×D412yes—
87C22×C4×C7#4112yes—
88C2×C22⋊D7—42no—
89C2×C22⋊D7—42no—
90C2×C22⋊D7—41no—
91C2×C22⋊D7—41no—
92C22×Dic7—21no—
93C22×Dic7—21no—
94C22×Dic7—21no—
95C22×Dic7—24no—
96C22×Dic7—42no—
97C22×Dic7—42no—
98C22×Dic7—42no—
99C22×Dic7—42no—
100C22×Dic7—42no—
101C22×Dic7—42no—
102C2×D28—22no—
103C2×D28—41no—
104C2×D28—41no—
105C2×Dic14—22no—
106C2×Dic14—41no—
107C2×Dic14—41no—
108C2×C7×C8—42no—
109C2×C7×C8—42no—
110C2×C7×C8—42no—
111C42×C7—22no—
112C42×C7—22no—
113C42×C7—41no—
114C42×C7—41no—
115C22⋊Dic7—42no—
116(C2×D7)⋊C4—42no—
117(C2×D7)⋊C4—42no—
118(C2×D7)⋊C4—42no—
119(C2×D7)⋊C4—42no—
120(C2×D7)⋊C4—41no—
121(C2×D7)⋊C4—41no—
122C4⋊Dic7—22no—
123C4⋊Dic7—22no—
124Dic7⋊C4—41no—
125Dic7⋊C4—41no—
126C2×#124—71no—
127C2×C22⋊Q8—71no—
128C2×#121—71no—
129C22×C42C2×D711yescharacteristic
130C2×C4⋊C8—21no—
131C2×C22⋊C8C2×D712yes—
132#391—71no—
133#390—71no—
134#388—141no—
135#388—141no—
136#386—141no—
137#386—141no—
138#382—71no—
139C2×#95—72no—
140C2×#95—141no—
141C2×#95—141no—
142#336—21no—
143#328—144no—
144#327—144no—
145C23×C7—21no—
146C23×C7—21no—
147C23×C7—21no—
148C23×C7—21no—
149C23×C7C2×C22⋊C411yescharacteristic
150C23×C7#12112yes—
151C23×C7#13512yes—
152C23×C7AGL(1,ℤ/8)11yescharacteristic
153C23×C7#13711yescharacteristic
154C22×D7—41no—
155C22×D7—41no—
156C22×D7—41no—
157C22×D7—41no—
158C22×D7—41no—
159C22×D7—41no—
160C22×D7—41no—
161C2×C4×C7—21no—
162C2×C4×C7—21no—
163C2×C4×C7—21no—
164C2×C4×C7—21no—
165C2×C4×C7—21no—
166C2×C4×C7—21no—
167C2×C4×C7—21no—
168C2×C4×C7—21no—
169C2×C4×C7—21no—
170C2×C4×C7—21no—
171C2×C4×C7—21no—
172C2×C4×C7—21no—
173C2×C4×C7—21no—
174C2×C4×C7—21no—
175C2×C4×C7—21no—
176C2×C4×C7—42no—
177C2×C4×C7—42no—
178C2×C4×C7—44no—
179C2×C4×C7—42no—
180C2×C4×C7—42no—
181C2×C4×C7#9912yes—
182C2×C4×C7C4×D412yes—
183C2×C4×C7#12411yescharacteristic
184C2×C4×C7#12711yescharacteristic
185C22⋊D7—82no—
186C22⋊D7—82no—
187C2×Dic7—44no—
188C2×Dic7—44no—
189C2×Dic7—41no—
190C2×Dic7—41no—
191C2×Dic7—41no—
192C2×Dic7—41no—
193C2×Dic7—41no—
194C2×Dic7—41no—
195C2×Dic7—41no—
196C2×Dic7—41no—
197C2×Dic7—41no—
198C2×Dic7—44no—
199C2×Dic7—82no—
200C2×Dic7—82no—
201C2×Dic7—82no—
202C2×Dic7—82no—
203D28—82no—
204Dic14—82no—
205C7×C8—82no—
206C22×Q8—71no—
207C22×D4—71no—
208C22×D4—141no—
209C23×C4—142no—
210C23×C4D2811yescharacteristic
211C23×C4D2811yescharacteristic
212C23×C4C22×D711yescharacteristic
213C22×C8—22no—
214#124—282no—
215C22⋊Q8—142no—
216C22⋊Q8—142no—
217#121—142no—
218#121—142no—
219C2×C4⋊C4—71no—
220C2×C4⋊C4—71no—
221C2×C4⋊C4—141no—
222C2×C22⋊C4—141no—
223C2×C22⋊C4—141no—
224C2×C22⋊C4—141no—
225C2×C22⋊C4—141no—
226C2×C22⋊C4—141no—
227C2×C22⋊C4—141no—
228C2×C42—42no—
229C2×C42C4×D711yescharacteristic
230C2×C42C4×D711yescharacteristic
231C2×C42C22⋊D711yescharacteristic
232C2×C42C22⋊D711yescharacteristic
233C4⋊C8—42no—
234C22⋊C8—22no—
235C22⋊C8—22no—
236#95—74no—
237#95—141no—
238#95—141no—
239#95—141no—
240#95—141no—
241#95—142no—
242#95—282no—
243#95—282no—
244C22×C7—22no—
245C22×C7—22no—
246C22×C7—21no—
247C22×C7—21no—
248C22×C7—21no—
249C22×C7—21no—
250C22×C7—22no—
251C22×C7—22no—
252C22×C7#39011yescharacteristic
253C22×C7C2×#9911yescharacteristic
254C22×C7#41011yescharacteristic
255C22×C7#41611yescharacteristic
256C22×C7#41711yescharacteristic
257C22×C7#42111yescharacteristic
258C22×C7#42111yescharacteristic
259C22×C7#46312yes—
260C22×C7#46412yes—
261C2×D7—81no—
262C2×D7—81no—
263C2×D7—81no—
264C2×D7—81no—
265C2×D7—81no—
266C2×D7—81no—
267C2×D7—81no—
268C4×C7—21no—
269C4×C7—22no—
270C4×C7—21no—
271C4×C7—22no—
272C4×C7—41no—
273C4×C7—41no—
274C4×C7—41no—
275Dic7—84no—
276Dic7—81no—
277Dic7—81no—
278Dic7—81no—
279C24—141no—
280C24C2×D2811yescharacteristic
281C2×Q8—142no—
282C2×Q8—281no—
283C2×Q8—281no—
284C2×D4—142no—
285C2×D4—281no—
286C2×D4—281no—
287C2×D4—282no—
288C2×D4—282no—
289C2×D4—281no—
290C2×D4—281no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—144no—
301C22×C4—141no—
302C22×C4—141no—
303C22×C4—141no—
304C22×C4—282no—
305C22×C4—282no—
306C22×C4—282no—
307C22×C4—282no—
308C22×C4—282no—
309C22×C4—282no—
310C22×C4(C2×D7)⋊C411yescharacteristic
311C22×C4(C2×D7)⋊C411yescharacteristic
312C22×C4(C2×D7)⋊C411yescharacteristic
313C22×C4(C2×D7)⋊C411yescharacteristic
314C22×C4C2×C4×D711yescharacteristic
315C22×C4D4×D712yes—
316C22×C4#116112yes—
317C22×C4C2×C22⋊D711yescharacteristic
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C4⋊C4—142no—
322C4⋊C4—142no—
323C4⋊C4—281no—
324C4⋊C4—281no—
325C22⋊C4—282no—
326C22⋊C4—282no—
327C22⋊C4—282no—
328C22⋊C4—282no—
329C22⋊C4—281no—
330C22⋊C4—281no—
331C22⋊C4—282no—
332C42—22no—
333C42—22no—
334C42—41no—
335C42—41no—
336C2×C7—22no—
337C2×C7—22no—
338C2×C7#151211yescharacteristic
339C2×C7#151311yescharacteristic
340C2×C7#151611yescharacteristic
341C2×C7#152111yescharacteristic
342C2×C7#196311yescharacteristic
343C2×C7#196411yescharacteristic
344C2×C7#198311yescharacteristic
345D7—161no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—281no—
351C23—281no—
352C23—281no—
353C23—281no—
354C23—281no—
355C23—281no—
356C23—281no—
357C23#645812yes—
358C23#646712yes—
359C23#647111yescharacteristic
360C23#647211yescharacteristic
361C23C2×(C2×D7)⋊C411yescharacteristic
362Q8—562no—
363D4—562no—
364D4—562no—
365D4—562no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—44no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—284no—
387C2×C4—284no—
388C2×C4—284no—
389C2×C4—281no—
390C2×C4—281no—
391C2×C4—281no—
392C2×C4—281no—
393C2×C4—281no—
394C2×C4—281no—
395C2×C4—281no—
396C2×C4—281no—
397C2×C4—281no—
398C2×C4—562no—
399C2×C4—562no—
400C2×C4—562no—
401C2×C4—562no—
402C2×C4#638012yes—
403C2×C4#645612yes—
404C2×C4#650311yescharacteristic
405C2×C4#651011yescharacteristic
406C8—82no—
407C7#971611yescharacteristic, complemented, Sylow
408C22—22no—
409C22—21no—
410C22—21no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—21no—
415C22—21no—
416C22—561no—
417C22—561no—
418C22—561no—
419C22—561no—
420C22—561no—
421C22—561no—
422C22—561no—
423C22#8961612yes—
424C22#8961712yes—
425C22C2×#638011yescharacteristic
426C22#8976011yescharacteristic
427C22#8977811yescharacteristic
428C22#8988511yescharacteristic
429C22#8990511yescharacteristic
430C22#8991111yescharacteristic
431C22#8991111yescharacteristic
432C4—22no—
433C4—21no—
434C4—22no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—564no—
440C4—561no—
441C4—561no—
442C4—561no—
443C2—22no—
444C2—22no—
445C2—1121no—
446C2#1172728211yescharacteristic
447C2#1172769711yescharacteristic
448C2#1172773311yescharacteristic
449C2#1172821211yescharacteristic
450C2#1172826711yescharacteristic
451C2#1172854511yescharacteristic
452C2#1172858811yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1797C2
socleC23×C7C2×C22⋊C4
prime radicalC2×#6493C22
cosocleC23×C4×C7C23
hypercenter#1797D7
hypocenterC7#9716
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C7×#1797C2semidirect
3. #11729288C2semidirect
4. C2×#89262C2semidirect
9. C2×#6438C4semidirect
19. #89711C4semidirect
20. #89708C4semidirect
21. #89701C4semidirect
65. #1797D7semidirect
407. C7#9716semidirect

Maximal subgroups

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

subgroupindex
#117395222
C7×#17972
#117292882
C2×#892622
C2×#892652
#97167