Finite Group Databasebeta

← #13252927

Subgroups — #13252927

Order 1792.

742 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739522C211yesmaximal, characteristic
2C4×C7×#95C211yesmaximal, characteristic, complemented
3#11729284C211yesmaximal, characteristic, complemented
4C2×#89247C212yesmaximal, complemented
5C2×#89246C212yesmaximal
6C22×C42×C7—21no—
7C22×C42×C7C2211yescharacteristic
8C2×#6493C2211yescharacteristic
9C2×#6487C2211yescharacteristic
10C2×#6438C411yescharacteristic, complemented
11C2×C7×#95—21no—
12C2×C7×#95C2212yes—
13#89985—21no—
14#89985—21no—
15C2×C22⋊(C7⋊C8)C2212yes—
16#89712—21no—
17#89712—21no—
18#89711C411yescharacteristic, complemented
19#89708C411yescharacteristic, complemented
20#89701C411yescharacteristic, complemented
21C2×C4⋊(C7⋊C8)—21no—
22#89319—21no—
23#89247—24no—
24#89246—24no—
25#9713—71nomaximal, Sylow
26C23×C4×C7—22no—
27C23×C4×C7D411yescharacteristic
28C23×C4×C7D411yescharacteristic
29C23×C4×C7C2311yescharacteristic
30C22×C22⋊D7—21no—
31C22×D28C2×C411yescharacteristic
32C22×Dic14C2×C411yescharacteristic
33C2×C42×C7—24no—
34C2×C42×C7—42no—
35C2×C42×C7—42no—
36C2×C42×C7—42no—
37C2×C42×C7C2×C411yescharacteristic
38C2×C42×C7C2×C411yescharacteristic
39C2×C42×C7D411yescharacteristic
40C2×C42×C7D411yescharacteristic
41C2×C22⋊Dic7—21no—
42#6493—22no—
43#6493—22no—
44C2×(C2×D7)⋊C4—21no—
45C2×(C2×D7)⋊C4—21no—
46C2×(C2×D7)⋊C4—21no—
47C2×(C2×D7)⋊C4—21no—
48C2×(C2×D7)⋊C4—21no—
49C2×C4⋊Dic7C2×C411yescharacteristic
50C2×C4⋊Dic7C2×C411yescharacteristic
51#6487—22no—
52#6487—22no—
53C2×Dic7⋊C4—21no—
54C22×C7⋊C8—22no—
55#6438—42no—
56C7×#95—24no—
57C7×#95—22no—
58C7×#95D414yes—
59C7⋊#95—21no—
60C7⋊#95—21no—
61C7⋊#95—21no—
62C7⋊#95—21no—
63C22⋊(C7⋊C8)—22no—
64C22⋊(C7⋊C8)—22no—
65C4⋊(C7⋊C8)—42no—
66#2850—71no—
67#1797—71no—
68C2×#328—72no—
69C2×#327—72no—
70C4×#95D711yescharacteristic, complemented
71C24×C7C2×D411yescharacteristic
72C23×D7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—22no—
76C22×C4×C7—22no—
77C22×C4×C7—24no—
78C22×C4×C7—24no—
79C22×C4×C7—24no—
80C22×C4×C7—22no—
81C22×C4×C7—22no—
82C22×C4×C7—41no—
83C22×C4×C7—41no—
84C22×C4×C7—41no—
85C22×C4×C7—42no—
86C22×C4×C7—42no—
87C22×C4×C7—42no—
88C22×C4×C7—42no—
89C22×C4×C7C22⋊C411yescharacteristic
90C22×C4×C7C22⋊C411yescharacteristic
91C22×C4×C7C22⋊C411yescharacteristic
92C22×C4×C7C22⋊C411yescharacteristic
93C22×C4×C7C22×C411yescharacteristic
94C22×C4×C7C2×D411yescharacteristic
95C22×C4×C7C2×D412yes—
96C22×C4×C7#4112yes—
97C2×C22⋊D7—42no—
98C2×C22⋊D7—42no—
99C2×C22⋊D7—41no—
100C2×C22⋊D7—41no—
101C22×Dic7—21no—
102C22×Dic7—21no—
103C22×Dic7—21no—
104C2×D28—22no—
105C2×D28—41no—
106C2×D28—41no—
107C2×Dic14—22no—
108C2×Dic14—41no—
109C2×Dic14—41no—
110C42×C7—22no—
111C42×C7—22no—
112C42×C7—41no—
113C42×C7—41no—
114C42×C7—48no—
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×C7⋊C8—42no—
127C2×C7⋊C8—42no—
128C2×C7⋊C8—42no—
129C2×#124—71no—
130C2×C22⋊Q8—71no—
131C2×#121—71no—
132C22×C42—21no—
133C22×C42C2×D711yescharacteristic
134C2×C4⋊C8—141no—
135C2×C22⋊C8—72no—
136#391—71no—
137#390—71no—
138#388—141no—
139#388—141no—
140#386—141no—
141#386—141no—
142#382—71no—
143C2×#95—21no—
144C2×#95C2×D712yes—
145#336—141no—
146#328—144no—
147#327—144no—
148C23×C7—21no—
149C23×C7—21no—
150C23×C7—21no—
151C23×C7—21no—
152C23×C7C2×C22⋊C411yescharacteristic
153C23×C7#12112yes—
154C23×C7#13512yes—
155C23×C7AGL(1,ℤ/8)11yescharacteristic
156C23×C7#13711yescharacteristic
157C22×D7—41no—
158C22×D7—41no—
159C22×D7—41no—
160C22×D7—41no—
161C22×D7—41no—
162C22×D7—41no—
163C22×D7—41no—
164C2×C4×C7—24no—
165C2×C4×C7—24no—
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—28no—
177C2×C4×C7—21no—
178C2×C4×C7—21no—
179C2×C4×C7—21no—
180C2×C4×C7—42no—
181C2×C4×C7—42no—
182C2×C4×C7—44no—
183C2×C4×C7—44no—
184C2×C4×C7—44no—
185C2×C4×C7—44no—
186C2×C4×C7—44no—
187C2×C4×C7—44no—
188C2×C4×C7—44no—
189C2×C4×C7#9912yes—
190C2×C4×C7#10412yes—
191C2×C4×C7#10412yes—
192C2×C4×C7C4×D412yes—
193C2×C4×C7#12411yescharacteristic
194C2×C4×C7#12711yescharacteristic
195C22⋊D7—82no—
196C22⋊D7—82no—
197C2×Dic7—41no—
198C2×Dic7—41no—
199C2×Dic7—41no—
200C2×Dic7—41no—
201C2×Dic7—41no—
202C2×Dic7—41no—
203C2×Dic7—41no—
204C2×Dic7—41no—
205C2×Dic7—41no—
206D28—82no—
207Dic14—82no—
208C7⋊C8—82no—
209C22×Q8—71no—
210C22×D4—71no—
211C22×D4—141no—
212C23×C4—22no—
213C23×C4C22⋊D711yescharacteristic
214C23×C4C22⋊D711yescharacteristic
215C23×C4C22×D711yescharacteristic
216C22×C8—142no—
217#124—282no—
218C22⋊Q8—142no—
219C22⋊Q8—142no—
220#121—142no—
221#121—142no—
222C2×C4⋊C4—71no—
223C2×C4⋊C4—71no—
224C2×C4⋊C4—141no—
225C2×C22⋊C4—141no—
226C2×C22⋊C4—141no—
227C2×C22⋊C4—141no—
228C2×C22⋊C4—141no—
229C2×C22⋊C4—141no—
230C2×C22⋊C4—141no—
231C2×C42—24no—
232C2×C42—42no—
233C2×C42—42no—
234C2×C42—42no—
235C2×C42C4×D711yescharacteristic
236C2×C42C4×D711yescharacteristic
237C2×C42D2811yescharacteristic
238C2×C42D2811yescharacteristic
239C4⋊C8—282no—
240C22⋊C8—142no—
241C22⋊C8—142no—
242#95—24no—
243#95—22no—
244#95—141no—
245#95—141no—
246#95—141no—
247#95—141no—
248#95D2814yes—
249C22×C7—22no—
250C22×C7—22no—
251C22×C7—22no—
252C22×C7—22no—
253C22×C7—21no—
254C22×C7—21no—
255C22×C7—21no—
256C22×C7—21no—
257C22×C7#39011yescharacteristic
258C22×C7C2×#9911yescharacteristic
259C22×C7#41011yescharacteristic
260C22×C7#41611yescharacteristic
261C22×C7#41711yescharacteristic
262C22×C7C2×#10411yescharacteristic
263C22×C7C2×#10411yescharacteristic
264C22×C7#46312yes—
265C22×C7#46412yes—
266C2×D7—81no—
267C2×D7—81no—
268C2×D7—81no—
269C2×D7—81no—
270C2×D7—81no—
271C2×D7—81no—
272C2×D7—81no—
273C4×C7—21no—
274C4×C7—22no—
275C4×C7—21no—
276C4×C7—22no—
277C4×C7—22no—
278C4×C7—22no—
279C4×C7—48no—
280C4×C7—41no—
281Dic7—81no—
282Dic7—81no—
283Dic7—81no—
284C24—141no—
285C24C2×C22⋊D711yescharacteristic
286C2×Q8—142no—
287C2×Q8—281no—
288C2×Q8—281no—
289C2×D4—142no—
290C2×D4—281no—
291C2×D4—281no—
292C2×D4—282no—
293C2×D4—281no—
294C2×D4—281no—
295C2×D4—282no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—141no—
313C22×C4—141no—
314C22×C4—141no—
315C22×C4(C2×D7)⋊C411yescharacteristic
316C22×C4(C2×D7)⋊C411yescharacteristic
317C22×C4(C2×D7)⋊C411yescharacteristic
318C22×C4(C2×D7)⋊C411yescharacteristic
319C22×C4C2×C4×D711yescharacteristic
320C22×C4C2×D2811yescharacteristic
321C22×C4C2×D2812yes—
322C22×C4#115712yes—
323C2×C8—282no—
324C2×C8—282no—
325C2×C8—282no—
326C4⋊C4—142no—
327C4⋊C4—142no—
328C4⋊C4—281no—
329C4⋊C4—281no—
330C22⋊C4—282no—
331C22⋊C4—282no—
332C22⋊C4—281no—
333C22⋊C4—281no—
334C22⋊C4—282no—
335C22⋊C4—282no—
336C22⋊C4—282no—
337C42—22no—
338C42—22no—
339C42—41no—
340C42—41no—
341C42—48no—
342C2×C7—22no—
343C2×C7—22no—
344C2×C7#150011yescharacteristic
345C2×C7#150111yescharacteristic
346C2×C7#150411yescharacteristic
347C2×C7#150911yescharacteristic
348C2×C7#196211yescharacteristic
349C2×C7#196411yescharacteristic
350C2×C7#198311yescharacteristic
351D7—161no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—281no—
357C23—281no—
358C23—281no—
359C23—281no—
360C23—281no—
361C23—281no—
362C23—281no—
363C23C2×(C2×D7)⋊C411yescharacteristic
364C23#649312yes—
365C23#649511yescharacteristic
366C23#650511yescharacteristic
367C23#651312yes—
368Q8—562no—
369D4—562no—
370D4—562no—
371D4—562no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—28no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—281no—
398C2×C4—281no—
399C2×C4—281no—
400C2×C4—281no—
401C2×C4—281no—
402C2×C4—281no—
403C2×C4—281no—
404C2×C4—281no—
405C2×C4—281no—
406C2×C4#637912yes—
407C2×C4#637912yes—
408C2×C4#638012yes—
409C2×C4C4×D2812yes—
410C2×C4#643711yescharacteristic
411C2×C4#643811yescharacteristic
412C8—562no—
413C7#971311yescharacteristic, complemented, Sylow
414C22—22no—
415C22—21no—
416C22—21no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—21no—
421C22—21no—
422C22—561no—
423C22—561no—
424C22—561no—
425C22—561no—
426C22—561no—
427C22—561no—
428C22—561no—
429C22C2×#637911yescharacteristic
430C22C2×#637911yescharacteristic
431C22#8971111yescharacteristic
432C22C2×#638011yescharacteristic
433C22#8973811yescharacteristic
434C22#8977411yescharacteristic
435C22#8977811yescharacteristic
436C22#8978812yes—
437C22#8980012yes—
438C4—22no—
439C4—22no—
440C4—22no—
441C4—21no—
442C4—22no—
443C4—21no—
444C4—48no—
445C4—41no—
446C4—561no—
447C4—561no—
448C4—561no—
449C2—22no—
450C2—22no—
451C2—1121no—
452C2#1172714911yescharacteristic
453C2#1172715211yescharacteristic
454C2#1172718511yescharacteristic
455C2#1172719711yescharacteristic
456C2#1172721011yescharacteristic
457C2#1172722411yescharacteristic
458C2#1172724211yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC4×C7×#95C2
socleC23×C7C2×C22⋊C4
prime radicalC2×#6493C22
cosocleC23×C4×C7C23
hypercenterC4×#95D7
hypocenterC7#9713
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C4×C7×#95C2semidirect
3. #11729284C2semidirect
4. C2×#89247C2semidirect
10. C2×#6438C4semidirect
18. #89711C4semidirect
19. #89708C4semidirect
20. #89701C4semidirect
70. C4×#95D7semidirect
413. C7#9713semidirect

Maximal subgroups

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

subgroupindex
#117395222
C4×C7×#952
#117292842
C2×#892472
C2×#892462
#97137