Finite Group Databasebeta

← #13249745

Subgroups — #13249745

Order 1792.

548 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2357C211yesmaximal, characteristic, complemented
2#11739752C211yesmaximal, characteristic
3#11729351C211yesmaximal, characteristic, complemented
4#11727299C211yesmaximal, characteristic, complemented
5#11727223C211yesmaximal, characteristic, complemented
6#11725437C211yesmaximal, characteristic, complemented
7#11725426C211yesmaximal, characteristic, complemented
8C2×C4×C7×D4C2211yescharacteristic
9C2×#6495—21no—
10#90168C2211yescharacteristic
11C7×#390—21no—
12C7×#388—22no—
13C7×#382C2211yescharacteristic
14C7×#381—21no—
15C4×C7×C4⋊C4—21no—
16C4×C7×C4⋊C4C2211yescharacteristic
17C4×C7×C22⋊C4—21no—
18#89791C412yescomplemented
19#89788—22no—
20#89787C412yescomplemented
21#89738—21no—
22#89697C2211yescharacteristic
23#89697C2211yescharacteristic
24#89696C2211yescharacteristic
25D4⋊(C7⋊C8)—22no—
26#89246—21no—
27#89246—21no—
28#89246—22no—
29#9181—71nomaximal, Sylow
30C22×C7×D4D411yescharacteristic
31C23×C4×C7—21no—
32C2×#1157—21no—
33C4×C7×D4—21no—
34C4×C7×D4—21no—
35C4×C7×D4C2×C412yes—
36C4×C7×D4D412yes—
37C2×C7×C4⋊C4—21no—
38C2×C7×C4⋊C4—21no—
39C2×C7×C4⋊C4D411yescharacteristic
40C2×C7×C22⋊C4—21no—
41C2×C7×C22⋊C4—22no—
42C2×C7×C22⋊C4—22no—
43C2×C42×C7—21no—
44C2×C42×C7—22no—
45C2×C42×C7C2311yescharacteristic
46C2×#1142—22no—
47#6495—42no—
48#6495—42no—
49C2×#1141—22no—
50#6493—21no—
51#6493—21no—
52C2×#1136—21no—
53#6438—21no—
54#6437C2×C411yescharacteristic
55C4×D28—21no—
56C4×D28—21no—
57#6432C2×C411yescharacteristic
58C7×#95—22no—
59C7×#95—21no—
60C7×#95D411yescharacteristic
61C7×#95D411yescharacteristic
62C7×#95D412yes—
63C22⋊(C7⋊C8)—21no—
64C22⋊(C7⋊C8)—21no—
65#6384—22no—
66#6383—22no—
67C4⋊(C7⋊C8)—21no—
68C4⋊(C7⋊C8)—21no—
69C4⋊(C7⋊C8)—21no—
70C4⋊(C7⋊C8)C2×C412yes—
71C4×C7⋊C8—21no—
72C4×C7⋊C8—21no—
73#3036—71no—
74#2357D711yescharacteristic, complemented
75#1517—71no—
76#1502—71no—
77#1478—71no—
78#1303—71no—
79#1286—71no—
80C24×C7—21no—
81C2×C7×D4—21no—
82C2×C7×D4—21no—
83C2×C7×D4—21no—
84C2×C7×D4—21no—
85C2×C7×D4—21no—
86C2×C7×D4C22⋊C412yes—
87C22×C4×C7—21no—
88C22×C4×C7—21no—
89C22×C4×C7—22no—
90C22×C4×C7—22no—
91C22×C4×C7—22no—
92C22×C4×C7—21no—
93C22×C4×C7—82no—
94C22×C4×C7C2×D411yescharacteristic
95C22×C4×C7C2×D411yescharacteristic
96C22×C4×C7C2×D411yescharacteristic
97C2×C22⋊D7—41no—
98#1157—41no—
99#1157—41no—
100#1157—41no—
101#1157—41no—
102C2×D28—21no—
103C2×D28—21no—
104C2×D28—21no—
105C2×C4×D7—41no—
106C2×Dic14—21no—
107C7×C4⋊C4—21no—
108C7×C4⋊C4—42no—
109C7×C4⋊C4—41no—
110C7×C4⋊C4—41no—
111C7×C4⋊C4C22⋊C412yes—
112C7×C22⋊C4—22no—
113C7×C22⋊C4—22no—
114C7×C22⋊C4—44no—
115C7×C22⋊C4—82no—
116C42×C7—41no—
117C42×C7—41no—
118C42×C7—82no—
119C42×C7C22×C411yescharacteristic
120C42×C7C2×D411yescharacteristic
121C42×C7#4111yescharacteristic
122C42×C7#4111yescharacteristic
123#1142—44no—
124#1141—44no—
125(C2×D7)⋊C4—41no—
126(C2×D7)⋊C4—41no—
127C4⋊Dic7—21no—
128C4⋊Dic7—21no—
129#1136—41no—
130#1136—41no—
131C2×C7⋊C8—22no—
132C2×C7⋊C8—41no—
133C2×C7⋊C8—41no—
134C2×AGL(1,ℤ/8)—141no—
135#532—71no—
136C2×C4×D4C2×D711yescharacteristic
137#463—142no—
138#461—72no—
139#459—72no—
140#431—71no—
141#431—71no—
142#423—71no—
143#417—141no—
144#390—21no—
145#388—22no—
146#382C2×D711yescharacteristic
147#381—21no—
148C4×C4⋊C4—21no—
149C4×C4⋊C4C2×D711yescharacteristic
150C4×C22⋊C4—21no—
151#327—141no—
152#327—141no—
153#327—142no—
154D4⋊C8—142no—
155C23×C7—22no—
156C23×C7—42no—
157C23×C7—42no—
158C23×C7—41no—
159C23×C7—41no—
160C23×C7#12011yescharacteristic
161C22×D7—41no—
162C7×D4—22no—
163C7×D4—22no—
164C7×D4—41no—
165C7×D4—41no—
166C2×C4×C7—22no—
167C2×C4×C7—22no—
168C2×C4×C7—41no—
169C2×C4×C7—41no—
170C2×C4×C7—41no—
171C2×C4×C7—42no—
172C2×C4×C7—41no—
173C2×C4×C7—42no—
174C2×C4×C7—42no—
175C2×C4×C7—41no—
176C2×C4×C7—41no—
177C2×C4×C7—41no—
178C2×C4×C7—42no—
179C2×C4×C7—82no—
180C2×C4×C7—82no—
181C2×C4×C7C2×C22⋊C411yescharacteristic
182C2×C4×C7C4×D411yescharacteristic
183C2×C4×C7C4×D411yescharacteristic
184C2×C4×C7#12111yescharacteristic
185C2×C4×C7#12111yescharacteristic
186C2×C4×C7#12311yescharacteristic
187C2×C4×C7#13511yescharacteristic
188C2×C4×C7#13511yescharacteristic
189C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
191C22⋊D7—81no—
192C22⋊D7—81no—
193C2×Dic7—41no—
194D28—41no—
195D28—41no—
196D28—81no—
197D28—81no—
198C4×D7—81no—
199C4×D7—81no—
200Dic14—41no—
201Dic14—41no—
202C7⋊C8—42no—
203C7⋊C8—81no—
204C7⋊C8—81no—
205C2×#41—141no—
206C22×D4C22⋊D711yescharacteristic
207C23×C4—21no—
208AGL(1,ℤ/8)—282no—
209AGL(1,ℤ/8)—282no—
210C2×SD16—142no—
211C2×D8—142no—
212C2×M16—141no—
213C4⋊Q8—71no—
214#127—71no—
215#124—141no—
216#121—141no—
217#121—141no—
218C4×D4—21no—
219C4×D4—21no—
220C4×D4—141no—
221C4×D4—141no—
222C4×D4C4×D712yes—
223C4×D4D2812yes—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C22⋊D711yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C42—21no—
231C2×C42—22no—
232C2×C42C22×D711yescharacteristic
233C4⋊C8—72no—
234C4⋊C8—141no—
235C4⋊C8—141no—
236C4⋊C8—141no—
237#103—142no—
238#102—142no—
239C22⋊C8—141no—
240C22⋊C8—141no—
241C4×C8—141no—
242C4×C8—141no—
243#95—22no—
244#95—21no—
245#95C22⋊D711yescharacteristic
246#95C22⋊D711yescharacteristic
247#95C22⋊D712yes—
248C22×C7—21no—
249C22×C7—21no—
250C22×C7—42no—
251C22×C7—42no—
252C22×C7—42no—
253C22×C7—82no—
254C22×C7—82no—
255C22×C7#38611yescharacteristic
256C22×C7#44911yescharacteristic
257C22×C7#44911yescharacteristic
258C2×D7—81no—
259C2×D7—81no—
260C2×D7—81no—
261C4×C7—21no—
262C4×C7—21no—
263C4×C7—21no—
264C4×C7—21no—
265C4×C7—42no—
266C4×C7—42no—
267C4×C7—81no—
268C4×C7—82no—
269C4×C7#41611yescharacteristic
270C4×C7#41811yescharacteristic
271C4×C7#48211yescharacteristic
272C4×C7#48211yescharacteristic
273Dic7—81no—
274C24—21no—
275#41—281no—
276#41—281no—
277#41—281no—
278#41—281no—
279C2×Q8—141no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—141no—
286C2×D4—141no—
287C2×D4—141no—
288C2×D4—281no—
289C2×D4(C2×D7)⋊C412yes—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—82no—
297C22×C4—281no—
298C22×C4C2×C22⋊D711yescharacteristic
299C22×C4C2×C22⋊D711yescharacteristic
300C22×C4C2×C22⋊D711yescharacteristic
301SD16—284no—
302D8—284no—
303M16—281no—
304M16—281no—
305C2×C8—142no—
306C2×C8—281no—
307C2×C8—281no—
308C4⋊C4—21no—
309C4⋊C4—42no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—141no—
313C4⋊C4—141no—
314C4⋊C4(C2×D7)⋊C412yes—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—44no—
318C22⋊C4—82no—
319C22⋊C4—281no—
320C22⋊C4—281no—
321C42—41no—
322C42—41no—
323C42—82no—
324C42C2×C4×D711yescharacteristic
325C42C2×D2811yescharacteristic
326C42#115711yescharacteristic
327C42#115711yescharacteristic
328C2×C7—21no—
329C2×C7—21no—
330C2×C7—82no—
331C2×C7#187511yescharacteristic
332C2×C7#190411yescharacteristic
333C2×C7#190611yescharacteristic
334D7—161no—
335C23—22no—
336C23—42no—
337C23—42no—
338C23—41no—
339C23—41no—
340C23—281no—
341C23#651611yescharacteristic
342Q8—281no—
343Q8—281no—
344D4—22no—
345D4—22no—
346D4—41no—
347D4—41no—
348D4—281no—
349D4—281no—
350D4—561no—
351D4—561no—
352D4—561no—
353D4—561no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—281no—
370C2×C4—561no—
371C2×C4—561no—
372C2×C4C2×(C2×D7)⋊C411yescharacteristic
373C2×C4C4×C22⋊D711yescharacteristic
374C2×C4C4×C22⋊D711yescharacteristic
375C2×C4#649211yescharacteristic
376C2×C4#649311yescharacteristic
377C2×C4#649311yescharacteristic
378C2×C4#651211yescharacteristic
379C2×C4#651211yescharacteristic
380C2×C4#651311yescharacteristic
381C2×C4#651311yescharacteristic
382C8—282no—
383C8—561no—
384C8—561no—
385C7#918111yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—82no—
392C22—82no—
393C22—561no—
394C22—561no—
395C22—561no—
396C22#8998511yescharacteristic
397C22#9001011yescharacteristic
398C22#9001011yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C4—81no—
406C4—82no—
407C4—561no—
408C4#8977311yescharacteristic
409C4#8977411yescharacteristic
410C4#8977511yescharacteristic
411C4#8977511yescharacteristic
412C2—21no—
413C2—21no—
414C2—82no—
415C2—1121no—
416C2#1172934011yescharacteristic
417C2#1172939911yescharacteristic
418C2#1172940511yescharacteristic
subgroupG/H
centerC22#89985
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2357C2
socleC22×C7#386
prime radical#11739752C2
cosocleC2×C42×C7C23
hypercenter#2357D7
hypocenterC7#9181
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2357

Complements

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

NH ≅ G/Ntype
1. C7×#2357C2semidirect
3. #11729351C2semidirect
4. #11727299C2semidirect
5. #11727223C2semidirect
6. #11725437C2semidirect
7. #11725426C2semidirect
18. #89791C4semidirect
20. #89787C4semidirect
74. #2357D7semidirect
385. C7#9181semidirect

Maximal subgroups

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

subgroupindex
C7×#23572
#117397522
#117293512
#117272992
#117272232
#117254372
#117254262
#91817