Finite Group Databasebeta

← #13257180

Subgroups — #13257180

Order 1792.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740705C211yesmaximal, characteristic
2C7×#1956C211yesmaximal, characteristic, complemented
3C2×#89341C211yesmaximal, characteristic, complemented
4C2×#89254C211yesmaximal, characteristic
5#11727338C211yesmaximal, characteristic
6#11727322C211yesmaximal, characteristic, complemented
7#11725461C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×C4×D28C2211yescharacteristic
10C2×C7×#103—22no—
11C2×C4×C7×C8C2211yescharacteristic
12C7×#384C2211yescharacteristic
13#90003—22no—
14#89760—21no—
15#89759—21no—
16#89759—21no—
17#89749—21no—
18C2×#6383—21no—
19C2×#6382—21no—
20C4×C4⋊Dic7C2211yescharacteristic
21C2×C4⋊(C7⋊C8)C2211yescharacteristic
22C2×C4⋊(C7⋊C8)C2211yescharacteristic
23#89341—22no—
24#89324—21no—
25#89324—21no—
26#89254—22no—
27#10412—71nomaximal, Sylow
28C22×C7×Q8D412yes—
29C22×D28D411yescharacteristic
30C22×C4×D7—21no—
31C22×C7×C8—21no—
32C7×C4⋊Q8—21no—
33C7×C4⋊Q8—21no—
34C7×C4⋊Q8—21no—
35C7×C4⋊Q8—21no—
36C2×C7×C4⋊C4—21no—
37C2×C7×C4⋊C4—21no—
38C2×C7×C4⋊C4—21no—
39C2×C7×C4⋊C4—21no—
40C2×C7×C4⋊C4—21no—
41C2×C42×C7C2311yescharacteristic
42C2×(C2×D7)⋊C4—21no—
43C2×(C2×D7)⋊C4—22no—
44C2×(C2×D7)⋊C4—22no—
45C2×C4⋊Dic7D411yescharacteristic
46C2×C4⋊Dic7D411yescharacteristic
47C2×C4⋊Dic7D411yescharacteristic
48C2×C4×Dic7—21no—
49C22×C7⋊C8—21no—
50C22×C7⋊C8—21no—
51C4×D28—21no—
52C4×D28—21no—
53C4×D28—21no—
54C4×D28—21no—
55C7×#103—44no—
56C4×C7×C8—21no—
57C4×C7×C8—21no—
58C7⋊#95—22no—
59C7⋊#95—22no—
60C7⋊#95—21no—
61#6383—42no—
62#6382—42no—
63C4⋊(C7⋊C8)—21no—
64C4⋊(C7⋊C8)—21no—
65C4⋊(C7⋊C8)—21no—
66C4⋊(C7⋊C8)D412yes—
67#2563—71no—
68#1956D711yescharacteristic, complemented
69#1948—71no—
70#1802—71no—
71C2×#333—71no—
72C2×D4⋊C8—71no—
73#1279—71no—
74C23×D7—21no—
75C2×C7×Q8—22no—
76C2×C7×Q8—22no—
77C2×C7×Q8—42no—
78C2×C7×Q8—42no—
79C22×C4×C7—22no—
80C22×C4×C7—41no—
81C22×C4×C7C2×D411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C22×C4×C7C2×D411yescharacteristic
84C22×Dic7—21no—
85C22×Dic7—21no—
86C22×Dic7—21no—
87C2×D28—21no—
88C2×D28—21no—
89C2×D28—21no—
90C2×D28—21no—
91C2×D28—21no—
92C2×D28SD1612yes—
93C2×C4×D7—41no—
94C2×C4×D7—41no—
95C2×C4×D7—41no—
96C2×C4×D7—41no—
97C2×C4×D7—41no—
98C2×C4×D7—41no—
99C2×C7×C8—22no—
100C2×C7×C8—41no—
101C2×C7×C8—41no—
102C7×C4⋊C4—42no—
103C7×C4⋊C4—41no—
104C7×C4⋊C4—41no—
105C7×C4⋊C4—41no—
106C7×C4⋊C4—41no—
107C7×C4⋊C4—41no—
108C7×C4⋊C4—41no—
109C7×C4⋊C4—41no—
110C7×C4⋊C4—41no—
111C42×C7C2×D411yescharacteristic
112C42×C7#4111yescharacteristic
113C42×C7#4111yescharacteristic
114C42×C7#4111yescharacteristic
115(C2×D7)⋊C4—41no—
116(C2×D7)⋊C4—41no—
117(C2×D7)⋊C4—82no—
118(C2×D7)⋊C4—82no—
119C4⋊Dic7—21no—
120C4⋊Dic7—21no—
121C4⋊Dic7—21no—
122C4⋊Dic7—21no—
123C4⋊Dic7—21no—
124C4⋊Dic7—21no—
125C4×Dic7—41no—
126C4×Dic7—41no—
127C2×C7⋊C8—22no—
128C2×C7⋊C8—41no—
129C2×C7⋊C8—41no—
130C2×C7⋊C8—41no—
131C2×C7⋊C8—41no—
132C2×C7⋊C8—41no—
133C2×C4⋊Q8C2×D711yescharacteristic
134C2×C4×D4—71no—
135C2×#106—141no—
136C2×C4⋊C8—71no—
137C2×C4⋊C8—71no—
138C2×#103—22no—
139C2×#102—141no—
140C2×C4×C8C2×D711yescharacteristic
141#393—142no—
142#390—141no—
143#384C2×D711yescharacteristic
144#382—141no—
145#380—141no—
146#380—141no—
147C4×C4⋊C4—71no—
148#340—141no—
149#340—141no—
150#333—142no—
151D4⋊C8—142no—
152C23×C7#12011yescharacteristic
153C22×D7—22no—
154C22×D7—41no—
155C22×D7—41no—
156C22×D7—41no—
157C22×D7—41no—
158C22×D7—41no—
159C22×D7—41no—
160C7×Q8—44no—
161C7×Q8—82no—
162C2×C4×C7—21no—
163C2×C4×C7—21no—
164C2×C4×C7—42no—
165C2×C4×C7—42no—
166C2×C4×C7—42no—
167C2×C4×C7—81no—
168C2×C4×C7—81no—
169C2×C4×C7—81no—
170C2×C4×C7#12111yescharacteristic
171C2×C4×C7#12111yescharacteristic
172C2×C4×C7#12111yescharacteristic
173C2×C4×C7#12311yescharacteristic
174C2×C4×C7#12311yescharacteristic
175C2×C4×C7#12411yescharacteristic
176C2×C4×C7C2×SD1611yescharacteristic
177C2×C4×C7#13511yescharacteristic
178C2×C4×C7#13511yescharacteristic
179C2×C4×C7#13511yescharacteristic
180C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C7#13711yescharacteristic
182C2×C4×C7#13711yescharacteristic
183C2×C4×C7#13711yescharacteristic
184C2×Dic7—41no—
185C2×Dic7—41no—
186C2×Dic7—41no—
187C2×Dic7—41no—
188C2×Dic7—41no—
189C2×Dic7—41no—
190C2×Dic7—41no—
191C2×Dic7—41no—
192C2×Dic7—41no—
193D28—22no—
194D28—22no—
195D28—41no—
196D28—41no—
197C4×D7—81no—
198C4×D7—81no—
199C4×D7—81no—
200C4×D7—81no—
201C7×C8—42no—
202C7⋊C8—42no—
203C7⋊C8—81no—
204C22×Q8C22⋊D712yes—
205C22×D4—71no—
206C23×C4—141no—
207C22×C8—21no—
208C22×C8—141no—
209C22×C8—141no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4×D4—141no—
215C4×D4—141no—
216C4×D4—141no—
217C4×D4—141no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—71no—
224C2×C4⋊C4—71no—
225C2×C4⋊C4—71no—
226C2×C22⋊C4—141no—
227C2×C22⋊C4—142no—
228C2×C22⋊C4—142no—
229C2×C42—141no—
230C2×C42C22×D711yescharacteristic
231#106—282no—
232C4⋊C8—72no—
233C4⋊C8—141no—
234C4⋊C8—141no—
235C4⋊C8—141no—
236#103—44no—
237#102—282no—
238C4×C8—21no—
239C4×C8—21no—
240#95—142no—
241#95—142no—
242#95—141no—
243C22×C7#39411yescharacteristic
244C22×C7#44811yescharacteristic
245C22×C7#44911yescharacteristic
246C22×C7#45211yescharacteristic
247C22×C7#45211yescharacteristic
248C22×C7#45311yescharacteristic
249C22×C7#45511yescharacteristic
250C2×D7—42no—
251C2×D7—42no—
252C2×D7—42no—
253C2×D7—81no—
254C2×D7—81no—
255C2×D7—81no—
256C2×D7—81no—
257C4×C7—21no—
258C4×C7—21no—
259C4×C7—82no—
260C4×C7—161no—
261C4×C7#46311yescharacteristic
262C4×C7#46411yescharacteristic
263C4×C7#46511yescharacteristic
264C4×C7#47011yescharacteristic
265C4×C7#48311yescharacteristic
266C4×C7#48511yescharacteristic
267C4×C7#48811yescharacteristic
268C4×C7#48911yescharacteristic
269Dic7—81no—
270Dic7—81no—
271Dic7—81no—
272C24—141no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×D4—72no—
278C2×D4—141no—
279C2×D4—141no—
280C2×D4—141no—
281C2×D4—141no—
282C2×D4—141no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—141no—
286C22×C4—141no—
287C22×C4—141no—
288C22×C4—281no—
289C22×C4—281no—
290C22×C4—281no—
291C22×C4—281no—
292C22×C4—281no—
293C22×C4—281no—
294C22×C4D4×D711yescharacteristic
295C22×C4D4×D711yescharacteristic
296C22×C4C2×C22⋊D711yescharacteristic
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—142no—
301C2×C8—281no—
302C2×C8—281no—
303C2×C8—281no—
304C2×C8—281no—
305C2×C8—281no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—141no—
316C4⋊C4—141no—
317C4⋊C4—141no—
318C4⋊C4—141no—
319C4⋊C4—141no—
320C4⋊C4—141no—
321C22⋊C4—281no—
322C22⋊C4—281no—
323C22⋊C4—562no—
324C22⋊C4—562no—
325C42—281no—
326C42—281no—
327C42#115711yescharacteristic
328C42#115711yescharacteristic
329C42D4×D711yescharacteristic
330C42#115911yescharacteristic
331C2×C7#162211yescharacteristic
332C2×C7#163411yescharacteristic
333C2×C7#164311yescharacteristic
334C2×C7#164611yescharacteristic
335C2×C7#203511yescharacteristic
336C2×C7#203711yescharacteristic
337C2×C7#204211yescharacteristic
338D7—82no—
339C23—142no—
340C23—281no—
341C23—281no—
342C23—281no—
343C23—281no—
344C23—281no—
345C23—281no—
346C23#650011yescharacteristic
347Q8—44no—
348Q8—82no—
349D4—142no—
350D4—142no—
351D4—281no—
352D4—281no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—281no—
362C2×C4—281no—
363C2×C4—281no—
364C2×C4—281no—
365C2×C4—281no—
366C2×C4—281no—
367C2×C4—281no—
368C2×C4—281no—
369C2×C4—281no—
370C2×C4—561no—
371C2×C4—561no—
372C2×C4—561no—
373C2×C4—561no—
374C2×C4#644611yescharacteristic
375C2×C4#644711yescharacteristic
376C2×C4#644711yescharacteristic
377C2×C4#644811yescharacteristic
378C2×C4D7×SD1611yescharacteristic
379C2×C4#647711yescharacteristic
380C2×C4#647811yescharacteristic
381C2×C4#647911yescharacteristic
382C2×C4#648111yescharacteristic
383C2×C4#648111yescharacteristic
384C2×C4#648211yescharacteristic
385C2×C4#648211yescharacteristic
386C2×C4#649211yescharacteristic
387C2×C4#650211yescharacteristic
388C8—42no—
389C8—282no—
390C8—561no—
391C7#1041211yescharacteristic, complemented, Sylow
392C22—282no—
393C22—282no—
394C22—282no—
395C22—561no—
396C22—561no—
397C22—561no—
398C22—561no—
399C22#8973111yescharacteristic
400C22#8983311yescharacteristic
401C22#8984911yescharacteristic
402C22#8994211yescharacteristic
403C22#8994411yescharacteristic
404C22#8995911yescharacteristic
405C22#8995911yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—161no—
410C4—561no—
411C4—561no—
412C4—561no—
413C4#8956711yescharacteristic
414C4#8957011yescharacteristic
415C4#8957211yescharacteristic
416C4#8957711yescharacteristic
417C4#8957911yescharacteristic
418C4#8958611yescharacteristic
419C4#8958811yescharacteristic
420C4#8959111yescharacteristic
421C2—562no—
422C2#1172741911yescharacteristic
423C2#1172802811yescharacteristic
424C2#1172803311yescharacteristic
425C2#1172898411yescharacteristic
426C2#1172898511yescharacteristic
427C2#1172901811yescharacteristic
428C2#1172905811yescharacteristic
subgroupG/H
centerC23#6500
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1956C2
socleC23×C7#120
prime radicalC22×D28D4
hypercenter#1956D7
hypocenterC7#10412
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
2. C7×#1956C2semidirect
3. C2×#89341C2semidirect
6. #11727322C2semidirect
7. #11725461C2semidirect
68. #1956D7semidirect
391. C7#10412semidirect

Maximal subgroups

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

subgroupindex
#117407052
C7×#19562
C2×#893412
C2×#892542
#117273382
#117273222
#117254612
#104127