Finite Group Databasebeta

← #13257169

Subgroups — #13257169

Order 1792.

572 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#11739921C211yesmaximal, characteristic
2C2×C7×Q8⋊C8C211yesmaximal, characteristic, complemented
3#11729380C211yesmaximal, characteristic, complemented
4#11728208C211yesmaximal, characteristic, complemented
5C2×#89280C211yesmaximal, characteristic
6#11727526C211yesmaximal, characteristic
7#11725461C211yesmaximal, characteristic, complemented
8C2×C4×C7×Q8C2211yescharacteristic
9C2×#6510—21no—
10C2×#6437C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12C2×C4×C7×C8C2211yescharacteristic
13C2×#6409—21no—
14C2×#6395—22no—
15C2×#6391—21no—
16#89763—22no—
17#89760—21no—
18#89711—21no—
19#89711—21no—
20#89707C2211yescharacteristic
21C4×C4⋊Dic7C2211yescharacteristic
22C2×C4⋊(C7⋊C8)C2211yescharacteristic
23C7×Q8⋊C8—22no—
24#89346—21no—
25#89324—21no—
26#89280—22no—
27#10410—71nomaximal, Sylow
28C22×C7×Q8D411yescharacteristic
29C22×D28—21no—
30C22×D28—21no—
31C22×D28D412yes—
32C22×C7×C8—21no—
33C22×C7×C8—21no—
34C4×C7×Q8—21no—
35C4×C7×Q8—21no—
36C4×C7×Q8—21no—
37C4×C7×Q8—21no—
38C2×C7×C4⋊C4—21no—
39C2×C7×C4⋊C4D411yescharacteristic
40C2×C42×C7—21no—
41C2×C42×C7C2311yescharacteristic
42#6510—42no—
43#6510—42no—
44C2×(C2×D7)⋊C4—22no—
45C2×(C2×D7)⋊C4—22no—
46C2×(C2×D7)⋊C4—22no—
47C2×(C2×D7)⋊C4—22no—
48C2×C4⋊Dic7—21no—
49C2×C4⋊Dic7—21no—
50C2×C4⋊Dic7—21no—
51C2×C4⋊Dic7D411yescharacteristic
52C2×C4⋊Dic7D411yescharacteristic
53C2×C4×Dic7—21no—
54C22×C7⋊C8—21no—
55#6437—21no—
56#6437—21no—
57#6437—21no—
58#6437—21no—
59C7×C4⋊C8—21no—
60C7×C4⋊C8D412yes—
61C4×C7×C8—21no—
62C4×C7×C8—21no—
63#6409—42no—
64C7⋊#95—21no—
65#6395—44no—
66#6391—42no—
67C4⋊(C7⋊C8)—21no—
68C4⋊(C7⋊C8)—21no—
69#2548—71no—
70#1957—71no—
71#1948—71no—
72#1803—71no—
73C2×#331—71no—
74C2×Q8⋊C8D711yescharacteristic, complemented
75#1279—71no—
76C23×D7—22no—
77C2×C7×Q8—21no—
78C2×C7×Q8—21no—
79C2×C7×Q8—21no—
80C2×C7×Q8—21no—
81C2×C7×Q8—21no—
82C2×C7×Q8SD1612yes—
83C22×C4×C7—21no—
84C22×C4×C7—21no—
85C22×C4×C7C2×D411yescharacteristic
86C22×C4×C7C2×D411yescharacteristic
87C22×C4×C7C2×D411yescharacteristic
88C22×Dic7—21no—
89C22×Dic7—21no—
90C22×Dic7—41no—
91C2×D28—22no—
92C2×D28—22no—
93C2×D28—42no—
94C2×D28—42no—
95C2×D28—41no—
96C2×D28—41no—
97C2×D28—41no—
98C2×D28—41no—
99C2×D28—41no—
100C2×D28—41no—
101C2×D28—41no—
102C2×D28—41no—
103C2×D28—41no—
104C2×D28—41no—
105C2×D28—41no—
106C2×D28—41no—
107C2×C7×C8—22no—
108C2×C7×C8—22no—
109C2×C7×C8—41no—
110C2×C7×C8—41no—
111C2×C7×C8—41no—
112C2×C7×C8—41no—
113C7×C4⋊C4—21no—
114C7×C4⋊C4—21no—
115C7×C4⋊C4—41no—
116C7×C4⋊C4—41no—
117C42×C7—41no—
118C42×C7—41no—
119C42×C7C2×D411yescharacteristic
120C42×C7#4111yescharacteristic
121C42×C7#4111yescharacteristic
122C42×C7#4111yescharacteristic
123(C2×D7)⋊C4—44no—
124(C2×D7)⋊C4—44no—
125(C2×D7)⋊C4—82no—
126(C2×D7)⋊C4—82no—
127C4⋊Dic7—21no—
128C4⋊Dic7—21no—
129C4⋊Dic7—21no—
130C4⋊Dic7—21no—
131C4⋊Dic7—42no—
132C4⋊Dic7—41no—
133C4⋊Dic7—41no—
134C4⋊Dic7—41no—
135C4⋊Dic7—41no—
136C4×Dic7—41no—
137C4×Dic7—41no—
138C2×C7⋊C8—41no—
139C2×C7⋊C8—41no—
140C2×C7⋊C8—41no—
141C2×#127—71no—
142C2×#124—141no—
143C2×C4×Q8C2×D711yescharacteristic
144C2×#106—141no—
145C2×C4⋊C8—71no—
146C2×C4⋊C8C2×D711yescharacteristic
147C2×#103—141no—
148C2×#102—142no—
149C2×C4×C8C2×D711yescharacteristic
150#394—142no—
151#390—141no—
152#390—141no—
153#390—141no—
154#384—71no—
155C4×C4⋊C4—71no—
156#340—141no—
157#340—141no—
158#331—142no—
159Q8⋊C8—22no—
160C23×C7#12011yescharacteristic
161C22×D7—42no—
162C22×D7—42no—
163C22×D7—42no—
164C22×D7—42no—
165C22×D7—42no—
166C22×D7—42no—
167C22×D7—42no—
168C7×Q8—22no—
169C7×Q8—22no—
170C7×Q8—41no—
171C7×Q8—41no—
172C2×C4×C7—21no—
173C2×C4×C7—21no—
174C2×C4×C7—22no—
175C2×C4×C7—41no—
176C2×C4×C7—41no—
177C2×C4×C7—41no—
178C2×C4×C7—41no—
179C2×C4×C7—41no—
180C2×C4×C7#12111yescharacteristic
181C2×C4×C7#12111yescharacteristic
182C2×C4×C7#12111yescharacteristic
183C2×C4×C7#12311yescharacteristic
184C2×C4×C7#12311yescharacteristic
185C2×C4×C7#12411yescharacteristic
186C2×C4×C7C2×SD1611yescharacteristic
187C2×C4×C7#13511yescharacteristic
188C2×C4×C7#13511yescharacteristic
189C2×C4×C7#13511yescharacteristic
190C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C7#13711yescharacteristic
194C2×Dic7—41no—
195C2×Dic7—41no—
196C2×Dic7—41no—
197C2×Dic7—41no—
198C2×Dic7—41no—
199C2×Dic7—41no—
200C2×Dic7—81no—
201C2×Dic7—81no—
202C2×Dic7—81no—
203D28—44no—
204D28—82no—
205D28—81no—
206D28—81no—
207D28—81no—
208D28—81no—
209D28—81no—
210D28—81no—
211D28—81no—
212D28—81no—
213C7×C8—42no—
214C7×C8—42no—
215C7⋊C8—81no—
216C22×Q8D2811yescharacteristic
217C22×D4—72no—
218C22×D4—141no—
219C22×D4—141no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—141no—
223#127—141no—
224#127—141no—
225#127—141no—
226#127—141no—
227#124—282no—
228#124—282no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—71no—
235C2×C4⋊C4—71no—
236C2×C4⋊C4—141no—
237C2×C4⋊C4—141no—
238C2×C4⋊C4—141no—
239C2×C4⋊C4D2811yescharacteristic
240C2×C22⋊C4—142no—
241C2×C22⋊C4—142no—
242C2×C22⋊C4—142no—
243C2×C22⋊C4—142no—
244C2×C42—21no—
245C2×C42—141no—
246C2×C42C22×D711yescharacteristic
247#106—282no—
248C4⋊C8—21no—
249C4⋊C8—141no—
250C4⋊C8—141no—
251C4⋊C8C22⋊D712yes—
252#103—282no—
253#102—284no—
254C4×C8—21no—
255C4×C8—21no—
256#95—141no—
257C22×C7#39411yescharacteristic
258C22×C7#44911yescharacteristic
259C22×C7#44911yescharacteristic
260C22×C7#45011yescharacteristic
261C22×C7#45211yescharacteristic
262C22×C7#45311yescharacteristic
263C22×C7#45511yescharacteristic
264C2×D7—82no—
265C2×D7—82no—
266C2×D7—82no—
267C2×D7—82no—
268C2×D7—82no—
269C2×D7—82no—
270C2×D7—82no—
271C4×C7—21no—
272C4×C7—21no—
273C4×C7—42no—
274C4×C7—81no—
275C4×C7#46311yescharacteristic
276C4×C7#46411yescharacteristic
277C4×C7#46511yescharacteristic
278C4×C7#46911yescharacteristic
279C4×C7#48111yescharacteristic
280C4×C7#48211yescharacteristic
281C4×C7#48811yescharacteristic
282C4×C7#48911yescharacteristic
283Dic7—81no—
284Dic7—81no—
285Dic7—161no—
286C24—142no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8#113212yes—
293C2×D4—142no—
294C2×D4—142no—
295C2×D4—282no—
296C2×D4—282no—
297C2×D4—281no—
298C2×D4—281no—
299C2×D4—281no—
300C2×D4—281no—
301C2×D4—281no—
302C2×D4—281no—
303C2×D4—281no—
304C2×D4—281no—
305C2×D4—281no—
306C2×D4—281no—
307C2×D4—281no—
308C2×D4—281no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—141no—
312C22×C4—141no—
313C22×C4—281no—
314C22×C4C2×D2811yescharacteristic
315C22×C4D4×D711yescharacteristic
316C22×C4D4×D711yescharacteristic
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—281no—
324C2×C8—281no—
325C2×C8—281no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—141no—
331C4⋊C4—141no—
332C4⋊C4—141no—
333C4⋊C4—141no—
334C4⋊C4—282no—
335C4⋊C4—281no—
336C4⋊C4—281no—
337C4⋊C4—281no—
338C4⋊C4—281no—
339C22⋊C4—284no—
340C22⋊C4—284no—
341C22⋊C4—562no—
342C22⋊C4—562no—
343C42—41no—
344C42—41no—
345C42—281no—
346C42—281no—
347C42#115711yescharacteristic
348C42#115911yescharacteristic
349C42#115911yescharacteristic
350C42C2×C22⋊D711yescharacteristic
351C2×C7#162011yescharacteristic
352C2×C7#163111yescharacteristic
353C2×C7#164011yescharacteristic
354C2×C7#164211yescharacteristic
355C2×C7#203411yescharacteristic
356C2×C7#203711yescharacteristic
357C2×C7#204211yescharacteristic
358D7—162no—
359C23—282no—
360C23—282no—
361C23—282no—
362C23—282no—
363C23—282no—
364C23—282no—
365C23—282no—
366C23#644511yescharacteristic
367Q8—22no—
368Q8—22no—
369Q8—41no—
370Q8—41no—
371D4—284no—
372D4—562no—
373D4—561no—
374D4—561no—
375D4—561no—
376D4—561no—
377D4—561no—
378D4—561no—
379D4—561no—
380D4—561no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—281no—
390C2×C4—281no—
391C2×C4—281no—
392C2×C4—281no—
393C2×C4—281no—
394C2×C4—281no—
395C2×C4—561no—
396C2×C4—561no—
397C2×C4—561no—
398C2×C4#644611yescharacteristic
399C2×C4#644811yescharacteristic
400C2×C4#644911yescharacteristic
401C2×C4C2×#113211yescharacteristic
402C2×C4#646711yescharacteristic
403C2×C4#647111yescharacteristic
404C2×C4#647111yescharacteristic
405C2×C4#647711yescharacteristic
406C2×C4#647911yescharacteristic
407C2×C4#648111yescharacteristic
408C2×C4#648211yescharacteristic
409C2×C4#649311yescharacteristic
410C2×C4#650111yescharacteristic
411C2×C4#650211yescharacteristic
412C8—42no—
413C8—42no—
414C8—561no—
415C7#1041011yescharacteristic, complemented, Sylow
416C22—562no—
417C22—562no—
418C22—562no—
419C22—562no—
420C22—562no—
421C22—562no—
422C22—562no—
423C22#8950311yescharacteristic
424C22#8950611yescharacteristic
425C22#8958211yescharacteristic
426C22#8958311yescharacteristic
427C22#8959411yescharacteristic
428C22#8959711yescharacteristic
429C22#8973311yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—561no—
435C4—561no—
436C4—1121no—
437C4#8950711yescharacteristic
438C4#8950911yescharacteristic
439C4#8956711yescharacteristic
440C4#8957211yescharacteristic
441C4#8988611yescharacteristic
442C4#8990711yescharacteristic
443C4#8993711yescharacteristic
444C4#8995711yescharacteristic
445C2—1122no—
446C2#1172600211yescharacteristic
447C2#1172601211yescharacteristic
448C2#1172601511yescharacteristic
449C2#1172601611yescharacteristic
450C2#1172768911yescharacteristic
451C2#1172799911yescharacteristic
452C2#1172811311yescharacteristic
subgroupG/H
centerC23#6445
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC2×C7×Q8⋊C8C2
socleC23×C7#120
prime radicalC2×#6437C22
hypercenterC2×Q8⋊C8D7
hypocenterC7#10410
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C7×Q8⋊C8C2semidirect
3. #11729380C2semidirect
4. #11728208C2semidirect
7. #11725461C2semidirect
74. C2×Q8⋊C8D7semidirect
415. C7#10410semidirect

Maximal subgroups

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

subgroupindex
#117399212
C2×C7×Q8⋊C82
#117293802
#117282082
C2×#892802
#117275262
#117254612
#104107