Finite Group Databasebeta

← #13256145

Subgroups — #13256145

Order 1792.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739945C211yesmaximal, characteristic
2C2×#89793C211yesmaximal, characteristic, complemented
3C2×#89614C211yesmaximal, characteristic
4C2×C7×Q8⋊C8C211yesmaximal, characteristic, complemented
5#11727525C211yesmaximal, characteristic, complemented
6C2×#89254C211yesmaximal, characteristic
7#11725508C211yesmaximal, characteristic, complemented
8C2×C4×C7×Q8C2211yescharacteristic
9C2×#6509—21no—
10C2×C4×D28C2211yescharacteristic
11C2×#6432C2211yescharacteristic
12C2×C7×C4⋊C8C2211yescharacteristic
13C2×C4×C7×C8C2211yescharacteristic
14C2×#6409—21no—
15C2×#6395—21no—
16C2×#6391—21no—
17C2×#6390—22no—
18#89793—22no—
19#89793—22no—
20#89766—22no—
21#89759—21no—
22C2×#6381—21no—
23#89711—21no—
24#89707C2211yescharacteristic
25#89700—21no—
26C2×C4⋊(C7⋊C8)C2211yescharacteristic
27#89614—22no—
28#89614—22no—
29C7×Q8⋊C8—22no—
30#89254—22no—
31#10236—71nomaximal, Sylow
32C22×C7×Q8D411yescharacteristic
33C22×D28D411yescharacteristic
34C22×C4×D7—21no—
35C22×Dic14—21no—
36C22×C7×C8—21no—
37C22×C7×C8—21no—
38C4×C7×Q8—21no—
39C4×C7×Q8—21no—
40C4×C7×Q8—21no—
41C4×C7×Q8—21no—
42C2×C7×C4⋊C4—21no—
43C2×C7×C4⋊C4D411yescharacteristic
44C2×C42×C7—21no—
45C2×C42×C7C2311yescharacteristic
46#6509—42no—
47#6509—42no—
48C2×(C2×D7)⋊C4—22no—
49C2×(C2×D7)⋊C4—21no—
50C2×(C2×D7)⋊C4—22no—
51C2×C4⋊Dic7—21no—
52C2×C4⋊Dic7—21no—
53C2×C4⋊Dic7—21no—
54C2×C4⋊Dic7—21no—
55C2×C4⋊Dic7D411yescharacteristic
56C2×C4⋊Dic7D412yes—
57C2×Dic7⋊C4—22no—
58C22×C7⋊C8—21no—
59C4×D28—21no—
60C4×D28—21no—
61C4×D28—21no—
62C4×D28—21no—
63#6432—21no—
64#6432—21no—
65#6432—21no—
66#6432D412yes—
67C7×C4⋊C8—21no—
68C7×C4⋊C8D412yes—
69C4×C7×C8—21no—
70C4×C7×C8—21no—
71#6409—24no—
72C7⋊#95—22no—
73#6395—24no—
74#6391—24no—
75#6390—44no—
76#6381—24no—
77C4⋊(C7⋊C8)—21no—
78C4⋊(C7⋊C8)D412yes—
79C2×#477—71no—
80C2×#476—71no—
81#2538—71no—
82#1956—71no—
83C2×Q8⋊C8D711yescharacteristic, complemented
84C2×D4⋊C8—71no—
85#1296—71no—
86C23×D7—21no—
87C2×C7×Q8—21no—
88C2×C7×Q8—21no—
89C2×C7×Q8—21no—
90C2×C7×Q8—21no—
91C2×C7×Q8—21no—
92C2×C7×Q8SD1612yes—
93C22×C4×C7—21no—
94C22×C4×C7—21no—
95C22×C4×C7C2×D411yescharacteristic
96C22×C4×C7C2×D411yescharacteristic
97C22×C4×C7C2×D411yescharacteristic
98C22×Dic7—21no—
99C22×Dic7—22no—
100C22×Dic7—41no—
101C2×D28—21no—
102C2×D28—21no—
103C2×D28—21no—
104C2×D28—21no—
105C2×D28—21no—
106C2×D28Q1612yes—
107C2×C4×D7—41no—
108C2×C4×D7—41no—
109C2×C4×D7—41no—
110C2×C4×D7—41no—
111C2×C4×D7—41no—
112C2×C4×D7—41no—
113C2×Dic14—22no—
114C2×Dic14—42no—
115C2×Dic14—42no—
116C2×Dic14—41no—
117C2×C7×C8—22no—
118C2×C7×C8—22no—
119C2×C7×C8—41no—
120C2×C7×C8—41no—
121C2×C7×C8—41no—
122C2×C7×C8—41no—
123C7×C4⋊C4—21no—
124C7×C4⋊C4—21no—
125C7×C4⋊C4—41no—
126C7×C4⋊C4—41no—
127C42×C7—41no—
128C42×C7—41no—
129C42×C7C2×D411yescharacteristic
130C42×C7C2×D411yescharacteristic
131C42×C7C2×D411yescharacteristic
132C42×C7#4111yescharacteristic
133(C2×D7)⋊C4—44no—
134(C2×D7)⋊C4—41no—
135(C2×D7)⋊C4—41no—
136(C2×D7)⋊C4—82no—
137C4⋊Dic7—22no—
138C4⋊Dic7—22no—
139C4⋊Dic7—21no—
140C4⋊Dic7—21no—
141C4⋊Dic7—41no—
142C4⋊Dic7—41no—
143C4⋊Dic7—41no—
144C4⋊Dic7—41no—
145C4⋊Dic7—41no—
146C4⋊Dic7—41no—
147C4⋊Dic7—42no—
148Dic7⋊C4—44no—
149C2×C7⋊C8—22no—
150C2×C7⋊C8—41no—
151C2×C7⋊C8—41no—
152C2×C4⋊Q8—71no—
153C2×C22⋊Q8—141no—
154C2×C4×Q8C2×D711yescharacteristic
155C2×C4×D4—71no—
156#477—142no—
157#477—142no—
158#476—142no—
159#476—142no—
160C2×#107—141no—
161C2×#106—141no—
162C2×C4⋊C8—71no—
163C2×C4⋊C8C2×D711yescharacteristic
164C2×#103—141no—
165C2×#103—142no—
166C2×#102—141no—
167C2×C4×C8C2×D711yescharacteristic
168#396—142no—
169#390—141no—
170#389—141no—
171#384—71no—
172#380—141no—
173Q8⋊C8—22no—
174D4⋊C8—142no—
175C23×C7#12011yescharacteristic
176C22×D7—22no—
177C22×D7—41no—
178C22×D7—41no—
179C22×D7—41no—
180C22×D7—41no—
181C22×D7—41no—
182C22×D7—41no—
183C7×Q8—22no—
184C7×Q8—22no—
185C7×Q8—41no—
186C7×Q8—41no—
187C2×C4×C7—21no—
188C2×C4×C7—21no—
189C2×C4×C7—22no—
190C2×C4×C7—41no—
191C2×C4×C7—41no—
192C2×C4×C7—41no—
193C2×C4×C7—41no—
194C2×C4×C7—41no—
195C2×C4×C7#12011yescharacteristic
196C2×C4×C7#12011yescharacteristic
197C2×C4×C7#12111yescharacteristic
198C2×C4×C7#12111yescharacteristic
199C2×C4×C7#12111yescharacteristic
200C2×C4×C7#12711yescharacteristic
201C2×C4×C7C2×SD1611yescharacteristic
202C2×C4×C7C2×Q1611yescharacteristic
203C2×C4×C7#13511yescharacteristic
204C2×C4×C7#13511yescharacteristic
205C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C7#13711yescharacteristic
207C2×C4×C7#13711yescharacteristic
208C2×C4×C7#13711yescharacteristic
209C2×Dic7—42no—
210C2×Dic7—41no—
211C2×Dic7—41no—
212C2×Dic7—42no—
213C2×Dic7—42no—
214C2×Dic7—41no—
215C2×Dic7—42no—
216C2×Dic7—81no—
217C2×Dic7—81no—
218D28—22no—
219D28—22no—
220D28—41no—
221D28—41no—
222C4×D7—81no—
223C4×D7—81no—
224C4×D7—81no—
225C4×D7—81no—
226Dic14—44no—
227Dic14—82no—
228C7×C8—42no—
229C7×C8—42no—
230C7⋊C8—42no—
231C22×Q8—141no—
232C22×Q8D2811yescharacteristic
233C22×D4—71no—
234C23×C4—141no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—141no—
238C4⋊Q8—72no—
239C4⋊Q8—141no—
240C4⋊Q8—141no—
241C4⋊Q8—141no—
242C22⋊Q8—282no—
243C22⋊Q8—282no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×D4—141no—
249C4×D4—141no—
250C4×D4—141no—
251C4×D4—141no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—71no—
254C2×C4⋊C4—72no—
255C2×C4⋊C4—141no—
256C2×C4⋊C4—141no—
257C2×C4⋊C4—142no—
258C2×C4⋊C4—141no—
259C2×C4⋊C4—141no—
260C2×C4⋊C4D2811yescharacteristic
261C2×C22⋊C4—142no—
262C2×C22⋊C4—141no—
263C2×C22⋊C4—142no—
264C2×C42—21no—
265C2×C42C22×D711yescharacteristic
266#107—144no—
267#106—144no—
268C4⋊C8—21no—
269C4⋊C8—72no—
270C4⋊C8—141no—
271C4⋊C8C22⋊D712yes—
272#103—144no—
273#103—284no—
274#102—144no—
275C4×C8—21no—
276C4×C8—21no—
277#95—142no—
278C22×C7#39211yescharacteristic
279C22×C7#45011yescharacteristic
280C22×C7#45111yescharacteristic
281C22×C7#45211yescharacteristic
282C22×C7#45211yescharacteristic
283C22×C7#45311yescharacteristic
284C22×C7#45411yescharacteristic
285C2×D7—42no—
286C2×D7—42no—
287C2×D7—42no—
288C2×D7—81no—
289C2×D7—81no—
290C2×D7—81no—
291C2×D7—81no—
292C4×C7—21no—
293C4×C7—21no—
294C4×C7—42no—
295C4×C7—81no—
296C4×C7#44811yescharacteristic
297C4×C7#44911yescharacteristic
298C4×C7#45111yescharacteristic
299C4×C7#45211yescharacteristic
300C4×C7#46511yescharacteristic
301C4×C7#46711yescharacteristic
302C4×C7#46811yescharacteristic
303C4×C7#47011yescharacteristic
304Dic7—82no—
305Dic7—81no—
306Dic7—82no—
307C24—141no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—142no—
314C2×Q8—282no—
315C2×Q8—282no—
316C2×Q8—281no—
317C2×Q8#113212yes—
318C2×D4—72no—
319C2×D4—141no—
320C2×D4—141no—
321C2×D4—141no—
322C2×D4—141no—
323C2×D4—141no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—141no—
327C22×C4—142no—
328C22×C4—281no—
329C22×C4—281no—
330C22×C4—281no—
331C22×C4—281no—
332C22×C4—281no—
333C22×C4—281no—
334C22×C4—281no—
335C22×C4C2×D2811yescharacteristic
336C22×C4D4×D711yescharacteristic
337C22×C4D4×D711yescharacteristic
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—142no—
345C2×C8—281no—
346C2×C8—281no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—142no—
352C4⋊C4—141no—
353C4⋊C4—142no—
354C4⋊C4—141no—
355C4⋊C4—282no—
356C4⋊C4—284no—
357C4⋊C4—281no—
358C4⋊C4—281no—
359C4⋊C4—281no—
360C4⋊C4—281no—
361C4⋊C4—281no—
362C4⋊C4—281no—
363C22⋊C4—284no—
364C22⋊C4—281no—
365C22⋊C4—281no—
366C22⋊C4—562no—
367C42—41no—
368C42—41no—
369C42#115711yescharacteristic
370C42D4×D711yescharacteristic
371C42D4×D711yescharacteristic
372C42C2×C22⋊D711yescharacteristic
373C2×C7#163111yescharacteristic
374C2×C7#163211yescharacteristic
375C2×C7#163711yescharacteristic
376C2×C7#163811yescharacteristic
377C2×C7#200011yescharacteristic
378C2×C7#200111yescharacteristic
379C2×C7#200611yescharacteristic
380D7—82no—
381C23—142no—
382C23—281no—
383C23—281no—
384C23—281no—
385C23—281no—
386C23—281no—
387C23—281no—
388C23#644511yescharacteristic
389Q8—22no—
390Q8—22no—
391Q8—41no—
392Q8—41no—
393Q8—284no—
394Q8—562no—
395D4—142no—
396D4—142no—
397D4—281no—
398D4—281no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—281no—
408C2×C4—282no—
409C2×C4—282no—
410C2×C4—281no—
411C2×C4—281no—
412C2×C4—282no—
413C2×C4—282no—
414C2×C4—561no—
415C2×C4—561no—
416C2×C4—561no—
417C2×C4—561no—
418C2×C4—561no—
419C2×C4—561no—
420C2×C4#644511yescharacteristic
421C2×C4#644711yescharacteristic
422C2×C4#644711yescharacteristic
423C2×C4C2×#113211yescharacteristic
424C2×C4#646711yescharacteristic
425C2×C4#647111yescharacteristic
426C2×C4#647211yescharacteristic
427C2×C4#647811yescharacteristic
428C2×C4#647911yescharacteristic
429C2×C4D7×Q1611yescharacteristic
430C2×C4#648111yescharacteristic
431C2×C4#649311yescharacteristic
432C2×C4#650011yescharacteristic
433C2×C4#650311yescharacteristic
434C8—42no—
435C8—42no—
436C8—282no—
437C7#1023611yescharacteristic, complemented, Sylow
438C22—282no—
439C22—282no—
440C22—282no—
441C22—561no—
442C22—561no—
443C22—561no—
444C22—561no—
445C22#8950311yescharacteristic
446C22#8950511yescharacteristic
447C22#8958011yescharacteristic
448C22#8958211yescharacteristic
449C22#8959411yescharacteristic
450C22#8959911yescharacteristic
451C22#8973211yescharacteristic
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—562no—
457C4—561no—
458C4—562no—
459C4#8950611yescharacteristic
460C4#8951011yescharacteristic
461C4#8958511yescharacteristic
462C4#8958811yescharacteristic
463C4#8988611yescharacteristic
464C4#8990611yescharacteristic
465C4#8994511yescharacteristic
466C4#8995811yescharacteristic
467C2—562no—
468C2#1172600011yescharacteristic
469C2#1172600111yescharacteristic
470C2#1172601511yescharacteristic
471C2#1172602311yescharacteristic
472C2#1172771611yescharacteristic
473C2#1172802711yescharacteristic
474C2#1172814611yescharacteristic
subgroupG/H
centerC23#6445
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC2×C7×Q8⋊C8C2
socleC23×C7#120
prime radicalC22×D28D4
hypercenterC2×Q8⋊C8D7
hypocenterC7#10236
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×#89793C2semidirect
4. C2×C7×Q8⋊C8C2semidirect
5. #11727525C2semidirect
7. #11725508C2semidirect
83. C2×Q8⋊C8D7semidirect
437. C7#10236semidirect

Maximal subgroups

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

subgroupindex
#117399452
C2×#897932
C2×#896142
C2×C7×Q8⋊C82
#117275252
C2×#892542
#117255082
#102367