Finite Group Databasebeta

← #13256120

Subgroups — #13256120

Order 1792.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739945C211yesmaximal, characteristic
2C2×#89792C211yesmaximal, characteristic, complemented
3C2×#89613C211yesmaximal, characteristic
4C2×C7×Q8⋊C8C211yesmaximal, characteristic, complemented
5#11727531C211yesmaximal, characteristic, complemented
6C2×#89254C211yesmaximal, characteristic
7#11725508C211yesmaximal, characteristic, complemented
8C2×C4×C7×Q8C2211yescharacteristic
9C2×#6509—21no—
10C22×#1132—21no—
11C2×C4×D28C2211yescharacteristic
12C2×#6432C2211yescharacteristic
13C2×C7×C4⋊C8C2211yescharacteristic
14C2×C4×C7×C8C2211yescharacteristic
15C2×#6409—21no—
16C2×#6390—21no—
17#89792—22no—
18#89792—22no—
19#89766—22no—
20#89759—21no—
21C2×#6382—21no—
22#89711—21no—
23#89707C2211yescharacteristic
24#89700—21no—
25C2×C4⋊(C7⋊C8)C2211yescharacteristic
26#89613—22no—
27#89613—22no—
28C7×Q8⋊C8—22no—
29#89346—22no—
30#89254—22no—
31#10232—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—
59C2×#1132—24no—
60C2×#1132—42no—
61C2×#1132—42no—
62C4×D28—21no—
63C4×D28—21no—
64C4×D28—21no—
65C4×D28—21no—
66#6432—21no—
67#6432—21no—
68#6432—21no—
69#6432D412yes—
70C7×C4⋊C8—21no—
71C7×C4⋊C8D412yes—
72C4×C7×C8—21no—
73C4×C7×C8—21no—
74#6409—24no—
75C7⋊#95—22no—
76#6390—24no—
77#6382—24no—
78C4⋊(C7⋊C8)—21no—
79C4⋊(C7⋊C8)D412yes—
80C2×#475—71no—
81C2×#461—71no—
82#2538—71no—
83#1990—71no—
84C2×Q8⋊C8D711yescharacteristic, complemented
85C2×D4⋊C8—71no—
86#1296—71no—
87C23×D7—21no—
88C2×C7×Q8—21no—
89C2×C7×Q8—21no—
90C2×C7×Q8—21no—
91C2×C7×Q8—21no—
92C2×C7×Q8—21no—
93C2×C7×Q8SD1612yescomplemented
94C22×C4×C7—21no—
95C22×C4×C7—21no—
96C22×C4×C7C2×D411yescharacteristic
97C22×C4×C7C2×D411yescharacteristic
98C22×C4×C7C2×D411yescharacteristic
99C22×Dic7—21no—
100C22×Dic7—22no—
101C22×Dic7—41no—
102C2×D28—21no—
103C2×D28—21no—
104C2×D28—21no—
105C2×D28—21no—
106C2×D28—21no—
107C2×D28SD1612yes—
108C2×C4×D7—41no—
109C2×C4×D7—41no—
110C2×C4×D7—41no—
111C2×C4×D7—41no—
112C2×C4×D7—41no—
113C2×C4×D7—41no—
114C2×Dic14—22no—
115C2×Dic14—41no—
116C2×Dic14—41no—
117C2×Dic14—41no—
118C2×Dic14—41no—
119C2×Dic14—41no—
120C2×C7×C8—22no—
121C2×C7×C8—22no—
122C2×C7×C8—41no—
123C2×C7×C8—41no—
124C2×C7×C8—41no—
125C2×C7×C8—41no—
126C7×C4⋊C4—21no—
127C7×C4⋊C4—21no—
128C7×C4⋊C4—41no—
129C7×C4⋊C4—41no—
130C42×C7—41no—
131C42×C7—41no—
132C42×C7C2×D411yescharacteristic
133C42×C7C2×D411yescharacteristic
134C42×C7C2×D411yescharacteristic
135C42×C7#4111yescharacteristic
136(C2×D7)⋊C4—44no—
137(C2×D7)⋊C4—41no—
138(C2×D7)⋊C4—41no—
139(C2×D7)⋊C4—82no—
140C4⋊Dic7—22no—
141C4⋊Dic7—21no—
142C4⋊Dic7—22no—
143C4⋊Dic7—21no—
144C4⋊Dic7—41no—
145C4⋊Dic7—41no—
146C4⋊Dic7—41no—
147C4⋊Dic7—41no—
148C4⋊Dic7—41no—
149C4⋊Dic7—41no—
150C4⋊Dic7—42no—
151Dic7⋊C4—44no—
152C2×C7⋊C8—22no—
153C2×C7⋊C8—41no—
154C2×C7⋊C8—41no—
155#1132—48no—
156C22×SD16—141no—
157C2×C4⋊Q8—71no—
158C2×C22⋊Q8—141no—
159C2×C4×Q8C2×D711yescharacteristic
160C2×C4×D4—71no—
161#475—142no—
162#475—142no—
163#461—142no—
164#461—142no—
165C2×#106—141no—
166C2×C4⋊C8—71no—
167C2×C4⋊C8C2×D711yescharacteristic
168C2×#103—141no—
169C2×#103—141no—
170C2×C4×C8C2×D711yescharacteristic
171#396—142no—
172#390—141no—
173#389—141no—
174#384—71no—
175#380—141no—
176#340—142no—
177Q8⋊C8—22no—
178D4⋊C8—142no—
179C23×C7#12011yescharacteristic
180C22×D7—22no—
181C22×D7—41no—
182C22×D7—41no—
183C22×D7—41no—
184C22×D7—41no—
185C22×D7—41no—
186C22×D7—41no—
187C7×Q8—22no—
188C7×Q8—22no—
189C7×Q8—41no—
190C7×Q8—41no—
191C2×C4×C7—21no—
192C2×C4×C7—21no—
193C2×C4×C7—22no—
194C2×C4×C7—41no—
195C2×C4×C7—41no—
196C2×C4×C7—41no—
197C2×C4×C7—41no—
198C2×C4×C7—41no—
199C2×C4×C7#12011yescharacteristic
200C2×C4×C7#12011yescharacteristic
201C2×C4×C7#12111yescharacteristic
202C2×C4×C7#12111yescharacteristic
203C2×C4×C7#12111yescharacteristic
204C2×C4×C7#12711yescharacteristic
205C2×C4×C7C2×SD1611yescharacteristic
206C2×C4×C7C2×SD1611yescharacteristic
207C2×C4×C7#13511yescharacteristic
208C2×C4×C7#13511yescharacteristic
209C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
210C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C7#13711yescharacteristic
212C2×C4×C7#13711yescharacteristic
213C2×Dic7—42no—
214C2×Dic7—41no—
215C2×Dic7—42no—
216C2×Dic7—41no—
217C2×Dic7—42no—
218C2×Dic7—41no—
219C2×Dic7—42no—
220C2×Dic7—81no—
221C2×Dic7—81no—
222D28—22no—
223D28—22no—
224D28—41no—
225D28—41no—
226C4×D7—81no—
227C4×D7—81no—
228C4×D7—81no—
229C4×D7—81no—
230Dic14—42no—
231Dic14—42no—
232Dic14—81no—
233Dic14—81no—
234C7×C8—42no—
235C7×C8—42no—
236C7⋊C8—42no—
237C22×Q8—141no—
238C22×Q8D2811yescharacteristic
239C22×D4—71no—
240C23×C4—141no—
241C2×SD16—144no—
242C2×SD16—282no—
243C2×SD16—282no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—141no—
247C4⋊Q8—72no—
248C4⋊Q8—141no—
249C4⋊Q8—141no—
250C4⋊Q8—141no—
251C22⋊Q8—282no—
252C22⋊Q8—282no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×D4—141no—
258C4×D4—141no—
259C4×D4—141no—
260C4×D4—141no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—71no—
263C2×C4⋊C4—72no—
264C2×C4⋊C4—141no—
265C2×C4⋊C4—141no—
266C2×C4⋊C4—142no—
267C2×C4⋊C4—141no—
268C2×C4⋊C4—141no—
269C2×C4⋊C4D2811yescharacteristic
270C2×C22⋊C4—142no—
271C2×C22⋊C4—141no—
272C2×C22⋊C4—142no—
273C2×C42—21no—
274C2×C42C22×D711yescharacteristic
275#106—144no—
276C4⋊C8—21no—
277C4⋊C8—72no—
278C4⋊C8—141no—
279C4⋊C8C22⋊D712yes—
280#103—144no—
281#103—144no—
282C4×C8—21no—
283C4×C8—21no—
284#95—142no—
285C22×C7#39211yescharacteristic
286C22×C7#44811yescharacteristic
287C22×C7#44911yescharacteristic
288C22×C7#45011yescharacteristic
289C22×C7#45211yescharacteristic
290C22×C7#45511yescharacteristic
291C22×C7#45611yescharacteristic
292C2×D7—42no—
293C2×D7—42no—
294C2×D7—42no—
295C2×D7—81no—
296C2×D7—81no—
297C2×D7—81no—
298C2×D7—81no—
299C4×C7—21no—
300C4×C7—21no—
301C4×C7—42no—
302C4×C7—81no—
303C4×C7#44811yescharacteristic
304C4×C7#44911yescharacteristic
305C4×C7#45011yescharacteristic
306C4×C7#45211yescharacteristic
307C4×C7#46511yescharacteristic
308C4×C7#46511yescharacteristic
309C4×C7#46811yescharacteristic
310C4×C7#46811yescharacteristic
311Dic7—82no—
312Dic7—82no—
313Dic7—81no—
314C24—141no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—142no—
321C2×Q8—281no—
322C2×Q8—281no—
323C2×Q8—281no—
324C2×Q8—281no—
325C2×Q8—281no—
326C2×Q8#113212yescomplemented
327C2×D4—72no—
328C2×D4—141no—
329C2×D4—141no—
330C2×D4—141no—
331C2×D4—141no—
332C2×D4—141no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—141no—
336C22×C4—142no—
337C22×C4—281no—
338C22×C4—281no—
339C22×C4—281no—
340C22×C4—281no—
341C22×C4—281no—
342C22×C4—281no—
343C22×C4—281no—
344C22×C4C2×D2811yescharacteristic
345C22×C4D4×D711yescharacteristic
346C22×C4D4×D711yescharacteristic
347SD16—288no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—142no—
355C2×C8—281no—
356C2×C8—281no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—142no—
362C4⋊C4—141no—
363C4⋊C4—142no—
364C4⋊C4—141no—
365C4⋊C4—282no—
366C4⋊C4—284no—
367C4⋊C4—281no—
368C4⋊C4—281no—
369C4⋊C4—281no—
370C4⋊C4—281no—
371C4⋊C4—281no—
372C4⋊C4—281no—
373C22⋊C4—284no—
374C22⋊C4—281no—
375C22⋊C4—281no—
376C22⋊C4—562no—
377C42—41no—
378C42—41no—
379C42#115711yescharacteristic
380C42D4×D711yescharacteristic
381C42D4×D711yescharacteristic
382C42C2×C22⋊D711yescharacteristic
383C2×C7#164211yescharacteristic
384C2×C7#164311yescharacteristic
385C2×C7#165011yescharacteristic
386C2×C7#165111yescharacteristic
387C2×C7#200011yescharacteristic
388C2×C7#200011yescharacteristic
389C2×C7#200711yescharacteristic
390D7—82no—
391C23—142no—
392C23—281no—
393C23—281no—
394C23—281no—
395C23—281no—
396C23—281no—
397C23—281no—
398C23#644511yescharacteristic
399Q8—22no—
400Q8—22no—
401Q8—41no—
402Q8—41no—
403Q8—282no—
404Q8—282no—
405Q8—561no—
406Q8—561no—
407D4—142no—
408D4—142no—
409D4—281no—
410D4—281no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—281no—
420C2×C4—282no—
421C2×C4—282no—
422C2×C4—281no—
423C2×C4—281no—
424C2×C4—282no—
425C2×C4—282no—
426C2×C4—561no—
427C2×C4—561no—
428C2×C4—561no—
429C2×C4—561no—
430C2×C4—561no—
431C2×C4—561no—
432C2×C4#644511yescharacteristic
433C2×C4#644711yescharacteristic
434C2×C4#644711yescharacteristic
435C2×C4C2×#113211yescharacteristic
436C2×C4#646711yescharacteristic
437C2×C4#647111yescharacteristic
438C2×C4#647211yescharacteristic
439C2×C4D7×SD1611yescharacteristic
440C2×C4#647711yescharacteristic
441C2×C4#648111yescharacteristic
442C2×C4#648211yescharacteristic
443C2×C4#649311yescharacteristic
444C2×C4#650011yescharacteristic
445C2×C4#650311yescharacteristic
446C8—42no—
447C8—42no—
448C8—282no—
449C7#1023211yescharacteristic, complemented, Sylow
450C22—282no—
451C22—282no—
452C22—282no—
453C22—561no—
454C22—561no—
455C22—561no—
456C22—561no—
457C22#8950311yescharacteristic
458C22#8950511yescharacteristic
459C22#8957811yescharacteristic
460C22#8958311yescharacteristic
461C22#8959711yescharacteristic
462C22#8959811yescharacteristic
463C22#8973211yescharacteristic
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—561no—
469C4—562no—
470C4—562no—
471C4#8950611yescharacteristic
472C4#8951011yescharacteristic
473C4#8957911yescharacteristic
474C4#8958411yescharacteristic
475C4#8988611yescharacteristic
476C4#8990611yescharacteristic
477C4#8994111yescharacteristic
478C4#8995911yescharacteristic
479C2—562no—
480C2#1172600211yescharacteristic
481C2#1172600311yescharacteristic
482C2#1172600411yescharacteristic
483C2#1172600511yescharacteristic
484C2#1172771611yescharacteristic
485C2#1172802611yescharacteristic
486C2#1172814711yescharacteristic
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#10232
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×#89792C2semidirect
4. C2×C7×Q8⋊C8C2semidirect
5. #11727531C2semidirect
7. #11725508C2semidirect
84. C2×Q8⋊C8D7semidirect
93. C2×C7×Q8SD16semidirect
326. C2×Q8#1132semidirect
449. C7#10232semidirect

Maximal subgroups

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

subgroupindex
#117399452
C2×#897922
C2×#896132
C2×C7×Q8⋊C82
#117275312
C2×#892542
#117255082
#102327