Finite Group Databasebeta

← #13249136

Subgroups — #13249136

Order 1792.

610 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89457C211yesmaximal, characteristic
2C4×#6460C211yesmaximal, characteristic
3#11728229C211yesmaximal, characteristic
4C2×#89279C211yesmaximal, characteristic, complemented
5C2×#89251C211yesmaximal, characteristic, complemented
6C7×#1279C211yesmaximal, characteristic, complemented
7#11725425C211yesmaximal, characteristic, complemented
8C2×#6460C411yescharacteristic
9C2×C42×D7C2211yescharacteristic
10C2×C4×Dic14C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12C2×C4×C7×C8C2211yescharacteristic
13C4×C7×C4⋊C4C2211yescharacteristic
14C2×(C2×D7)⋊C8—21no—
15C2×(C2×D7)⋊C8—21no—
16C2×Dic7⋊C8—21no—
17#89759C411yescharacteristic
18#89757C411yescharacteristic
19#89746C411yescharacteristic
20C4×(C2×D7)⋊C4—21no—
21C4×C4⋊Dic7—21no—
22C2×C4⋊(C7⋊C8)C2211yescharacteristic
23C2×C4×C7⋊C8C2211yescharacteristic
24#89457—22no—
25#89457—22no—
26#89440—21no—
27#89425—21no—
28#89345—21no—
29#89279—22no—
30#89251—22no—
31#9073—71nomaximal, Sylow
32C22×C4×D7C2×C411yescharacteristic
33C22×C4×D7D411yescharacteristic
34C22×C4×D7D411yescharacteristic
35C22×Dic14C2×C411yescharacteristic
36C22×C7×C8—21no—
37C22×C7×C8—21no—
38C2×C7×C4⋊C4C2×C411yescharacteristic
39C2×C7×C4⋊C4C2×C411yescharacteristic
40C2×C42×C7—21no—
41C2×C42×C7C2311yescharacteristic
42C2×(C2×D7)⋊C4—21no—
43C2×(C2×D7)⋊C4—21no—
44C2×C4⋊Dic7—21no—
45C2×C4⋊Dic7—21no—
46C2×C4⋊Dic7C2×C411yescharacteristic
47C2×Dic7⋊C4—21no—
48C2×C4×Dic7—21no—
49C2×C4×Dic7C2×C411yescharacteristic
50C2×C4×Dic7D411yescharacteristic
51C2×C4×Dic7D411yescharacteristic
52C22×C7⋊C8—21no—
53C22×C7⋊C8—21no—
54#6460—22no—
55#6460C814yescomplemented
56C42×D7—21no—
57C42×D7—21no—
58C42×D7—21no—
59C42×D7—21no—
60C4×Dic14—21no—
61C4×Dic14—21no—
62C4×Dic14—21no—
63C4×Dic14—21no—
64C7×C4⋊C8—21no—
65C7×C4⋊C8—21no—
66C4×C7×C8—21no—
67C4×C7×C8D412yes—
68C7×#95—21no—
69C7⋊#95—21no—
70C7⋊#95—21no—
71C7⋊#95—21no—
72C7⋊#95—21no—
73(C2×D7)⋊C8—24no—
74(C2×D7)⋊C8—42no—
75Dic7⋊C8—24no—
76C4⋊(C7⋊C8)—21no—
77C4⋊(C7⋊C8)—21no—
78C4×C7⋊C8—21no—
79C4×C7⋊C8D412yes—
80C2×#431—71no—
81C4×C22⋊Q8—71no—
82#1797—71no—
83C2×Q8⋊C8—71no—
84C2×Q8⋊C8—71no—
85#1279—71no—
86#1279D711yescharacteristic, complemented
87C23×D7C22⋊C411yescharacteristic
88C22×C4×C7—21no—
89C22×C4×C7—21no—
90C22×C4×C7C22×C411yescharacteristic
91C22×C4×C7C2×D411yescharacteristic
92C22×C4×C7C2×D411yescharacteristic
93C22×Dic7—21no—
94C22×Dic7—21no—
95C22×Dic7C22⋊C411yescharacteristic
96C22×Dic7C22⋊C411yescharacteristic
97C22×Dic7C22⋊C411yescharacteristic
98C2×C4×D7—21no—
99C2×C4×D7—21no—
100C2×C4×D7—21no—
101C2×C4×D7—21no—
102C2×C4×D7—21no—
103C2×C4×D7—21no—
104C2×C4×D7—21no—
105C2×C4×D7—21no—
106C2×C4×D7—21no—
107C2×C4×D7—21no—
108C2×C4×D7—21no—
109C2×C4×D7—21no—
110C2×C4×D7—41no—
111C2×C4×D7—41no—
112C2×C4×D7C2×C812yes—
113C2×C4×D7M1612yes—
114C2×Dic14—21no—
115C2×Dic14—21no—
116C2×Dic14—21no—
117C2×Dic14—21no—
118C2×Dic14—21no—
119C2×Dic14C2×C812yes—
120C2×C7×C8—22no—
121C2×C7×C8—41no—
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—21no—
129C7×C4⋊C4C2×C812yes—
130C42×C7—41no—
131C42×C7—41no—
132C42×C7C2×D411yescharacteristic
133C42×C7C2×D411yescharacteristic
134C42×C7#4111yescharacteristic
135C42×C7#4111yescharacteristic
136(C2×D7)⋊C4—24no—
137(C2×D7)⋊C4—42no—
138C4⋊Dic7—24no—
139C4⋊Dic7—21no—
140C4⋊Dic7—21no—
141C4⋊Dic7—42no—
142Dic7⋊C4—41no—
143Dic7⋊C4—41no—
144C4×Dic7—21no—
145C4×Dic7—21no—
146C4×Dic7—21no—
147C4×Dic7—21no—
148C4×Dic7—21no—
149C4×Dic7—21no—
150C4×Dic7—41no—
151C4×Dic7—41no—
152C2×C7⋊C8—22no—
153C2×C7⋊C8—41no—
154C2×C7⋊C8—41no—
155C2×C7⋊C8—41no—
156C2×C7⋊C8—41no—
157C2×C7⋊C8—41no—
158C2×C22⋊Q8—71no—
159C2×C4×Q8—71no—
160C22×C42—71no—
161#431—142no—
162#431—142no—
163C2×C4⋊C8—71no—
164C2×C4⋊C8—141no—
165C2×C4⋊C8C2×D711yescharacteristic
166C2×C22⋊C8—141no—
167C2×C22⋊C8—141no—
168C2×C4×C8—71no—
169C2×C4×C8C2×D711yescharacteristic
170#391—71no—
171#389—71no—
172#387—141no—
173#385—141no—
174#380—71no—
175C4×C4⋊C4—141no—
176C4×C4⋊C4C2×D711yescharacteristic
177C4×C22⋊C4—141no—
178#336—141no—
179Q8⋊C8—142no—
180Q8⋊C8—142no—
181C23×C7C2×C22⋊C411yescharacteristic
182C22×D7—21no—
183C22×D7—21no—
184C22×D7—21no—
185C22×D7—21no—
186C22×D7—21no—
187C22×D7—21no—
188C22×D7C22⋊C812yes—
189C2×C4×C7—21no—
190C2×C4×C7—21no—
191C2×C4×C7—22no—
192C2×C4×C7—41no—
193C2×C4×C7—41no—
194C2×C4×C7—41no—
195C2×C4×C7—41no—
196C2×C4×C7—41no—
197C2×C4×C7C4×D411yescharacteristic
198C2×C4×C7C4×D411yescharacteristic
199C2×C4×C7#12011yescharacteristic
200C2×C4×C7#12111yescharacteristic
201C2×C4×C7#12111yescharacteristic
202C2×C4×C7#12311yescharacteristic
203C2×C4×C7C22×C811yescharacteristic
204C2×C4×C7C2×M1611yescharacteristic
205C2×C4×C7#13111yescharacteristic
206C2×C4×C7#13111yescharacteristic
207C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
208C2×C4×C7#13711yescharacteristic
209C2×C4×C7#13711yescharacteristic
210C2×C4×C7#13711yescharacteristic
211C2×Dic7—21no—
212C2×Dic7—21no—
213C2×Dic7—21no—
214C2×Dic7—21no—
215C2×Dic7—22no—
216C2×Dic7—21no—
217C2×Dic7—21no—
218C2×Dic7—21no—
219C2×Dic7—21no—
220C2×Dic7—41no—
221C2×Dic7—41no—
222C2×Dic7—41no—
223C2×Dic7—41no—
224C2×Dic7—41no—
225C2×Dic7C22⋊C812yes—
226C4×D7—22no—
227C4×D7—22no—
228C4×D7—22no—
229C4×D7—22no—
230C4×D7—42no—
231C4×D7—42no—
232C4×D7—41no—
233C4×D7—41no—
234C4×D7—41no—
235C4×D7—41no—
236Dic14—22no—
237Dic14—22no—
238Dic14—41no—
239Dic14—41no—
240C7×C8—42no—
241C7×C8—81no—
242C7⋊C8—42no—
243C7⋊C8—81no—
244C22×Q8—71no—
245C23×C4—71no—
246C23×C4—71no—
247C23×C4—71no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—141no—
251C22×C8—141no—
252C22⋊Q8—74no—
253C22⋊Q8—142no—
254C4×Q8—141no—
255C4×Q8—141no—
256C4×Q8—141no—
257C4×Q8—141no—
258C2×C4⋊C4—71no—
259C2×C4⋊C4—141no—
260C2×C4⋊C4—141no—
261C2×C4⋊C4—141no—
262C2×C4⋊C4C4×D711yescharacteristic
263C2×C4⋊C4C4×D711yescharacteristic
264C2×C22⋊C4—141no—
265C2×C22⋊C4—141no—
266C2×C42—21no—
267C2×C42—71no—
268C2×C42—71no—
269C2×C42—71no—
270C2×C42—141no—
271C2×C42—141no—
272C2×C42—141no—
273C2×C42—141no—
274C2×C42—141no—
275C2×C42C22×D711yescharacteristic
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—144no—
279C4⋊C8—141no—
280C4⋊C8—141no—
281C22⋊C8—144no—
282C22⋊C8—282no—
283C4×C8—21no—
284C4×C8—72no—
285C4×C8—141no—
286C4×C8D2812yes—
287#95—21no—
288#95—141no—
289#95—141no—
290#95—141no—
291#95—141no—
292C22×C7#38611yescharacteristic
293C22×C7C2×C22⋊C811yescharacteristic
294C22×C7#40811yescharacteristic
295C22×C7#41711yescharacteristic
296C22×C7#41911yescharacteristic
297C22×C7#42111yescharacteristic
298C22×C7#42111yescharacteristic
299C2×D7—22no—
300C2×D7—22no—
301C2×D7—22no—
302C2×D7—41no—
303C2×D7—41no—
304C2×D7—41no—
305C2×D7—41no—
306C4×C7—21no—
307C4×C7—21no—
308C4×C7—42no—
309C4×C7—81no—
310C4×C7C8×D411yescharacteristic
311C4×C7C8×D411yescharacteristic
312C4×C7#43511yescharacteristic
313C4×C7#43511yescharacteristic
314C4×C7#46811yescharacteristic
315C4×C7#46811yescharacteristic
316C4×C7#47011yescharacteristic
317C4×C7#47011yescharacteristic
318Dic7—22no—
319Dic7—42no—
320Dic7—41no—
321Dic7—41no—
322Dic7—81no—
323C24—71no—
324C2×Q8—72no—
325C2×Q8—141no—
326C2×Q8—141no—
327C2×Q8—141no—
328C2×Q8—141no—
329C2×Q8—141no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—71no—
333C22×C4—72no—
334C22×C4—72no—
335C22×C4—71no—
336C22×C4—71no—
337C22×C4—141no—
338C22×C4—141no—
339C22×C4—141no—
340C22×C4—141no—
341C22×C4—141no—
342C22×C4—141no—
343C22×C4—141no—
344C22×C4—141no—
345C22×C4—141no—
346C22×C4—141no—
347C22×C4—141no—
348C22×C4—141no—
349C22×C4—141no—
350C22×C4—141no—
351C22×C4—281no—
352C22×C4—281no—
353C22×C4C2×C4×D711yescharacteristic
354C22×C4D4×D711yescharacteristic
355C22×C4D4×D711yescharacteristic
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—142no—
363C2×C8—281no—
364C2×C8—281no—
365C2×C8—281no—
366C2×C8—281no—
367C2×C8—281no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—144no—
372C4⋊C4—141no—
373C4⋊C4—141no—
374C4⋊C4—282no—
375C4⋊C4—281no—
376C4⋊C4—281no—
377C4⋊C4C8×D712yes—
378C22⋊C4—144no—
379C22⋊C4—282no—
380C42—41no—
381C42—41no—
382C42—141no—
383C42—141no—
384C42—141no—
385C42—141no—
386C42—141no—
387C42—141no—
388C42—281no—
389C42—281no—
390C42C2×D2811yescharacteristic
391C42#115711yescharacteristic
392C42D4×D711yescharacteristic
393C42#116111yescharacteristic
394C2×C7#147711yescharacteristic
395C2×C7#147911yescharacteristic
396C2×C7#149511yescharacteristic
397C2×C7#149711yescharacteristic
398C2×C7#186911yescharacteristic
399C2×C7#189411yescharacteristic
400C2×C7#189711yescharacteristic
401D7—42no—
402C23—72no—
403C23—141no—
404C23—141no—
405C23—141no—
406C23—141no—
407C23—141no—
408C23—141no—
409C23D7×C22⋊C411yescharacteristic
410Q8—142no—
411Q8—142no—
412Q8—281no—
413Q8—281no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—72no—
423C2×C4—141no—
424C2×C4—141no—
425C2×C4—142no—
426C2×C4—142no—
427C2×C4—142no—
428C2×C4—142no—
429C2×C4—141no—
430C2×C4—141no—
431C2×C4—142no—
432C2×C4—141no—
433C2×C4—141no—
434C2×C4—141no—
435C2×C4—141no—
436C2×C4—282no—
437C2×C4—282no—
438C2×C4—281no—
439C2×C4—281no—
440C2×C4—281no—
441C2×C4—281no—
442C2×C4—281no—
443C2×C4—281no—
444C2×C4—281no—
445C2×C4—281no—
446C2×C4—281no—
447C2×C4C4×D2811yescharacteristic
448C2×C4#644511yescharacteristic
449C2×C4#644711yescharacteristic
450C2×C4#645611yescharacteristic
451C2×C4#645711yescharacteristic
452C2×C4#645811yescharacteristic
453C2×C4C2×C8×D711yescharacteristic
454C2×C4#646411yescharacteristic
455C2×C4D7×M1611yescharacteristic
456C2×C4#647011yescharacteristic
457C2×C4#647411yescharacteristic
458C2×C4#647811yescharacteristic
459C2×C4#647811yescharacteristic
460C2×C4#648111yescharacteristic
461C8—42no—
462C8—81no—
463C8—282no—
464C8—561no—
465C7#907311yescharacteristic, complemented, Sylow
466C22—142no—
467C22—142no—
468C22—142no—
469C22—281no—
470C22—281no—
471C22—281no—
472C22—281no—
473C22#8943711yescharacteristic
474C22D7×C22⋊C811yescharacteristic
475C22#8949911yescharacteristic
476C22#8954311yescharacteristic
477C22#8957411yescharacteristic
478C22#8959311yescharacteristic
479C22#8959311yescharacteristic
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—142no—
485C4—281no—
486C4—282no—
487C4—281no—
488C4—561no—
489C4C8×D2811yescharacteristic
490C4#8947811yescharacteristic
491C4#8955211yescharacteristic
492C4#8958811yescharacteristic
493C4#8960611yescharacteristic
494C4#8960811yescharacteristic
495C4#8964011yescharacteristic
496C4#8965811yescharacteristic
497C2—282no—
498C2#1172592011yescharacteristic
499C2#1172593211yescharacteristic
500C2#1172598511yescharacteristic
501C2#1172599711yescharacteristic
502C2#1172642211yescharacteristic
503C2#1172651111yescharacteristic
504C2#1172663811yescharacteristic
subgroupG/H
centerC22×C4D4×D7
commutatorC2×C4×C7C22×C8
FrattiniC2×C42C22×D7
FittingC7×#1279C2
socleC23×C7C2×C22⋊C4
prime radicalC23×D7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1279D7
hypocenterC7#9073
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. C2×#89279C2semidirect
5. C2×#89251C2semidirect
6. C7×#1279C2semidirect
7. #11725425C2semidirect
55. #6460C8semidirect
86. #1279D7semidirect
465. C7#9073semidirect

Maximal subgroups

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

subgroupindex
C2×#894572
C4×#64602
#117282292
C2×#892792
C2×#892512
C7×#12792
#117254252
#90737