Finite Group Databasebeta

← #13245302

Subgroups — #13245302

Order 1792.

802 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90419C211yesmaximal, characteristic
2C2×C7×#332C211yesmaximal, characteristic, complemented
3C2×#89342C211yesmaximal, characteristic, complemented
4#11728229C211yesmaximal, characteristic
5#11728229C211yesmaximal, characteristic
6C2×#89277C211yesmaximal, characteristic, complemented
7C2×#89281C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×#6509—21no—
10C2×Q8×Dic7—21no—
11#90419—22no—
12#90419—22no—
13#90419—22no—
14#90419—22no—
15C2×#6460—21no—
16C2×#6455C412yes—
17C2×#6453C412yes—
18C2×#6450—21no—
19C2×C42×D7C2211yescharacteristic
20C2×#6432C2211yescharacteristic
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×C4⋊C8C2211yescharacteristic
23C2×(C2×D7)⋊C8—21no—
24C2×(C2×D7)⋊C8—21no—
25C2×C4⋊(C7⋊C8)C2211yescharacteristic
26C2×C4⋊(C7⋊C8)C2211yescharacteristic
27C7×#332—22no—
28#89345—21no—
29#89345—21no—
30#89342—22no—
31#89281—22no—
32#89277—22no—
33#8345—71nomaximal, Sylow
34C22×C7×Q8—21no—
35C22×C4×D7C2×C411yescharacteristic
36C22×C4×D7D411yescharacteristic
37C22×C4×D7D411yescharacteristic
38C22×Dic14—21no—
39C22×C7×C8—21no—
40C22×C7×C8—21no—
41C7×C4⋊Q8—21no—
42C7×C4⋊Q8—21no—
43C7×C4⋊Q8D412yes—
44C7×C4⋊Q8D412yes—
45C2×C7×C4⋊C4—21no—
46C2×C7×C4⋊C4C2×C412yes—
47C2×C42×C7C2311yescharacteristic
48#6509—24no—
49#6509—24no—
50Q8×Dic7—24no—
51Q8×Dic7—24no—
52C2×(C2×D7)⋊C4—22no—
53C2×C4⋊Dic7—21no—
54C2×C4⋊Dic7—22no—
55C2×C4⋊Dic7C2×C412yes—
56C2×Dic7⋊C4—22no—
57C2×C4×Dic7—22no—
58C2×C4×Dic7C2×C411yescharacteristic
59C2×C4×Dic7D411yescharacteristic
60C2×C4×Dic7D411yescharacteristic
61C22×C7⋊C8—21no—
62C22×C7⋊C8—21no—
63#6460—24no—
64#6460—24no—
65#6455—24no—
66#6455—24no—
67#6453—24no—
68#6453—24no—
69#6450—24no—
70#6450—24no—
71C42×D7—21no—
72C42×D7—21no—
73C42×D7—21no—
74C42×D7—21no—
75#6432—21no—
76#6432—21no—
77#6432D412yes—
78#6432D412yes—
79C7×C4⋊C8—21no—
80C7×C4⋊C8—21no—
81C7×C4⋊C8—21no—
82C7×C4⋊C8—21no—
83(C2×D7)⋊C8—42no—
84(C2×D7)⋊C8—42no—
85C4⋊(C7⋊C8)—21no—
86C4⋊(C7⋊C8)—21no—
87C4⋊(C7⋊C8)—21no—
88C4⋊(C7⋊C8)—21no—
89C2×#533—71no—
90#1797—71no—
91#1797—71no—
92C2×#332—71no—
93C2×#332—71no—
94C2×#332—71no—
95C2×#332D711yescharacteristic, complemented
96C23×D7C22⋊C411yescharacteristic
97C2×C7×Q8—22no—
98C2×C7×Q8—22no—
99C2×C7×Q8—41no—
100C2×C7×Q8—41no—
101C2×C7×Q8—41no—
102C2×C7×Q8—41no—
103C22×C4×C7—22no—
104C22×C4×C7C22×C411yescharacteristic
105C22×C4×C7C2×D411yescharacteristic
106C22×C4×C7C2×D411yescharacteristic
107C22×Dic7—22no—
108C22×Dic7C22⋊C411yescharacteristic
109C22×Dic7C22⋊C411yescharacteristic
110C22×Dic7C22⋊C411yescharacteristic
111C2×C4×D7—22no—
112C2×C4×D7—21no—
113C2×C4×D7—21no—
114C2×C4×D7—22no—
115C2×C4×D7—21no—
116C2×C4×D7—21no—
117C2×C4×D7—21no—
118C2×C4×D7—21no—
119C2×C4×D7—21no—
120C2×C4×D7—21no—
121C2×C4×D7—21no—
122C2×C4×D7—21no—
123C2×C4×D7—21no—
124C2×C4×D7—21no—
125C2×C4×D7—21no—
126C2×C4×D7—21no—
127C2×Dic14—22no—
128C2×Dic14—22no—
129C2×Dic14—41no—
130C2×Dic14—41no—
131C2×Dic14—41no—
132C2×Dic14—41no—
133C2×C7×C8—41no—
134C2×C7×C8—41no—
135C2×C7×C8—41no—
136C2×C7×C8—41no—
137C2×C7×C8—41no—
138C2×C7×C8—41no—
139C7×C4⋊C4—22no—
140C7×C4⋊C4—22no—
141C7×C4⋊C4—22no—
142C7×C4⋊C4C22⋊C414yes—
143C42×C7C2×D411yescharacteristic
144C42×C7C2×D411yescharacteristic
145C42×C7C2×D411yescharacteristic
146C42×C7C2×D411yescharacteristic
147(C2×D7)⋊C4—28no—
148C4⋊Dic7—28no—
149C4⋊Dic7—22no—
150C4⋊Dic7—22no—
151C4⋊Dic7—22no—
152C4⋊Dic7C22⋊C414yes—
153Dic7⋊C4—28no—
154C4×Dic7—28no—
155C4×Dic7—21no—
156C4×Dic7—21no—
157C4×Dic7—21no—
158C4×Dic7—21no—
159C4×Dic7—21no—
160C4×Dic7—21no—
161C2×C7⋊C8—41no—
162C2×C7⋊C8—41no—
163C2×C7⋊C8—41no—
164C2×C7⋊C8—41no—
165C2×C7⋊C8—41no—
166C2×C7⋊C8—41no—
167#533—142no—
168#533—142no—
169#533—142no—
170#533—142no—
171C2×C4⋊Q8—71no—
172C2×C4⋊Q8C2×D711yescharacteristic
173C2×#125—72no—
174C2×C22⋊Q8—141no—
175C2×C22⋊Q8—141no—
176C2×C4×Q8—141no—
177C2×C4×Q8—141no—
178C2×#117—72no—
179C22×C42—71no—
180C2×C4⋊C8—71no—
181C2×C4⋊C8—71no—
182C2×C4⋊C8C2×D711yescharacteristic
183C2×C4⋊C8C2×D711yescharacteristic
184C2×C22⋊C8—141no—
185C2×C22⋊C8—141no—
186#336—141no—
187#336—141no—
188#332—22no—
189#332—142no—
190#332—142no—
191#332—142no—
192C23×C7C2×C22⋊C411yescharacteristic
193C22×D7—21no—
194C22×D7—21no—
195C22×D7—21no—
196C22×D7—21no—
197C22×D7—21no—
198C22×D7—21no—
199C22×D7#10112yes—
200C7×Q8—42no—
201C7×Q8—42no—
202C7×Q8—42no—
203C7×Q8—42no—
204C2×C4×C7—21no—
205C2×C4×C7—21no—
206C2×C4×C7—24no—
207C2×C4×C7—42no—
208C2×C4×C7—42no—
209C2×C4×C7C2×C22⋊C411yescharacteristic
210C2×C4×C7C2×C22⋊C411yescharacteristic
211C2×C4×C7#12011yescharacteristic
212C2×C4×C7#12011yescharacteristic
213C2×C4×C7#12011yescharacteristic
214C2×C4×C7#12011yescharacteristic
215C2×C4×C7#13511yescharacteristic
216C2×C4×C7#13511yescharacteristic
217C2×C4×C7#13511yescharacteristic
218C2×C4×C7#13511yescharacteristic
219C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
220C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
221C2×C4×C7#13711yescharacteristic
222C2×C4×C7#13711yescharacteristic
223C2×Dic7—21no—
224C2×Dic7—21no—
225C2×Dic7—21no—
226C2×Dic7—21no—
227C2×Dic7—24no—
228C2×Dic7—21no—
229C2×Dic7—21no—
230C2×Dic7—21no—
231C2×Dic7—21no—
232C2×Dic7—42no—
233C2×Dic7—42no—
234C2×Dic7#10112yes—
235C4×D7—24no—
236C4×D7—24no—
237C4×D7—41no—
238C4×D7—41no—
239C4×D7—41no—
240C4×D7—41no—
241C4×D7—41no—
242C4×D7—41no—
243C4×D7—41no—
244C4×D7—41no—
245Dic14—42no—
246Dic14—42no—
247Dic14—42no—
248Dic14—42no—
249C7×C8—81no—
250C7×C8—81no—
251C7⋊C8—81no—
252C7⋊C8—81no—
253C22×Q8—21no—
254C22×Q8—141no—
255C23×C4—71no—
256C23×C4—71no—
257C23×C4—71no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—141no—
261C22×C8—141no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—72no—
265C4⋊Q8—72no—
266C4⋊Q8—141no—
267C4⋊Q8—141no—
268C4⋊Q8D2812yes—
269C4⋊Q8C22⋊D712yes—
270#125—144no—
271#125—144no—
272C22⋊Q8—144no—
273C22⋊Q8—144no—
274C22⋊Q8—144no—
275C22⋊Q8—144no—
276C4×Q8—144no—
277C4×Q8—144no—
278C4×Q8—144no—
279C4×Q8—144no—
280#117—144no—
281#117—144no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—72no—
284C2×C4⋊C4—142no—
285C2×C4⋊C4—142no—
286C2×C4⋊C4—141no—
287C2×C4⋊C4C4×D712yes—
288C2×C22⋊C4—142no—
289C2×C42—71no—
290C2×C42—71no—
291C2×C42—71no—
292C2×C42—142no—
293C2×C42—141no—
294C2×C42—141no—
295C2×C42—141no—
296C2×C42—141no—
297C2×C42C22×D711yescharacteristic
298C4⋊C8—21no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301C4⋊C8—21no—
302C4⋊C8—141no—
303C4⋊C8—141no—
304C4⋊C8—141no—
305C4⋊C8—141no—
306C22⋊C8—282no—
307C22⋊C8—282no—
308C22×C7#37911yescharacteristic
309C22×C7C2×#10111yescharacteristic
310C22×C7C2×#10111yescharacteristic
311C22×C7#41611yescharacteristic
312C22×C7#41611yescharacteristic
313C22×C7#41711yescharacteristic
314C22×C7#41711yescharacteristic
315C2×D7—22no—
316C2×D7—22no—
317C2×D7—22no—
318C2×D7—41no—
319C2×D7—41no—
320C2×D7—41no—
321C2×D7—41no—
322C4×C7—21no—
323C4×C7—21no—
324C4×C7—44no—
325C4×C7#44911yescharacteristic
326C4×C7#44911yescharacteristic
327C4×C7#44911yescharacteristic
328C4×C7#44911yescharacteristic
329C4×C7#45211yescharacteristic
330C4×C7#45211yescharacteristic
331C4×C7#45211yescharacteristic
332C4×C7#45211yescharacteristic
333Dic7—22no—
334Dic7—44no—
335Dic7—41no—
336Dic7—41no—
337C24—71no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—142no—
345C2×Q8—142no—
346C2×Q8—281no—
347C2×Q8—281no—
348C2×Q8—281no—
349C2×Q8—281no—
350C22×C4—22no—
351C22×C4—71no—
352C22×C4—71no—
353C22×C4—71no—
354C22×C4—142no—
355C22×C4—142no—
356C22×C4—141no—
357C22×C4—141no—
358C22×C4—142no—
359C22×C4—141no—
360C22×C4—141no—
361C22×C4—141no—
362C22×C4—141no—
363C22×C4—141no—
364C22×C4—141no—
365C22×C4—141no—
366C22×C4—141no—
367C22×C4—141no—
368C22×C4—141no—
369C22×C4—141no—
370C22×C4—141no—
371C22×C4C2×C4×D711yescharacteristic
372C22×C4D4×D711yescharacteristic
373C22×C4D4×D711yescharacteristic
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—41no—
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—41no—
380C2×C8—281no—
381C2×C8—281no—
382C2×C8—281no—
383C2×C8—281no—
384C2×C8—281no—
385C2×C8—281no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—74no—
390C4⋊C4—148no—
391C4⋊C4—148no—
392C4⋊C4—142no—
393C4⋊C4—142no—
394C4⋊C4—142no—
395C4⋊C4(C2×D7)⋊C414yes—
396C22⋊C4—148no—
397C42—148no—
398C42—141no—
399C42—141no—
400C42—141no—
401C42—141no—
402C42—141no—
403C42—141no—
404C42C2×D2811yescharacteristic
405C42D4×D711yescharacteristic
406C42D4×D711yescharacteristic
407C42C2×C22⋊D711yescharacteristic
408C2×C7#154411yescharacteristic
409C2×C7#155211yescharacteristic
410C2×C7#155211yescharacteristic
411C2×C7#156111yescharacteristic
412C2×C7#178411yescharacteristic
413C2×C7#178811yescharacteristic
414C2×C7#178811yescharacteristic
415D7—42no—
416C23—72no—
417C23—141no—
418C23—141no—
419C23—141no—
420C23—141no—
421C23—141no—
422C23—141no—
423C23D7×C22⋊C411yescharacteristic
424Q8—42no—
425Q8—42no—
426Q8—42no—
427Q8—42no—
428Q8—282no—
429Q8—282no—
430Q8—282no—
431Q8—282no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—24no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—72no—
438C2×C4—144no—
439C2×C4—144no—
440C2×C4—141no—
441C2×C4—141no—
442C2×C4—141no—
443C2×C4—141no—
444C2×C4—144no—
445C2×C4—141no—
446C2×C4—141no—
447C2×C4—141no—
448C2×C4—141no—
449C2×C4—282no—
450C2×C4—282no—
451C2×C4—281no—
452C2×C4—281no—
453C2×C4—281no—
454C2×C4—281no—
455C2×C4—281no—
456C2×C4—281no—
457C2×C4—281no—
458C2×C4—281no—
459C2×C4D7×C22⋊C411yescharacteristic
460C2×C4#644511yescharacteristic
461C2×C4#644511yescharacteristic
462C2×C4#647411yescharacteristic
463C2×C4#647511yescharacteristic
464C2×C4#647711yescharacteristic
465C2×C4#647811yescharacteristic
466C2×C4#647911yescharacteristic
467C2×C4#647911yescharacteristic
468C2×C4#648111yescharacteristic
469C2×C4#648211yescharacteristic
470C2×C4C2×(C2×D7)⋊C411yescharacteristic
471C2×C4#650011yescharacteristic
472C2×C4#650011yescharacteristic
473C8—81no—
474C8—81no—
475C8—561no—
476C8—561no—
477C7#834511yescharacteristic, complemented, Sylow
478C22—142no—
479C22—142no—
480C22—142no—
481C22—281no—
482C22—281no—
483C22—281no—
484C22—281no—
485C22D7×#10111yescharacteristic
486C22D7×#10111yescharacteristic
487C22#8954311yescharacteristic
488C22#8954411yescharacteristic
489C22#8957511yescharacteristic
490C22#8957611yescharacteristic
491C22#8972711yescharacteristic
492C4—21no—
493C4—21no—
494C4—44no—
495C4—142no—
496C4—281no—
497C4—281no—
498C4—284no—
499C4#8955311yescharacteristic
500C4#8955511yescharacteristic
501C4#8958211yescharacteristic
502C4#8958311yescharacteristic
503C4#8993011yescharacteristic
504C4#8994411yescharacteristic
505C4#8994511yescharacteristic
506C4#8995911yescharacteristic
507C2—282no—
508C2#1172617311yescharacteristic
509C2#1172617811yescharacteristic
510C2#1172617911yescharacteristic
511C2#1172618511yescharacteristic
512C2#1172786711yescharacteristic
513C2#1172795311yescharacteristic
514C2#1172802111yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC2×C7×#332C2
socleC23×C7C2×C22⋊C4
prime radicalC23×D7C22⋊C4
cosocleC2×C42×C7C23
hypercenterC2×#332D7
hypocenterC7#8345
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. C2×C7×#332C2semidirect
3. C2×#89342C2semidirect
6. C2×#89277C2semidirect
7. C2×#89281C2semidirect
95. C2×#332D7semidirect
477. C7#8345semidirect

Maximal subgroups

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

subgroupindex
C2×#904192
C2×C7×#3322
C2×#893422
#117282292
C2×#892772
C2×#892812
#83457