Finite Group Databasebeta

← #13249129

Subgroups — #13249129

Order 1792.

810 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6501C211yesmaximal, characteristic
2C2×C4×C8×D7C211yesmaximal, characteristic, complemented
3C2×C7×D4⋊C8C211yesmaximal, characteristic, complemented
4C2×D4⋊(C7⋊C8)C211yesmaximal, characteristic, complemented
5#11728229C211yesmaximal, characteristic, complemented
6#11725510C211yesmaximal, characteristic, complemented
7#11725461C211yesmaximal, characteristic, complemented
8C2×C4×C7×D4C2211yescharacteristic
9C2×#6501C411yescharacteristic
10C2×C4×C22⋊D7—21no—
11C22×C8×D7—21no—
12C2×C42×D7C2211yescharacteristic
13C2×C7×C4⋊C8C2211yescharacteristic
14C2×C4×C7×C8C2211yescharacteristic
15#89993C411yescharacteristic
16C4×C22⋊Dic7—21no—
17C2×(C2×D7)⋊C8—21no—
18C2×C8×Dic7—21no—
19#89759C411yescharacteristic
20#89745C411yescharacteristic
21#89728—21no—
22#89716—21no—
23C4×C4⋊Dic7C2211yescharacteristic
24C2×C4⋊(C7⋊C8)C2211yescharacteristic
25C2×C4×C7⋊C8C2211yescharacteristic
26C4×C8×D7—22no—
27C4×C8×D7—22no—
28C7×D4⋊C8—22no—
29#89345—21no—
30D4⋊(C7⋊C8)—22no—
31#9072—71nomaximal, Sylow
32C22×C7×D4C2×C411yescharacteristic
33C23×C4×C7—21no—
34C22×C22⋊D7—21no—
35C22×C4×D7C2×C411yescharacteristic
36C22×C4×D7D411yescharacteristic
37C22×C4×D7D411yescharacteristic
38C22×C7×C8—21no—
39C22×C7×C8—21no—
40C4×C7×D4—21no—
41C4×C7×D4—21no—
42C4×C7×D4—21no—
43C4×C7×D4—21no—
44C2×C7×C4⋊C4C2×C411yescharacteristic
45C2×C7×C22⋊C4—21no—
46C2×C42×C7C2311yescharacteristic
47C2×C22⋊Dic7—21no—
48C2×C22⋊Dic7—21no—
49C2×C22⋊Dic7—21no—
50#6501—22no—
51#6501C814yescomplemented
52C4×C22⋊D7—42no—
53C4×C22⋊D7—42no—
54C2×(C2×D7)⋊C4—21no—
55C2×C4⋊Dic7C2×C411yescharacteristic
56C2×C4⋊Dic7C2×C411yescharacteristic
57C2×Dic7⋊C4—21no—
58C2×C4×Dic7—21no—
59C2×C4×Dic7C2×C411yescharacteristic
60C2×C4×Dic7D411yescharacteristic
61C2×C4×Dic7D411yescharacteristic
62C22×C7⋊C8—21no—
63C22×C7⋊C8—21no—
64C2×C8×D7—24no—
65C2×C8×D7—24no—
66C2×C8×D7—24no—
67C42×D7—21no—
68C42×D7—21no—
69C42×D7—21no—
70C42×D7—21no—
71C7×C4⋊C8—21no—
72C7×C4⋊C8—21no—
73C4×C7×C8—21no—
74C4×C7×C8D412yescomplemented
75C7⋊#95—21no—
76C7⋊#95—21no—
77C7⋊#95—21no—
78(C2×D7)⋊C8—42no—
79C8×Dic7—24no—
80C4⋊(C7⋊C8)—21no—
81C4⋊(C7⋊C8)—21no—
82C4×C7⋊C8—21no—
83C4×C7⋊C8D412yescomplemented
84C22×C4×C8—71no—
85C4×#121—71no—
86#1797—71no—
87C2×D4⋊C8—71no—
88C2×D4⋊C8D711yescharacteristic, complemented
89#1279—71no—
90#1279—71no—
91C24×C7—21no—
92C23×D7C22⋊C411yescharacteristic
93C2×C7×D4—21no—
94C2×C7×D4—21no—
95C2×C7×D4—21no—
96C2×C7×D4—21no—
97C2×C7×D4—21no—
98C2×C7×D4C2×C812yescomplemented
99C22×C4×C7—21no—
100C22×C4×C7—41no—
101C22×C4×C7—41no—
102C22×C4×C7—41no—
103C22×C4×C7—41no—
104C22×C4×C7—41no—
105C22×C4×C7—41no—
106C22×C4×C7C22×C411yescharacteristic
107C22×C4×C7C2×D411yescharacteristic
108C22×C4×C7C2×D411yescharacteristic
109C2×C22⋊D7—24no—
110C2×C22⋊D7—42no—
111C2×C22⋊D7—42no—
112C22×Dic7—21no—
113C22×Dic7—21no—
114C22×Dic7C22⋊C411yescharacteristic
115C22×Dic7C22⋊C411yescharacteristic
116C22×Dic7C22⋊C411yescharacteristic
117C2×C4×D7—22no—
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×C4×D7—21no—
128C2×C4×D7—22no—
129C2×C4×D7C2×C812yes—
130C2×C4×D7M1612yes—
131C2×C4×D7D812yes—
132C2×C4×D7SD1612yes—
133C2×C7×C8—22no—
134C2×C7×C8—22no—
135C2×C7×C8—22no—
136C2×C7×C8—41no—
137C2×C7×C8—41no—
138C2×C7×C8—41no—
139C7×C4⋊C4—21no—
140C7×C4⋊C4—21no—
141C7×C22⋊C4—41no—
142C7×C22⋊C4—41no—
143C42×C7C2×D411yescharacteristic
144C42×C7C2×D411yescharacteristic
145C42×C7#4111yescharacteristic
146C42×C7#4111yescharacteristic
147C22⋊Dic7—24no—
148C22⋊Dic7—42no—
149C22⋊Dic7—42no—
150(C2×D7)⋊C4—42no—
151C4⋊Dic7—21no—
152C4⋊Dic7—21no—
153C4⋊Dic7—21no—
154C4⋊Dic7C2×C812yescomplemented
155Dic7⋊C4—42no—
156C4×Dic7—21no—
157C4×Dic7—21no—
158C4×Dic7—21no—
159C4×Dic7—21no—
160C4×Dic7—21no—
161C4×Dic7—21no—
162C4×Dic7—41no—
163C4×Dic7—41no—
164C2×C7⋊C8—22no—
165C2×C7⋊C8—22no—
166C2×C7⋊C8—22no—
167C2×C7⋊C8—41no—
168C2×C7⋊C8—41no—
169C2×C7⋊C8—41no—
170C8×D7—216no—
171C23×C8—141no—
172C2×#121—71no—
173C2×C4×D4—141no—
174C2×C4×D4C2×D711yescharacteristic
175C22×C42—71no—
176C2×C4⋊C8—71no—
177C2×C4⋊C8C2×D711yescharacteristic
178C2×C22⋊C8—141no—
179C2×C4×C8—71no—
180C2×C4×C8—142no—
181C2×C4×C8—141no—
182C2×C4×C8—142no—
183C2×C4×C8C2×D711yescharacteristic
184#390—71no—
185#389—71no—
186#388—141no—
187#386—141no—
188#380—71no—
189C4×C4⋊C4—71no—
190C4×C22⋊C4—141no—
191#336—141no—
192D4⋊C8—22no—
193D4⋊C8—142no—
194C23×C7—22no—
195C23×C7—41no—
196C23×C7—41no—
197C23×C7—41no—
198C23×C7—41no—
199C23×C7—41no—
200C23×C7—41no—
201C23×C7C2×C22⋊C411yescharacteristic
202C22×D7—21no—
203C22×D7—21no—
204C22×D7—21no—
205C22×D7—21no—
206C22×D7C22⋊C812yes—
207C22×D7#10212yes—
208C22×D7#10412yes—
209C7×D4—22no—
210C7×D4—22no—
211C7×D4—41no—
212C7×D4—41no—
213C2×C4×C7—21no—
214C2×C4×C7—21no—
215C2×C4×C7—41no—
216C2×C4×C7—41no—
217C2×C4×C7—41no—
218C2×C4×C7—81no—
219C2×C4×C7—81no—
220C2×C4×C7—81no—
221C2×C4×C7—81no—
222C2×C4×C7C4×D411yescharacteristic
223C2×C4×C7C4×D411yescharacteristic
224C2×C4×C7#12011yescharacteristic
225C2×C4×C7#12111yescharacteristic
226C2×C4×C7#12111yescharacteristic
227C2×C4×C7#12311yescharacteristic
228C2×C4×C7C22×C811yescharacteristic
229C2×C4×C7C2×M1611yescharacteristic
230C2×C4×C7#13111yescharacteristic
231C2×C4×C7#13111yescharacteristic
232C2×C4×C7C2×D811yescharacteristic
233C2×C4×C7C2×SD1611yescharacteristic
234C2×C4×C7#13511yescharacteristic
235C2×C4×C7#13511yescharacteristic
236C22⋊D7—48no—
237C2×Dic7—21no—
238C2×Dic7—21no—
239C2×Dic7—21no—
240C2×Dic7—21no—
241C2×Dic7—21no—
242C2×Dic7—21no—
243C2×Dic7—22no—
244C2×Dic7—41no—
245C2×Dic7—41no—
246C2×Dic7—41no—
247C2×Dic7—41no—
248C2×Dic7—41no—
249C2×Dic7C22⋊C812yes—
250C2×Dic7#10212yes—
251C2×Dic7#10412yes—
252C4×D7—24no—
253C4×D7—24no—
254C4×D7—22no—
255C4×D7—22no—
256C4×D7—22no—
257C4×D7—22no—
258C4×D7—22no—
259C4×D7—22no—
260C4×D7—22no—
261C4×D7—22no—
262C7×C8—24no—
263C7×C8—81no—
264C7⋊C8—24no—
265C7⋊C8—81no—
266C22×D4—141no—
267C22×D4C4×D711yescharacteristic
268C23×C4—21no—
269C23×C4—71no—
270C23×C4—71no—
271C23×C4—71no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—144no—
275C22×C8—144no—
276C22×C8—144no—
277C22×C8—141no—
278C22×C8—141no—
279#121—74no—
280#121—142no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—282no—
286C4×D4—282no—
287C2×C4⋊C4—71no—
288C2×C4⋊C4—71no—
289C2×C4⋊C4—141no—
290C2×C4⋊C4C4×D711yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—141no—
293C2×C22⋊C4—141no—
294C2×C22⋊C4—141no—
295C2×C22⋊C4—141no—
296C2×C42—71no—
297C2×C42—71no—
298C2×C42—71no—
299C2×C42—141no—
300C2×C42—141no—
301C2×C42—141no—
302C2×C42—141no—
303C2×C42—141no—
304C2×C42C22×D711yescharacteristic
305C4⋊C8—21no—
306C4⋊C8—21no—
307C4⋊C8—141no—
308C4⋊C8—141no—
309C22⋊C8—282no—
310C4×C8—21no—
311C4×C8—72no—
312C4×C8—144no—
313C4×C8—141no—
314C4×C8C22⋊D712yescomplemented
315#95—141no—
316#95—141no—
317#95—141no—
318C22×C7—42no—
319C22×C7—42no—
320C22×C7—42no—
321C22×C7—81no—
322C22×C7—81no—
323C22×C7—81no—
324C22×C7—81no—
325C22×C7#38611yescharacteristic
326C22×C7C2×C22⋊C811yescharacteristic
327C22×C7#40811yescharacteristic
328C22×C7C2×#10211yescharacteristic
329C22×C7#41611yescharacteristic
330C22×C7C2×#10411yescharacteristic
331C22×C7C2×#10411yescharacteristic
332C2×D7—22no—
333C2×D7—22no—
334C2×D7—22no—
335C2×D7—22no—
336C2×D7—22no—
337C2×D7—22no—
338C2×D7D4⋊C814yescomplemented
339C4×C7—21no—
340C4×C7—21no—
341C4×C7—81no—
342C4×C7C8×D411yescharacteristic
343C4×C7C8×D411yescharacteristic
344C4×C7#43511yescharacteristic
345C4×C7#43511yescharacteristic
346C4×C7#46511yescharacteristic
347C4×C7#46511yescharacteristic
348C4×C7#46611yescharacteristic
349C4×C7#46611yescharacteristic
350Dic7—22no—
351Dic7—22no—
352Dic7—22no—
353Dic7—42no—
354Dic7—81no—
355C24—21no—
356C24—71no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—144no—
363C2×D4—282no—
364C2×D4—282no—
365C2×D4C8×D712yescomplemented
366C22×C4—21no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—71no—
374C22×C4—71no—
375C22×C4—71no—
376C22×C4—72no—
377C22×C4—72no—
378C22×C4—72no—
379C22×C4—72no—
380C22×C4—142no—
381C22×C4—142no—
382C22×C4—141no—
383C22×C4—141no—
384C22×C4—141no—
385C22×C4—141no—
386C22×C4—141no—
387C22×C4—141no—
388C22×C4—141no—
389C22×C4—141no—
390C22×C4—141no—
391C22×C4—141no—
392C22×C4—141no—
393C22×C4—141no—
394C22×C4C2×C4×D711yescharacteristic
395C22×C4D4×D711yescharacteristic
396C22×C4D4×D711yescharacteristic
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—41no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—1416no—
404C2×C8—142no—
405C2×C8—142no—
406C2×C8—142no—
407C2×C8—281no—
408C2×C8—281no—
409C2×C8—281no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—72no—
413C4⋊C4—141no—
414C4⋊C4—141no—
415C4⋊C4—141no—
416C4⋊C4—282no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—144no—
420C22⋊C4—282no—
421C22⋊C4—282no—
422C22⋊C4—282no—
423C42—141no—
424C42—141no—
425C42—141no—
426C42—141no—
427C42—141no—
428C42—141no—
429C42—281no—
430C42—281no—
431C42#115711yescharacteristic
432C42D4×D711yescharacteristic
433C42#115911yescharacteristic
434C42C2×C22⋊D711yescharacteristic
435C2×C7—82no—
436C2×C7C2×D4⋊C811yescharacteristic
437C2×C7#147611yescharacteristic
438C2×C7#149211yescharacteristic
439C2×C7#149411yescharacteristic
440C2×C7#186911yescharacteristic
441C2×C7#189311yescharacteristic
442C2×C7#189611yescharacteristic
443D7—24no—
444C23—22no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—72no—
452C23—72no—
453C23—72no—
454C23—141no—
455C23—141no—
456C23—141no—
457C23—141no—
458C23D7×C22⋊C411yescharacteristic
459D4—22no—
460D4—22no—
461D4—41no—
462D4—41no—
463D4—288no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—72no—
470C2×C4—72no—
471C2×C4—72no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—144no—
477C2×C4—144no—
478C2×C4—141no—
479C2×C4—141no—
480C2×C4—141no—
481C2×C4—141no—
482C2×C4—141no—
483C2×C4—141no—
484C2×C4—142no—
485C2×C4—142no—
486C2×C4—142no—
487C2×C4—142no—
488C2×C4—142no—
489C2×C4—142no—
490C2×C4—142no—
491C2×C4—142no—
492C2×C4—142no—
493C2×C4—281no—
494C2×C4—281no—
495C2×C4—281no—
496C2×C4—281no—
497C2×C4—281no—
498C2×C4(C22⋊D7)⋊C411yescharacteristic
499C2×C4#644611yescharacteristic
500C2×C4#644711yescharacteristic
501C2×C4C2×C8×D711yescharacteristic
502C2×C4#646411yescharacteristic
503C2×C4D7×M1611yescharacteristic
504C2×C4#647011yescharacteristic
505C2×C4D7×D811yescharacteristic
506C2×C4#647511yescharacteristic
507C2×C4D7×SD1611yescharacteristic
508C2×C4#647911yescharacteristic
509C2×C4C4×C22⋊D711yescharacteristic
510C2×C4#650011yescharacteristic
511C2×C4#650111yescharacteristic
512C8—24no—
513C8—81no—
514C8—144no—
515C8—561no—
516C7#907211yescharacteristic, complemented, Sylow
517C22—42no—
518C22—42no—
519C22—42no—
520C22—74no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—142no—
526C22—142no—
527C22—142no—
528C22—142no—
529C22—142no—
530C22—142no—
531C22D7×C22⋊C811yescharacteristic
532C22#8949911yescharacteristic
533C22D7×#10211yescharacteristic
534C22#8954411yescharacteristic
535C22D7×#10411yescharacteristic
536C22D7×#10411yescharacteristic
537C22#8972811yescharacteristic
538C4—21no—
539C4—21no—
540C4—81no—
541C4—142no—
542C4—142no—
543C4—142no—
544C4—282no—
545C4—561no—
546C4(C22⋊D7)⋊C811yescharacteristic
547C4#8950011yescharacteristic
548C4#8954711yescharacteristic
549C4#8955011yescharacteristic
550C4C8×C22⋊D711yescharacteristic
551C4#8989911yescharacteristic
552C4#8992911yescharacteristic
553C4#8994311yescharacteristic
554C2—82no—
555C2—144no—
556C2D7×D4⋊C811yescharacteristic
557C2#1172591911yescharacteristic
558C2#1172593011yescharacteristic
559C2#1172593111yescharacteristic
560C2#1172771111yescharacteristic
561C2#1172795611yescharacteristic
562C2#1172813611yescharacteristic
subgroupG/H
centerC22×C4D4×D7
commutatorC2×C4×C7C22×C8
FrattiniC2×C42C22×D7
FittingC2×C7×D4⋊C8C2
socleC23×C7C2×C22⋊C4
prime radicalC2×#6501C4
cosocleC2×C42×C7C23
hypercenterC2×D4⋊C8D7
hypocenterC7#9072
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C4×C8×D7C2semidirect
3. C2×C7×D4⋊C8C2semidirect
4. C2×D4⋊(C7⋊C8)C2semidirect
5. #11728229C2semidirect
6. #11725510C2semidirect
7. #11725461C2semidirect
51. #6501C8semidirect
74. C4×C7×C8D4semidirect
83. C4×C7⋊C8D4semidirect
88. C2×D4⋊C8D7semidirect
98. C2×C7×D4C2×C8semidirect
154. C4⋊Dic7C2×C8semidirect
314. C4×C8C22⋊D7semidirect
338. C2×D7D4⋊C8semidirect
365. C2×D4C8×D7semidirect
516. C7#9072semidirect

Maximal subgroups

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

subgroupindex
C4×#65012
C2×C4×C8×D72
C2×C7×D4⋊C82
C2×D4⋊(C7⋊C8)2
#117282292
#117255102
#117254612
#90727