Finite Group Databasebeta

← #13325438

Subgroups — #13325438

Order 1792.

624 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11737409C211yesmaximal, characteristic, complemented
2C4×#6478C211yesmaximal, characteristic
3#11736969C211yesmaximal, characteristic
4C7×#1590C211yesmaximal, characteristic, complemented
5#11728711C211yesmaximal, characteristic, complemented
6#11728654C211yesmaximal, characteristic, complemented
7#11728619C211yesmaximal, characteristic, complemented
8#11726285C211yesmaximal, characteristic, complemented
9#11726271C211yesmaximal, characteristic, complemented
10#11725990C211yesmaximal, characteristic, complemented
11#11725973C211yesmaximal, characteristic, complemented
12#11725927C211yesmaximal, characteristic
13#11725909C211yesmaximal, characteristic, complemented
14C8×Dic28C211yesmaximal, characteristic, complemented
15#11725802C211yesmaximal, characteristic, complemented
16C2×#6478C411yescharacteristic
17C4×Q8×D7C2211yescharacteristic
18C4×#1159C2211yescharacteristic
19C7×#446C2211yescharacteristic
20C4×C7×SD16C2211yescharacteristic
21C7×#436C2211yescharacteristic
22#89936C411yescharacteristic
23#89900—21no—
24#89890—21no—
25C4×#1144C2211yescharacteristic
26#89796C2211yescharacteristic
27C4×#1142C2211yescharacteristic
28#89784C2211yescharacteristic
29#89633C411yescharacteristic
30#89625C411yescharacteristic
31#89609C2211yescharacteristic
32#89607C2211yescharacteristic
33#89605—21no—
34#89602C2211yescharacteristic
35#89602C2211yescharacteristic
36#89600—21no—
37#89574C411yescharacteristic
38#89561C411yescharacteristic
39#89543C411yescharacteristic
40#89529C411yescharacteristic
41#89501—21no—
42#89490—21no—
43#89477—21no—
44#89473—21no—
45C4×Dic28C2211yescharacteristic
46C4×#1131C2211yescharacteristic
47#89457C2211yescharacteristic
48#89457C2211yescharacteristic
49C8×Dic14C2211yescharacteristic
50C8×Dic14C2211yescharacteristic
51C7×#334C2211yescharacteristic
52C7×Q8⋊C8C2211yescharacteristic
53C7×D4⋊C8C2211yescharacteristic
54C7×C82C2211yescharacteristic
55Q8⋊(C7⋊C8)C2211yescharacteristic
56D4⋊(C7⋊C8)C2211yescharacteristic
57#89279C2211yescharacteristic
58#89279C2211yescharacteristic
59#89275C2211yescharacteristic
60#89274C2211yescharacteristic
61#89253C2211yescharacteristic
62#89251C2211yescharacteristic
63#89251C2211yescharacteristic
64#89250C2211yescharacteristic
65#89249C2211yescharacteristic
66#89249C2211yescharacteristic
67#18053—71nomaximal, Sylow
68C2×Q8×D7C2×C411yescharacteristic
69C2×#1159C2×C411yescharacteristic
70C2×C7×SD16C2×C411yescharacteristic
71C2×C7×M16—21no—
72C4×C7×Q8C2311yescharacteristic
73C4×C7×D4C2311yescharacteristic
74Q8×Dic7C2×C411yescharacteristic
75C2×#1144C2×C411yescharacteristic
76D4×Dic7C2×C411yescharacteristic
77C2×#1142C2×C411yescharacteristic
78C4×C22⋊D7—21no—
79C2×C4×Dic7—21no—
80C2×#1136—21no—
81#6478—24no—
82C2×Dic28C2×C411yescharacteristic
83C2×#1131—21no—
84C2×#1131C2×C411yescharacteristic
85C2×#1131C2×C411yescharacteristic
86#6455C2×C411yescharacteristic
87D7×C4⋊C4—21no—
88D7×C4⋊C4C2×C411yescharacteristic
89#6450—21no—
90#6450C2×C411yescharacteristic
91#6450C2×C411yescharacteristic
92(C22⋊D7)⋊C4—21no—
93#6440—21no—
94C42×D7—21no—
95C42×D7C2311yescharacteristic
96C4×Dic14—21no—
97C4×Dic14C2311yescharacteristic
98C4×Dic14C2311yescharacteristic
99C7×#106C2×C411yescharacteristic
100C7×C4⋊C8—21no—
101C7×C4⋊C8C2311yescharacteristic
102C7×C4⋊C8C2311yescharacteristic
103C7×#103C2×C411yescharacteristic
104C7×#102C2×C411yescharacteristic
105C7×C22⋊C8—21no—
106C7×#97—21no—
107C4×C7×C8C2311yescharacteristic
108C4×C7×C8C2311yescharacteristic
109C4×C7×C8C2311yescharacteristic
110#6409C2×C411yescharacteristic
111#6406C2×C411yescharacteristic
112C22⋊(C7⋊C8)—21no—
113(C2×D7)⋊C8—21no—
114(C2×D7)⋊C8—21no—
115(C2×D7)⋊C8D411yescharacteristic
116(C2×D7)⋊C8D411yescharacteristic
117#6392C2×C411yescharacteristic
118#6390C2×C411yescharacteristic
119#6390C2×C411yescharacteristic
120#6389—21no—
121#6389C2×C411yescharacteristic
122#6389C2×C411yescharacteristic
123Dic7⋊C8—21no—
124Dic7⋊C8—21no—
125Dic7⋊C8—21no—
126Dic7⋊C8—21no—
127Dic7⋊C8—21no—
128Dic7⋊C8—21no—
129Dic7⋊C8D411yescharacteristic
130Dic7⋊C8D411yescharacteristic
131C8×Dic7—21no—
132C8×Dic7—21no—
133C8×Dic7—21no—
134C8×Dic7—21no—
135#6384C2×C411yescharacteristic
136#6384C2×C411yescharacteristic
137#6382C2×C411yescharacteristic
138#6381C2×C411yescharacteristic
139C4⋊(C7⋊C8)—21no—
140C4⋊(C7⋊C8)C2311yescharacteristic
141C4⋊(C7⋊C8)C2311yescharacteristic
142#6377—21no—
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145C4×C7⋊C8C2311yescharacteristic
146#2991—71no—
147#2984—71no—
148C4×#137—71no—
149#1592—71no—
150#1590D711yescharacteristic, complemented
151#1588—71no—
152#1587—71no—
153#1584—71no—
154#1583—71no—
155#1579—71no—
156C8×Q16—71no—
157#1569—71no—
158#1488—71no—
159#1487—71no—
160#1453—71no—
161C2×C7×Q8C22×C411yescharacteristic
162C2×C7×D4C22×C411yescharacteristic
163C22×C4×C7—21no—
164C2×C22⋊D7—21no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167Q8×D7—22no—
168Q8×D7—41no—
169#1159—22no—
170#1159—41no—
171C2×C4×D7—21no—
172C2×C4×D7—21no—
173C2×C4×D7C22×C411yescharacteristic
174C2×C4×D7C2×D411yescharacteristic
175C2×C4×D7#4111yescharacteristic
176C2×Dic14—21no—
177C2×Dic14C22×C411yescharacteristic
178C2×Dic14C22×C411yescharacteristic
179C7×SD16—22no—
180C7×M16—81no—
181C2×C7×C8—21no—
182C2×C7×C8—21no—
183C2×C7×C8—21no—
184C2×C7×C8C22×C411yescharacteristic
185C2×C7×C8C22×C411yescharacteristic
186C2×C7×C8C2×D411yescharacteristic
187C2×C7×C8C2×D411yescharacteristic
188C7×C4⋊C4—21no—
189C7×C4⋊C4C22×C411yescharacteristic
190C7×C4⋊C4C22×C411yescharacteristic
191C7×C22⋊C4—21no—
192C42×C7—21no—
193C42×C7C2411yescharacteristic
194C22⋊Dic7—21no—
195#1144—22no—
196#1142—22no—
197(C2×D7)⋊C4—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7C22×C411yescharacteristic
200C4⋊Dic7C22×C411yescharacteristic
201Dic7⋊C4—21no—
202Dic7⋊C4—21no—
203Dic7⋊C4—21no—
204Dic7⋊C4—21no—
205Dic7⋊C4—21no—
206C4×Dic7—21no—
207C4×Dic7—21no—
208C4×Dic7—21no—
209C4×Dic7—21no—
210C4×Dic7—21no—
211C4×Dic7—21no—
212C4×Dic7C22×C411yescharacteristic
213C4×Dic7C2×D411yescharacteristic
214C4×Dic7#4111yescharacteristic
215#1136—81no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8—21no—
219C2×C7⋊C8C22×C411yescharacteristic
220C2×C7⋊C8C22×C411yescharacteristic
221C2×C7⋊C8C2×D411yescharacteristic
222C2×C7⋊C8C2×D411yescharacteristic
223Dic28M1614yescomplemented
224#1131—22no—
225#1131—41no—
226#1131—81no—
227C2×#137—71no—
228C4×#41—71no—
229C2×C4×Q8—71no—
230#446—71no—
231#446—141no—
232#446—141no—
233#446C2×D711yescharacteristic
234C8×Q8—71no—
235C8×Q8—71no—
236C8×Q8—71no—
237C8×Q8—71no—
238#441—71no—
239#441—71no—
240#440—71no—
241#440—71no—
242C4×Q16—71no—
243C4×Q16—71no—
244C4×SD16—71no—
245C4×SD16C2×D711yescharacteristic
246#436—71no—
247#436—141no—
248#436—141no—
249#436C2×D711yescharacteristic
250#432—71no—
251#432—141no—
252#431—71no—
253#431—71no—
254#431—141no—
255#431—141no—
256#428—71no—
257#423—71no—
258#423—141no—
259#419—71no—
260#417—71no—
261C4×M16—71no—
262#335—71no—
263#335—71no—
264#334—71no—
265#334C2×D711yescharacteristic
266Q8⋊C8—71no—
267Q8⋊C8—71no—
268Q8⋊C8—71no—
269Q8⋊C8—71no—
270Q8⋊C8—71no—
271Q8⋊C8C2×D711yescharacteristic
272D4⋊C8—71no—
273D4⋊C8C2×D711yescharacteristic
274#322—71no—
275#322—71no—
276#322—71no—
277C82C2×D711yescharacteristic
278C23×C7—21no—
279C22×D7C4×D411yescharacteristic
280C7×Q8—21no—
281C7×Q8—21no—
282C7×D4—21no—
283C7×D4—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—41no—
288C2×C4×C7—41no—
289C2×C4×C7C23×C411yescharacteristic
290C2×C4×C7C22×D411yescharacteristic
291C2×C4×C7C2×#4111yescharacteristic
292C22⋊D7—42no—
293C2×Dic7—21no—
294C2×Dic7—21no—
295C2×Dic7—21no—
296C2×Dic7—21no—
297C2×Dic7—42no—
298C2×Dic7—42no—
299C2×Dic7C4×D411yescharacteristic
300C2×Dic7C4×D411yescharacteristic
301C2×Dic7C4×D411yescharacteristic
302C4×D7—21no—
303C4×D7—21no—
304C4×D7—21no—
305C4×D7—21no—
306C4×D7—41no—
307C4×D7—42no—
308C4×D7—42no—
309Dic14—21no—
310Dic14—21no—
311Dic14—42no—
312Dic14C2×M1612yes—
313Dic14C2×M1612yes—
314C7×C8—21no—
315C7×C8—21no—
316C7×C8—21no—
317C7×C8—41no—
318C7×C8—41no—
319C7×C8—41no—
320C7×C8C2×M1612yes—
321C7⋊C8—21no—
322C7⋊C8—21no—
323C7⋊C8—21no—
324C7⋊C8—21no—
325C7⋊C8—41no—
326C7⋊C8—41no—
327C7⋊C8—41no—
328C2×#41—71no—
329C22×Q8—71no—
330#137—144no—
331C2×Q16—71no—
332C2×Q16—71no—
333C2×SD16—71no—
334C2×SD16C4×D711yescharacteristic
335C2×M16—21no—
336C2×M16—71no—
337C2×M16—71no—
338C2×M16—141no—
339C2×M16—141no—
340C4×Q8—71no—
341C4×Q8—71no—
342C4×Q8—71no—
343C4×Q8—71no—
344C4×Q8—71no—
345C4×Q8—141no—
346C4×Q8—141no—
347C4×Q8C22×D711yescharacteristic
348C4×D4—71no—
349C4×D4—141no—
350C4×D4—141no—
351C4×D4C22×D711yescharacteristic
352#117—71no—
353#117—141no—
354C2×C4⋊C4—71no—
355C2×C4⋊C4—141no—
356C2×C42—71no—
357C2×C42—141no—
358C2×C42—141no—
359#107—71no—
360#107—71no—
361#106—71no—
362#106C4×D711yescharacteristic
363C4⋊C8—21no—
364C4⋊C8—71no—
365C4⋊C8—71no—
366C4⋊C8—71no—
367C4⋊C8—71no—
368C4⋊C8—141no—
369C4⋊C8—141no—
370C4⋊C8—141no—
371C4⋊C8—141no—
372C4⋊C8—141no—
373C4⋊C8—141no—
374C4⋊C8—141no—
375C4⋊C8C22×D711yescharacteristic
376C4⋊C8C22×D711yescharacteristic
377#103—71no—
378#103—71no—
379#103—71no—
380#103—71no—
381#103—71no—
382#103C4×D711yescharacteristic
383#102—71no—
384#102C4×D711yescharacteristic
385C22⋊C8—21no—
386C22⋊C8—71no—
387C22⋊C8—71no—
388C22⋊C8—141no—
389C22⋊C8—141no—
390C22⋊C8—141no—
391#97—21no—
392#97—71no—
393#97—71no—
394#97—141no—
395#97—141no—
396C4×C8—71no—
397C4×C8—71no—
398C4×C8—71no—
399C4×C8—141no—
400C4×C8—141no—
401C4×C8—141no—
402C4×C8—141no—
403C4×C8C22×D711yescharacteristic
404C4×C8C22×D711yescharacteristic
405C4×C8C22×D711yescharacteristic
406C22×C7—41no—
407C22×C7—41no—
408C22×C7—41no—
409C22×C7C2×C4×D411yescharacteristic
410C2×D7—21no—
411C2×D7—21no—
412C2×D7—21no—
413C4×C7—21no—
414C4×C7—41no—
415C4×C7—41no—
416C4×C7—41no—
417C4×C7C22×M1611yescharacteristic
418C4×C7#56811yescharacteristic
419C4×C7#57711yescharacteristic
420C4×C7#57811yescharacteristic
421Dic7—22no—
422Dic7—22no—
423Dic7—21no—
424Dic7—21no—
425Dic7—21no—
426Dic7—41no—
427Dic7—41no—
428#41—142no—
429#41—281no—
430C2×Q8—71no—
431C2×Q8—71no—
432C2×Q8—141no—
433C2×Q8—142no—
434C2×Q8—281no—
435C2×Q8C2×C4×D711yescharacteristic
436C2×D4—141no—
437C2×D4C2×C4×D711yescharacteristic
438C22×C4—21no—
439C22×C4—71no—
440C22×C4—71no—
441C22×C4—71no—
442C22×C4—141no—
443C22×C4—141no—
444C22×C4—141no—
445C22×C4—141no—
446Q16—74no—
447Q16—142no—
448SD16—22no—
449SD16—142no—
450M16—81no—
451M16—142no—
452M16—281no—
453M16—561no—
454M16—561no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—71no—
459C2×C8—71no—
460C2×C8—71no—
461C2×C8—71no—
462C2×C8—141no—
463C2×C8—141no—
464C2×C8—141no—
465C2×C8C2×C4×D711yescharacteristic
466C2×C8C2×C4×D711yescharacteristic
467C2×C8D4×D711yescharacteristic
468C2×C8D4×D711yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—71no—
471C4⋊C4—71no—
472C4⋊C4—141no—
473C4⋊C4—141no—
474C4⋊C4—141no—
475C4⋊C4—141no—
476C4⋊C4—141no—
477C4⋊C4—141no—
478C4⋊C4C2×C4×D711yescharacteristic
479C4⋊C4C2×C4×D711yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—141no—
482C22⋊C4—141no—
483C42—21no—
484C42—71no—
485C42—71no—
486C42—71no—
487C42—141no—
488C42—141no—
489C42—141no—
490C42—141no—
491C42—141no—
492C42—141no—
493C42C23×D711yescharacteristic
494C2×C7—81no—
495C2×C7D4×M1611yescharacteristic
496C2×C7#294711yescharacteristic
497C2×C7#295511yescharacteristic
498D7—41no—
499C23—21no—
500C23—71no—
501Q8—21no—
502Q8—21no—
503Q8—72no—
504Q8—72no—
505Q8—141no—
506Q8—141no—
507Q8—282no—
508D4—21no—
509D4—21no—
510D4—282no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—71no—
517C2×C4—71no—
518C2×C4—71no—
519C2×C4—141no—
520C2×C4—141no—
521C2×C4—141no—
522C2×C4—141no—
523C2×C4—141no—
524C2×C4—141no—
525C2×C4—141no—
526C2×C4—141no—
527C2×C4—281no—
528C2×C4—282no—
529C2×C4—282no—
530C2×C4—282no—
531C2×C4—282no—
532C2×C4C22×C4×D711yescharacteristic
533C2×C4C2×D4×D711yescharacteristic
534C2×C4D7×#4111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—141no—
542C8—141no—
543C8—141no—
544C8—141no—
545C8—281no—
546C8—281no—
547C8—281no—
548C8D7×M1612yes—
549C7#1805311yescharacteristic, complemented, Sylow
550C22—41no—
551C22—41no—
552C22—41no—
553C22—141no—
554C22—141no—
555C22—141no—
556C22C4×D4×D711yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—141no—
562C4—141no—
563C4—142no—
564C4—142no—
565C4—141no—
566C4—281no—
567C4—281no—
568C4C2×D7×M1611yescharacteristic
569C4#9044111yescharacteristic
570C4#9045311yescharacteristic
571C4#9046211yescharacteristic
572C2—81no—
573C2—281no—
574C2#1173698511yescharacteristic
575C2#1173709311yescharacteristic
576C2#1173733311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1590C2
socleC22×C7C2×C4×D4
prime radicalC2×#1159C2×C4
cosocleC42×C7C24
hypercenter#1590D7
hypocenterC7#18053
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
1. #11737409C2semidirect
4. C7×#1590C2semidirect
5. #11728711C2semidirect
6. #11728654C2semidirect
7. #11728619C2semidirect
8. #11726285C2semidirect
9. #11726271C2semidirect
10. #11725990C2semidirect
11. #11725973C2semidirect
13. #11725909C2semidirect
14. C8×Dic28C2semidirect
15. #11725802C2semidirect
150. #1590D7semidirect
223. Dic28M16semidirect
549. C7#18053semidirect

Maximal subgroups

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

subgroupindex
#117374092
C4×#64782
#117369692
C7×#15902
#117287112
#117286542
#117286192
#117262852
#117262712
#117259902
#117259732
#117259272
#117259092
C8×Dic282
#117258022
#180537