Finite Group Databasebeta

← #13325203

Subgroups — #13325203

Order 1792.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11736744C211yesmaximal, characteristic
2#11736497C211yesmaximal, characteristic, complemented
3#11736462C211yesmaximal, characteristic, complemented
4C7×#1571C211yesmaximal, characteristic, complemented
5#11728498C211yesmaximal, characteristic, complemented
6#11728253C211yesmaximal, characteristic, complemented
7#11728179C211yesmaximal, characteristic, complemented
8#11726319C211yesmaximal, characteristic, complemented
9#11726317C211yesmaximal, characteristic, complemented
10#11726316C211yesmaximal, characteristic, complemented
11#11726316C211yesmaximal, characteristic, complemented
12#11726314C211yesmaximal, characteristic, complemented
13#11726313C211yesmaximal, characteristic, complemented
14#11726312C211yesmaximal, characteristic, complemented
15#11726311C211yesmaximal, characteristic, complemented
16#90170C2211yescharacteristic
17C4×#1157C2211yescharacteristic
18C7×#431C2211yescharacteristic
19C7×#423C2211yescharacteristic
20C2×C7×C4⋊C8C2211yescharacteristic
21#89900—21no—
22#89900—21no—
23#89883—21no—
24C8×C22⋊D7—21no—
25#89697C2211yescharacteristic
26#89697C2211yescharacteristic
27#89619C411yescharacteristic
28#89617C411yescharacteristic
29#89616C411yescharacteristic
30#89612—21no—
31#89611—21no—
32#89610C2211yescharacteristic
33#89610C2211yescharacteristic
34#89610C2211yescharacteristic
35#89609—21no—
36#89606C2211yescharacteristic
37#89605—21no—
38#89603C2211yescharacteristic
39#89602C2211yescharacteristic
40#89602C2211yescharacteristic
41#89602C2211yescharacteristic
42#89601C411yescharacteristic
43#89509C411yescharacteristic
44#89506C411yescharacteristic
45#89505C411yescharacteristic
46#89495C411yescharacteristic
47C4×Dic28C2211yescharacteristic
48C4×D56C2211yescharacteristic
49C4×#1132C2211yescharacteristic
50C4×#1132C2211yescharacteristic
51C7×#335C2211yescharacteristic
52C7×#335C2211yescharacteristic
53C7×#335C2211yescharacteristic
54C7×#335C2211yescharacteristic
55#89279C2211yescharacteristic
56#89279C2211yescharacteristic
57#89279C2211yescharacteristic
58#89279C2211yescharacteristic
59#89278C2211yescharacteristic
60#89278C2211yescharacteristic
61#89278C2211yescharacteristic
62#89278C2211yescharacteristic
63#89250C2211yescharacteristic
64#89249C2211yescharacteristic
65#89249C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#18033—71nomaximal, Sylow
68C2×#1157C2×C411yescharacteristic
69C2×C7×M16—21no—
70C22×C7×C8—21no—
71C2×C42×C7C2311yescharacteristic
72#6493C2×C411yescharacteristic
73#6492—21no—
74C4×C22⋊D7—21no—
75C4×C22⋊D7—21no—
76C4×C22⋊D7—21no—
77#6489C2×C411yescharacteristic
78#6487C2×C411yescharacteristic
79C2×Dic28C2×C411yescharacteristic
80C2×D56C2×C411yescharacteristic
81C2×#1132C2×C411yescharacteristic
82C2×#1132C2×C411yescharacteristic
83C2×#1131—21no—
84C2×#1131—21no—
85C2×#1131—21no—
86C2×C8×D7—21no—
87#6439—21no—
88#6438C2×C411yescharacteristic
89C4×D28C2×C411yescharacteristic
90C4×D28C2311yescharacteristic
91C4×D28C2311yescharacteristic
92#6435—21no—
93#6435—21no—
94C42×D7—21no—
95#6433C2×C411yescharacteristic
96C4×Dic14C2×C411yescharacteristic
97C4×Dic14C2311yescharacteristic
98C4×Dic14C2311yescharacteristic
99C7×C4⋊C8—21no—
100C7×C4⋊C8—21no—
101C7×C4⋊C8C2×C411yescharacteristic
102C7×C4⋊C8C2×C411yescharacteristic
103C7×C4⋊C8C2311yescharacteristic
104C7×C4⋊C8C2311yescharacteristic
105C7×C4⋊C8C2311yescharacteristic
106C7×C4⋊C8C2311yescharacteristic
107C7×C22⋊C8C2×C411yescharacteristic
108C7×C22⋊C8C2×C411yescharacteristic
109C4×C7×C8C2311yescharacteristic
110C4×C7×C8C2311yescharacteristic
111C22⋊(C7⋊C8)—21no—
112C22⋊(C7⋊C8)D411yescharacteristic
113C22⋊(C7⋊C8)D411yescharacteristic
114#6395C2×C411yescharacteristic
115#6395C2×C411yescharacteristic
116#6395C2×C411yescharacteristic
117#6395C2×C411yescharacteristic
118(C2×D7)⋊C8—21no—
119(C2×D7)⋊C8—21no—
120(C2×D7)⋊C8—21no—
121(C2×D7)⋊C8—21no—
122#6392C2×C411yescharacteristic
123#6392C2×C411yescharacteristic
124#6391C2×C411yescharacteristic
125#6391C2×C411yescharacteristic
126#6390C2×C411yescharacteristic
127#6390C2×C411yescharacteristic
128#6390C2×C411yescharacteristic
129#6390C2×C411yescharacteristic
130#6389—21no—
131Dic7⋊C8—21no—
132Dic7⋊C8—21no—
133Dic7⋊C8—21no—
134Dic7⋊C8—21no—
135C8×Dic7—21no—
136C8×Dic7—21no—
137C8×Dic7—21no—
138C4⋊(C7⋊C8)—21no—
139C4⋊(C7⋊C8)D411yescharacteristic
140C4⋊(C7⋊C8)D411yescharacteristic
141C4×C7⋊C8C2311yescharacteristic
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3102—71no—
146#2994—71no—
147#2991—71no—
148#1592—71no—
149#1589—71no—
150#1588—71no—
151#1588—71no—
152#1584—71no—
153#1581—71no—
154SD16⋊C8—71no—
155C8×Q16—71no—
156#1571D711yescharacteristic, complemented
157#1495—71no—
158#1477—71no—
159#1454—71no—
160C22×C4×C7C22×C411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7#4111yescharacteristic
163C2×C22⋊D7—21no—
164C2×C22⋊D7—21no—
165#1157—22no—
166#1157—41no—
167C2×D28C22×C411yescharacteristic
168C2×D28C22×C411yescharacteristic
169C2×C4×D7—21no—
170C2×C4×D7—21no—
171C2×C4×D7—21no—
172C2×C4×D7—21no—
173C2×Dic14C22×C411yescharacteristic
174C2×Dic14C22×C411yescharacteristic
175C7×M16—81no—
176C2×C7×C8—21no—
177C2×C7×C8—21no—
178C2×C7×C8—21no—
179C2×C7×C8—21no—
180C2×C7×C8—81no—
181C2×C7×C8C22×C411yescharacteristic
182C2×C7×C8C22×C411yescharacteristic
183C2×C7×C8C22×C411yescharacteristic
184C2×C7×C8C22×C411yescharacteristic
185C42×C7C22×C411yescharacteristic
186C42×C7C2×D411yescharacteristic
187C42×C7#4111yescharacteristic
188C42×C7C2411yescharacteristic
189C22⋊Dic7—21no—
190C22⋊Dic7—21no—
191(C2×D7)⋊C4—21no—
192(C2×D7)⋊C4—21no—
193(C2×D7)⋊C4—21no—
194(C2×D7)⋊C4—21no—
195(C2×D7)⋊C4—21no—
196(C2×D7)⋊C4—21no—
197C4⋊Dic7C22×C411yescharacteristic
198C4⋊Dic7C22×C411yescharacteristic
199C4⋊Dic7C22×C411yescharacteristic
200C4⋊Dic7C22×C411yescharacteristic
201Dic7⋊C4—21no—
202Dic7⋊C4—21no—
203Dic7⋊C4—21no—
204Dic7⋊C4—21no—
205Dic7⋊C4—21no—
206Dic7⋊C4—21no—
207C4×Dic7—21no—
208C4×Dic7—21no—
209C4×Dic7—21no—
210C4×Dic7—21no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8C2×D411yescharacteristic
214C2×C7⋊C8C2×D411yescharacteristic
215C2×C7⋊C8C2×D411yescharacteristic
216C2×C7⋊C8C2×D411yescharacteristic
217Dic28—22no—
218D56—41no—
219#1132—22no—
220#1132—41no—
221#1131—81no—
222#1131—81no—
223#1131—81no—
224C8×D7—81no—
225#529—71no—
226C4×#41—71no—
227#485—71no—
228#482—71no—
229#479—71no—
230#478—71no—
231#464—71no—
232#463—71no—
233#452—71no—
234#449—71no—
235#446—71no—
236C8×Q8—71no—
237C8×Q8—71no—
238C8×Q8—71no—
239C4×Q16—71no—
240C4×SD16—71no—
241C4×SD16—71no—
242C4×D8—71no—
243#436—71no—
244#436—71no—
245#436—71no—
246#436—141no—
247#436—141no—
248#435—141no—
249C8×D4—71no—
250C8×D4—141no—
251#433—141no—
252#431—71no—
253#431—71no—
254#431—141no—
255#431C2×D711yescharacteristic
256#424—141no—
257#423—141no—
258#423C2×D711yescharacteristic
259C2×C4⋊C8C2×D711yescharacteristic
260#335C2×D711yescharacteristic
261#335C2×D711yescharacteristic
262#335C2×D711yescharacteristic
263#335C2×D711yescharacteristic
264Q8⋊C8—71no—
265Q8⋊C8—71no—
266Q8⋊C8—71no—
267Q8⋊C8—71no—
268D4⋊C8—71no—
269D4⋊C8—71no—
270D4⋊C8—71no—
271D4⋊C8—71no—
272#322—71no—
273#322—71no—
274#322—71no—
275C82—71no—
276C23×C7C4×D411yescharacteristic
277C22×D7—21no—
278C22×D7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—41no—
284C2×C4×C7C4×D411yescharacteristic
285C2×C4×C7C4×D411yescharacteristic
286C2×C4×C7C4×D411yescharacteristic
287C2×C4×C7C23×C411yescharacteristic
288C2×C4×C7C22×D411yescharacteristic
289C2×C4×C7C2×#4111yescharacteristic
290C22⋊D7—42no—
291C22⋊D7—42no—
292C2×Dic7—21no—
293C2×Dic7—21no—
294C2×Dic7—21no—
295C2×Dic7—21no—
296C2×Dic7—21no—
297C2×Dic7—21no—
298D28—21no—
299D28—21no—
300D28—21no—
301D28—21no—
302C4×D7—42no—
303C4×D7—42no—
304C4×D7—41no—
305C4×D7—41no—
306C4×D7—41no—
307C4×D7—41no—
308Dic14—21no—
309Dic14—21no—
310Dic14—21no—
311Dic14#13112yes—
312C7×C8—21no—
313C7×C8—21no—
314C7×C8—21no—
315C7×C8—21no—
316C7×C8—41no—
317C7×C8—41no—
318C7×C8—41no—
319C7×C8—41no—
320C7⋊C8—21no—
321C7⋊C8—21no—
322C7⋊C8—21no—
323C7⋊C8—21no—
324C7⋊C8—41no—
325C7⋊C8—41no—
326C2×#41—71no—
327C2×Q16—71no—
328C2×SD16—71no—
329C2×SD16—71no—
330C2×D8—71no—
331C2×M16—21no—
332C2×M16—141no—
333C2×M16—141no—
334C2×M16—141no—
335C22×C8—21no—
336C22×C8—141no—
337#126—141no—
338#125—71no—
339#124—71no—
340#123—141no—
341C22⋊Q8—71no—
342#121—71no—
343C4×Q8—71no—
344C4×Q8—71no—
345C4×Q8—71no—
346C4×D4—71no—
347C4×D4—71no—
348C4×D4—71no—
349C4×D4—141no—
350C4×D4—141no—
351C4×D4—141no—
352#117—71no—
353#117—141no—
354#117—141no—
355C2×C42—141no—
356C2×C42C22×D711yescharacteristic
357#107—71no—
358#107—71no—
359#106—71no—
360#106—71no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8—71no—
364C4⋊C8—71no—
365C4⋊C8—141no—
366C4⋊C8—141no—
367C4⋊C8—141no—
368C4⋊C8—141no—
369C4⋊C8—141no—
370C4⋊C8C4×D711yescharacteristic
371C4⋊C8C4×D711yescharacteristic
372C4⋊C8C22×D711yescharacteristic
373C4⋊C8C22×D711yescharacteristic
374C4⋊C8C22×D711yescharacteristic
375C4⋊C8C22×D711yescharacteristic
376#103—71no—
377#103—71no—
378#103—71no—
379#103—71no—
380#102—71no—
381#102—71no—
382#102—71no—
383#102—71no—
384C22⋊C8—71no—
385C22⋊C8—71no—
386C22⋊C8—141no—
387C22⋊C8—141no—
388C22⋊C8—141no—
389C22⋊C8—141no—
390C22⋊C8—141no—
391C22⋊C8C4×D711yescharacteristic
392C22⋊C8C4×D711yescharacteristic
393#97—141no—
394C4×C8—71no—
395C4×C8—71no—
396C4×C8—71no—
397C4×C8—71no—
398C4×C8—141no—
399C4×C8—141no—
400C4×C8—141no—
401C4×C8C22×D711yescharacteristic
402C4×C8C22×D711yescharacteristic
403C22×C7—21no—
404C22×C7—21no—
405C22×C7—21no—
406C22×C7C2×C4×D411yescharacteristic
407C2×D7—41no—
408C2×D7—41no—
409C2×D7—41no—
410C2×D7—41no—
411C2×D7—41no—
412C2×D7—41no—
413C4×C7—21no—
414C4×C7—21no—
415C4×C7—21no—
416C4×C7—21no—
417C4×C7C2×#13111yescharacteristic
418C4×C7#56811yescharacteristic
419C4×C7#57611yescharacteristic
420C4×C7#57811yescharacteristic
421Dic7—22no—
422Dic7—41no—
423Dic7—41no—
424Dic7—41no—
425Dic7—41no—
426Dic7—41no—
427#41—142no—
428#41—281no—
429C2×Q8—71no—
430C2×Q8—71no—
431C2×D4—71no—
432C2×D4—71no—
433C2×D4—141no—
434C2×D4—141no—
435C22×C4—141no—
436C22×C4—141no—
437C22×C4—141no—
438C22×C4—141no—
439C22×C4C2×C4×D711yescharacteristic
440C22×C4D4×D711yescharacteristic
441C22×C4#116111yescharacteristic
442Q16—142no—
443SD16—142no—
444SD16—281no—
445D8—281no—
446M16—81no—
447M16—561no—
448M16—561no—
449M16—561no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—71no—
455C2×C8—71no—
456C2×C8—71no—
457C2×C8—71no—
458C2×C8—81no—
459C2×C8—141no—
460C2×C8—141no—
461C2×C8—561no—
462C2×C8C2×C4×D711yescharacteristic
463C2×C8C2×C4×D711yescharacteristic
464C2×C8C2×C4×D711yescharacteristic
465C2×C8C2×C4×D711yescharacteristic
466C4⋊C4—71no—
467C4⋊C4—71no—
468C4⋊C4—71no—
469C4⋊C4—71no—
470C4⋊C4—141no—
471C4⋊C4—141no—
472C4⋊C4—141no—
473C4⋊C4—141no—
474C4⋊C4—141no—
475C4⋊C4—141no—
476C22⋊C4—141no—
477C22⋊C4—141no—
478C22⋊C4—141no—
479C22⋊C4—141no—
480C22⋊C4—141no—
481C22⋊C4—141no—
482C22⋊C4—141no—
483C22⋊C4—141no—
484C42—141no—
485C42—141no—
486C42—141no—
487C42—141no—
488C42C2×C4×D711yescharacteristic
489C42D4×D711yescharacteristic
490C42#116111yescharacteristic
491C42C23×D711yescharacteristic
492C2×C7—41no—
493C2×C7#293311yescharacteristic
494C2×C7#295111yescharacteristic
495C2×C7#295511yescharacteristic
496D7—81no—
497D7—81no—
498C23—141no—
499C23—141no—
500C23#645611yescharacteristic
501Q8—72no—
502Q8—141no—
503Q8—141no—
504Q8—141no—
505D4—141no—
506D4—141no—
507D4—141no—
508D4—141no—
509D4—282no—
510D4—282no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—141no—
517C2×C4—141no—
518C2×C4—141no—
519C2×C4—141no—
520C2×C4—141no—
521C2×C4—141no—
522C2×C4—282no—
523C2×C4—282no—
524C2×C4—281no—
525C2×C4—281no—
526C2×C4—281no—
527C2×C4—281no—
528C2×C4#645611yescharacteristic
529C2×C4#645611yescharacteristic
530C2×C4#645611yescharacteristic
531C2×C4C22×C4×D711yescharacteristic
532C2×C4C2×D4×D711yescharacteristic
533C2×C4C2×#116111yescharacteristic
534C8—21no—
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—141no—
543C8—141no—
544C8—141no—
545C8—141no—
546C8—281no—
547C8—281no—
548C7#1803311yescharacteristic, complemented, Sylow
549C22—21no—
550C22—21no—
551C22—21no—
552C22—281no—
553C22—281no—
554C22—281no—
555C22—281no—
556C22—281no—
557C22—281no—
558C22C2×#645611yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—142no—
564C4—281no—
565C4—281no—
566C4—281no—
567C4—281no—
568C4—281no—
569C4D7×#13111yescharacteristic
570C4#9044111yescharacteristic
571C4#9044811yescharacteristic
572C4#9045711yescharacteristic
573C2—41no—
574C2—561no—
575C2—561no—
576C2#1173652011yescharacteristic
577C2#1173658111yescharacteristic
578C2#1173670211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1571C2
socleC22×C7C2×C4×D4
prime radical#89506C4
cosocleC42×C7C24
hypercenter#1571D7
hypocenterC7#18033
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
2. #11736497C2semidirect
3. #11736462C2semidirect
4. C7×#1571C2semidirect
5. #11728498C2semidirect
6. #11728253C2semidirect
7. #11728179C2semidirect
8. #11726319C2semidirect
9. #11726317C2semidirect
10. #11726316C2semidirect
11. #11726316C2semidirect
12. #11726314C2semidirect
13. #11726313C2semidirect
14. #11726312C2semidirect
15. #11726311C2semidirect
156. #1571D7semidirect
548. C7#18033semidirect

Maximal subgroups

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

subgroupindex
#117367442
#117364972
#117364622
C7×#15712
#117284982
#117282532
#117281792
#117263192
#117263172
#117263162
#117263142
#117263132
#117263122
#117263112
#180337