Finite Group Databasebeta

← #13371429

Subgroups — #13371429

Order 1792.

778 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
1C2×#89632C211yesmaximal, characteristic
2#11733425C211yesmaximal, characteristic
3#11733424C211yesmaximal, characteristic
4C7×#1941C211yesmaximal, characteristic, complemented
5#11728331C211yesmaximal, characteristic
6#11728314C211yesmaximal, characteristic, complemented
7Dic7×#106C211yesmaximal, characteristic, complemented
8C8×(C2×D7)⋊C4C211yesmaximal, characteristic
9C4×#6391C211yesmaximal, characteristic, complemented
10#11727357C211yesmaximal, characteristic, complemented
11#11727354C211yesmaximal, characteristic, complemented
12#11726627C211yesmaximal, characteristic
13#11726575C211yesmaximal, characteristic, complemented
14#11726569C211yesmaximal, characteristic, complemented
15#11726567C211yesmaximal, characteristic
16C22×C8×D7C2211yescharacteristic
17C2×#6455C2211yescharacteristic
18C2×#6455C2211yescharacteristic
19C2×C7×#106C2211yescharacteristic
20C2×C7×#106C2211yescharacteristic
21C2×C4×C7×C8C2211yescharacteristic
22C7×#389C2211yescharacteristic
23C7×#389C2211yescharacteristic
24C2×(C2×D7)⋊C8C2211yescharacteristic
25C2×#6391C2211yescharacteristic
26C2×#6391C2211yescharacteristic
27C2×C8×Dic7C2211yescharacteristic
28#89762—21no—
29#89762—21no—
30#89759C2211yescharacteristic
31#89759C2211yescharacteristic
32#89757C2211yescharacteristic
33#89757C2211yescharacteristic
34#89749—21no—
35C4⋊C4×Dic7—21no—
36C4⋊C4×Dic7C2211yescharacteristic
37C4⋊C4×Dic7C2211yescharacteristic
38C2×#6381C2211yescharacteristic
39C2×#6381C2211yescharacteristic
40C4×(C2×D7)⋊C4C2211yescharacteristic
41C4×C4⋊Dic7C2211yescharacteristic
42C4×C4⋊Dic7C2211yescharacteristic
43#89632C418yescomplemented
44#89442—21no—
45#89442—21no—
46#89423—21no—
47#89420—21no—
48C7×#340C2211yescharacteristic
49C7×#340C2211yescharacteristic
50#89346C2211yescharacteristic
51#89346C2211yescharacteristic
52#89345C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89319C2211yescharacteristic
60#22610—71nomaximal, Sylow
61C22×C4×D7C2311yescharacteristic
62C22×C7×C8C2311yescharacteristic
63C22×C7×C8C2311yescharacteristic
64C2×C7×C4⋊C4—21no—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4C2311yescharacteristic
67C2×C7×C4⋊C4C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C42×C7C2311yescharacteristic
71C2×(C2×D7)⋊C4—21no—
72C2×(C2×D7)⋊C4—21no—
73C2×(C2×D7)⋊C4—21no—
74C2×(C2×D7)⋊C4—21no—
75C2×(C2×D7)⋊C4D411yescharacteristic
76C2×(C2×D7)⋊C4D411yescharacteristic
77C2×C4⋊Dic7—21no—
78C2×C4⋊Dic7—21no—
79C2×C4⋊Dic7C2311yescharacteristic
80C2×C4⋊Dic7C2311yescharacteristic
81C2×C4⋊Dic7C2311yescharacteristic
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4×Dic7—21no—
84C2×C4×Dic7—21no—
85C2×C4×Dic7—21no—
86C2×C4×Dic7—21no—
87C2×C4×Dic7—21no—
88C2×C4×Dic7—21no—
89C2×C4×Dic7C2311yescharacteristic
90C22×C7⋊C8C2311yescharacteristic
91C22×C7⋊C8C2311yescharacteristic
92C2×C8×D7—22no—
93C2×C8×D7—22no—
94C2×C8×D7C2×C414yes—
95#6455—22no—
96#6455—22no—
97#6455C2×C414yes—
98#6455C2×C414yes—
99C7×#106—22no—
100C7×#106C2×C414yes—
101C4×C7×C8—22no—
102C7×#95—21no—
103C7×#95—21no—
104C7⋊#95—21no—
105C7⋊#95—21no—
106C7⋊#95—21no—
107C7⋊#95—21no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95D411yescharacteristic
113C7⋊#95D411yescharacteristic
114(C2×D7)⋊C8—22no—
115#6391—22no—
116#6391C2×C414yes—
117C8×Dic7—22no—
118#6381C2×C414yes—
119#6381C2×C414yes—
120C2×#427—71no—
121#2347—71no—
122#2346—71no—
123#1941—71no—
124#1941D711yescharacteristic, complemented
125#1921—71no—
126#1921—71no—
127#1918—71no—
128#1918—71no—
129#1825—71no—
130#1825—71no—
131#1807—71no—
132C4×#106—71no—
133C4×#106—71no—
134C8×C22⋊C4—71no—
135C23×D7C2×D411yescharacteristic
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7C2×D411yescharacteristic
141C22×C4×C7C2×D411yescharacteristic
142C22×C4×C7C2411yescharacteristic
143C22×Dic7—21no—
144C22×Dic7—21no—
145C22×Dic7—21no—
146C22×Dic7—21no—
147C22×Dic7C2×D411yescharacteristic
148C22×Dic7C2×D411yescharacteristic
149C22×Dic7C2×D411yescharacteristic
150C2×C4×D7—21no—
151C2×C4×D7—21no—
152C2×C4×D7—21no—
153C2×C4×D7—21no—
154C2×C4×D7C22×C412yes—
155C2×C4×D7#4112yes—
156C2×C7×C8—21no—
157C2×C7×C8—21no—
158C2×C7×C8—21no—
159C2×C7×C8C22×C412yes—
160C2×C7×C8#4112yes—
161C2×C7×C8#4112yes—
162C7×C4⋊C4—21no—
163C7×C4⋊C4—21no—
164C7×C4⋊C4—21no—
165C7×C4⋊C4—21no—
166C7×C4⋊C4—21no—
167C7×C4⋊C4—21no—
168C7×C4⋊C4—42no—
169C7×C4⋊C4—81no—
170C7×C4⋊C4C22×C412yes—
171C7×C4⋊C4C22×C412yes—
172C42×C7—21no—
173C42×C7—21no—
174(C2×D7)⋊C4—24no—
175(C2×D7)⋊C4—24no—
176(C2×D7)⋊C4—22no—
177(C2×D7)⋊C4—22no—
178(C2×D7)⋊C4—81no—
179(C2×D7)⋊C4—81no—
180C4⋊Dic7—21no—
181C4⋊Dic7—21no—
182C4⋊Dic7—21no—
183C4⋊Dic7—21no—
184C4⋊Dic7—21no—
185C4⋊Dic7—21no—
186C4⋊Dic7—42no—
187C4⋊Dic7—81no—
188C4⋊Dic7C22×C412yes—
189C4⋊Dic7C22×C412yes—
190C4×Dic7—21no—
191C4×Dic7—21no—
192C4×Dic7—24no—
193C4×Dic7—24no—
194C4×Dic7—42no—
195C4×Dic7—42no—
196C4×Dic7—81no—
197C4×Dic7—81no—
198C2×C7⋊C8—21no—
199C2×C7⋊C8—21no—
200C2×C7⋊C8—21no—
201C2×C7⋊C8—21no—
202C2×C7⋊C8—21no—
203C2×C7⋊C8C22×C412yes—
204C8×D7—28no—
205C23×C8—71no—
206C2×#117—71no—
207C2×#117—71no—
208#427—78no—
209C2×#107—71no—
210C2×#107—71no—
211C2×#106—71no—
212C2×#106—71no—
213C2×#106C2×D711yescharacteristic
214C2×#106C2×D711yescharacteristic
215C2×C22⋊C8—71no—
216C2×C4×C8—71no—
217C2×C4×C8C2×D711yescharacteristic
218#389—71no—
219#389—71no—
220#389C2×D711yescharacteristic
221#389C2×D711yescharacteristic
222#388—141no—
223#388—141no—
224#388—141no—
225#388—141no—
226#383—141no—
227#382—141no—
228#380—71no—
229#380—71no—
230C4×C4⋊C4—71no—
231C4×C4⋊C4—71no—
232C4×C4⋊C4—71no—
233C4×C4⋊C4—71no—
234C4×C4⋊C4—141no—
235C4×C22⋊C4—71no—
236#376—141no—
237#340—71no—
238#340—71no—
239#340—71no—
240#340—71no—
241#340—71no—
242#340—71no—
243#340—71no—
244#340—71no—
245#340C2×D711yescharacteristic
246#340C2×D711yescharacteristic
247#336—71no—
248#336—71no—
249C23×C7C22×D411yescharacteristic
250C22×D7—21no—
251C22×D7—21no—
252C22×D7—21no—
253C22×D7—21no—
254C22×D7—21no—
255C22×D7—21no—
256C22×D7C4×D412yes—
257C2×C4×C7—21no—
258C2×C4×C7—21no—
259C2×C4×C7—22no—
260C2×C4×C7—22no—
261C2×C4×C7—21no—
262C2×C4×C7—21no—
263C2×C4×C7—21no—
264C2×C4×C7—41no—
265C2×C4×C7—41no—
266C2×C4×C7—41no—
267C2×C4×C7—41no—
268C2×C4×C7—41no—
269C2×C4×C7—41no—
270C2×C4×C7—41no—
271C2×C4×C7—41no—
272C2×C4×C7—41no—
273C2×C4×C7—41no—
274C2×C4×C7#13512yes—
275C2×C4×C7C23×C411yescharacteristic
276C2×C4×C7C2×#4111yescharacteristic
277C2×C4×C7C2×#4111yescharacteristic
278C2×C4×C7C2×#4111yescharacteristic
279C2×C4×C72−1+411yescharacteristic
280C2×C4×C72−1+411yescharacteristic
281C2×Dic7—21no—
282C2×Dic7—21no—
283C2×Dic7—21no—
284C2×Dic7—21no—
285C2×Dic7—22no—
286C2×Dic7—22no—
287C2×Dic7—21no—
288C2×Dic7—21no—
289C2×Dic7—21no—
290C2×Dic7—41no—
291C2×Dic7—41no—
292C2×Dic7—41no—
293C2×Dic7—41no—
294C2×Dic7—41no—
295C2×Dic7—41no—
296C2×Dic7—41no—
297C2×Dic7—41no—
298C2×Dic7—41no—
299C2×Dic7—41no—
300C2×Dic7C4×D412yes—
301C2×Dic7#13512yes—
302C4×D7—22no—
303C4×D7—22no—
304C4×D7—22no—
305C4×D7—22no—
306C7×C8—41no—
307C7×C8#11714yes—
308C7⋊C8—22no—
309C7⋊C8—41no—
310C23×C4—71no—
311C22×C8—71no—
312C22×C8—74no—
313C22×C8—71no—
314C22×C8—142no—
315C22×C8—142no—
316C22×C8C22×D711yescharacteristic
317C22×C8C22×D711yescharacteristic
318#117—74no—
319#117—74no—
320#117—142no—
321#117—142no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—71no—
325C2×C4⋊C4—71no—
326C2×C4⋊C4—71no—
327C2×C4⋊C4—71no—
328C2×C4⋊C4—141no—
329C2×C4⋊C4—141no—
330C2×C4⋊C4C22×D711yescharacteristic
331C2×C4⋊C4C22×D711yescharacteristic
332C2×C4⋊C4C22×D711yescharacteristic
333C2×C4⋊C4C22×D711yescharacteristic
334C2×C22⋊C4—71no—
335C2×C22⋊C4—71no—
336C2×C22⋊C4—141no—
337C2×C22⋊C4—141no—
338C2×C22⋊C4—141no—
339C2×C22⋊C4—141no—
340C2×C42—71no—
341C2×C42—141no—
342C2×C42—141no—
343C2×C42—141no—
344C2×C42—141no—
345C2×C42—141no—
346C2×C42—141no—
347C2×C42C22×D711yescharacteristic
348#107—74no—
349#107—74no—
350#106—22no—
351#106—74no—
352#106—142no—
353#106C4×D714yes—
354C22⋊C8—142no—
355C4×C8—22no—
356C4×C8—142no—
357#95—21no—
358#95—21no—
359#95—71no—
360#95—71no—
361#95—141no—
362#95—141no—
363#95—141no—
364#95—141no—
365#95—141no—
366#95—141no—
367#95—141no—
368#95—141no—
369C22×C7C2×C4×D411yescharacteristic
370C22×C7#54711yescharacteristic
371C22×C7#54711yescharacteristic
372C22×C7C2×#13511yescharacteristic
373C22×C7C2×#13511yescharacteristic
374C22×C7#57711yescharacteristic
375C22×C7#57711yescharacteristic
376C2×D7—22no—
377C2×D7—22no—
378C2×D7—22no—
379C2×D7—41no—
380C2×D7—41no—
381C2×D7—41no—
382C2×D7—41no—
383C4×C7—22no—
384C4×C7—41no—
385C4×C7—42no—
386C4×C7—42no—
387C4×C7—81no—
388C4×C7—81no—
389C4×C7C2×#11711yescharacteristic
390C4×C7#51911yescharacteristic
391C4×C7#55211yescharacteristic
392C4×C7#55211yescharacteristic
393Dic7—22no—
394Dic7—22no—
395Dic7—41no—
396Dic7—42no—
397Dic7—42no—
398Dic7—81no—
399Dic7—81no—
400C24—71no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—71no—
406C22×C4—71no—
407C22×C4—72no—
408C22×C4—72no—
409C22×C4—71no—
410C22×C4—141no—
411C22×C4—141no—
412C22×C4—141no—
413C22×C4—141no—
414C22×C4—141no—
415C22×C4—141no—
416C22×C4—141no—
417C22×C4—141no—
418C22×C4D4×D711yescharacteristic
419C22×C4D4×D711yescharacteristic
420C22×C4C23×D711yescharacteristic
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—72no—
425C2×C8—141no—
426C2×C8—141no—
427C2×C8—148no—
428C2×C8—141no—
429C2×C8—141no—
430C2×C8—141no—
431C2×C8C2×C4×D712yes—
432C2×C8#115912yes—
433C2×C8#116112yes—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—42no—
441C4⋊C4—72no—
442C4⋊C4—72no—
443C4⋊C4—81no—
444C4⋊C4—141no—
445C4⋊C4—141no—
446C4⋊C4—141no—
447C4⋊C4—141no—
448C4⋊C4—141no—
449C4⋊C4—141no—
450C4⋊C4—282no—
451C4⋊C4—561no—
452C4⋊C4C2×C4×D712yes—
453C4⋊C4C2×C4×D712yes—
454C22⋊C4—142no—
455C22⋊C4—144no—
456C22⋊C4—144no—
457C22⋊C4—142no—
458C22⋊C4—561no—
459C22⋊C4—561no—
460C42—21no—
461C42—21no—
462C42—144no—
463C42—144no—
464C42—141no—
465C42—141no—
466C42—282no—
467C42—282no—
468C42—561no—
469C42—561no—
470C2×C7#234411yescharacteristic
471C2×C7C4×#13511yescharacteristic
472C2×C7#295211yescharacteristic
473C2×C7#333711yescharacteristic
474C2×C7#333711yescharacteristic
475C2×C7#334011yescharacteristic
476C2×C7#334011yescharacteristic
477D7—42no—
478C23—72no—
479C23—141no—
480C23—141no—
481C23—141no—
482C23—141no—
483C23—141no—
484C23—141no—
485C23C2×D4×D711yescharacteristic
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—72no—
504C2×C4—72no—
505C2×C4—141no—
506C2×C4—141no—
507C2×C4—141no—
508C2×C4—141no—
509C2×C4—142no—
510C2×C4—142no—
511C2×C4—142no—
512C2×C4—142no—
513C2×C4—141no—
514C2×C4—141no—
515C2×C4—141no—
516C2×C4—142no—
517C2×C4—142no—
518C2×C4—281no—
519C2×C4—281no—
520C2×C4—281no—
521C2×C4—281no—
522C2×C4—281no—
523C2×C4—281no—
524C2×C4—281no—
525C2×C4—281no—
526C2×C4—281no—
527C2×C4—281no—
528C2×C4#647912yes—
529C2×C4C22×C4×D711yescharacteristic
530C2×C4C2×#115911yescharacteristic
531C2×C4C2×#116111yescharacteristic
532C2×C4#655111yescharacteristic
533C2×C4D7×#4111yescharacteristic
534C2×C4#655411yescharacteristic
535C8—41no—
536C8—142no—
537C8—281no—
538C8#645514yes—
539C7#2261011yescharacteristic, complemented, Sylow
540C22—142no—
541C22—142no—
542C22—142no—
543C22—281no—
544C22—281no—
545C22—281no—
546C22—281no—
547C22C4×D4×D711yescharacteristic
548C22#9030211yescharacteristic
549C22#9041711yescharacteristic
550C22C2×#647911yescharacteristic
551C22#9045311yescharacteristic
552C22D7×#13511yescharacteristic
553C22#9046111yescharacteristic
554C4—22no—
555C4—42no—
556C4—42no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—142no—
561C4—142no—
562C4—282no—
563C4—282no—
564C4—281no—
565C4—561no—
566C4—561no—
567C4C2×#645511yescharacteristic
568C4#9026311yescharacteristic
569C4#9033011yescharacteristic
570C4#9038511yescharacteristic
571C2—282no—
572C2#1173364511yescharacteristic
573C2C4×#647911yescharacteristic
574C2#1173709511yescharacteristic
575C2#1173809411yescharacteristic
576C2#1173809511yescharacteristic
577C2#1173934511yescharacteristic
578C2#1173937011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1941C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
cosocleC22×C4×C7C24
hypercenter#1941D7
hypocenterC7#22610
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

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

NH ≅ G/Ntype
4. C7×#1941C2semidirect
6. #11728314C2semidirect
7. Dic7×#106C2semidirect
9. C4×#6391C2semidirect
10. #11727357C2semidirect
11. #11727354C2semidirect
13. #11726575C2semidirect
14. #11726569C2semidirect
43. #89632C4semidirect
124. #1941D7semidirect
539. C7#22610semidirect

Maximal subgroups

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

subgroupindex
C2×#896322
#117334252
#117334242
C7×#19412
#117283312
#117283142
Dic7×#1062
C8×(C2×D7)⋊C42
C4×#63912
#117273572
#117273542
#117266272
#117265752
#117265692
#117265672
#226107