Finite Group Databasebeta

← #13405948

Subgroups — #13405948

Order 1792.

648 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#478C211yesmaximal, characteristic
2#11740460C211yesmaximal, characteristic, complemented
3#11739741C211yesmaximal, characteristic
4#11736453C211yesmaximal, characteristic, complemented
5#11729496C211yesmaximal, characteristic, complemented
6C4×#6407C211yesmaximal, characteristic
7#11728380C211yesmaximal, characteristic, complemented
8#11728379C211yesmaximal, characteristic, complemented
9#11728327C211yesmaximal, characteristic, complemented
10#11728326C211yesmaximal, characteristic, complemented
11#11728228C211yesmaximal, characteristic, complemented
12#11727951C211yesmaximal, characteristic
13#11727951C211yesmaximal, characteristic
14#11727949C211yesmaximal, characteristic
15#11727949C211yesmaximal, characteristic
16C2×C7×#125C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18#90161C2211yescharacteristic
19C7×#478—21no—
20C7×#478—21no—
21C7×#478—21no—
22C7×#478—21no—
23C2×C7×#107C2211yescharacteristic
24C2×C7×#106C2211yescharacteristic
25C2×C7×C4⋊C8C2211yescharacteristic
26C2×C7×#102C2211yescharacteristic
27C2×C7×#102C2211yescharacteristic
28C2×#6407C2211yescharacteristic
29C2×#6407C2211yescharacteristic
30#89987C2211yescharacteristic
31#89987C2211yescharacteristic
32C2×#6393C2211yescharacteristic
33C2×#6393C2211yescharacteristic
34#89874C2211yescharacteristic
35#89874C2211yescharacteristic
36#89873C2211yescharacteristic
37#89873C2211yescharacteristic
38#89837—21no—
39#89837—21no—
40#89836—21no—
41#89836—21no—
42#89781—21no—
43#89781—21no—
44#89780—21no—
45#89779—21no—
46#89736C2211yescharacteristic
47#89736C2211yescharacteristic
48#89736C2211yescharacteristic
49#89736C2211yescharacteristic
50#89736C2211yescharacteristic
51#89736C2211yescharacteristic
52#89696C2211yescharacteristic
53C4×#1136C2211yescharacteristic
54C4×#1136C2211yescharacteristic
55#89603—21no—
56#89602—21no—
57#89600—21no—
58#89600—21no—
59#89347C2211yescharacteristic
60#89347C2211yescharacteristic
61#89325C2211yescharacteristic
62#89325C2211yescharacteristic
63#89325C2211yescharacteristic
64#89325C2211yescharacteristic
65#89325C2211yescharacteristic
66#89325C2211yescharacteristic
67#25493—71nomaximal, Sylow
68C22×C7×D4C2311yescharacteristic
69C23×C4×C7—21no—
70C22×C7×C8C2311yescharacteristic
71C22×C7×C8C2311yescharacteristic
72C7×#125—21no—
73C7×#125—21no—
74C7×#125—21no—
75C7×#125—21no—
76C4×C7×D4—21no—
77C4×C7×D4—21no—
78C4×C7×D4—21no—
79C4×C7×D4—21no—
80C2×C7×C4⋊C4—21no—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C4⋊C4C2311yescharacteristic
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C7×C22⋊C4—21no—
86C2×C42×C7C2311yescharacteristic
87#6489C2311yescharacteristic
88#6489C2311yescharacteristic
89#6487—21no—
90#6487—21no—
91C2×#1136C2311yescharacteristic
92C2×#1136C2311yescharacteristic
93C2×#1136C2311yescharacteristic
94C2×#1136C2311yescharacteristic
95C2×#1136C2311yescharacteristic
96C2×#1136C2311yescharacteristic
97#6433D411yescharacteristic
98#6433D411yescharacteristic
99#6432D411yescharacteristic
100#6432D411yescharacteristic
101C4×Dic14—21no—
102C4×Dic14—21no—
103C7×#107—21no—
104C7×#107—21no—
105C7×#106—21no—
106C7×#106—21no—
107C7×C4⋊C8D411yescharacteristic
108C7×C4⋊C8D411yescharacteristic
109C7×C4⋊C8D411yescharacteristic
110C7×C4⋊C8D411yescharacteristic
111C7×#102—21no—
112C7×#102—21no—
113C7×#102—21no—
114C7×#102—21no—
115#6407—22no—
116#6407Q814yescomplemented
117#6406—21no—
118#6406—21no—
119#6406—21no—
120#6406—21no—
121#6393—22no—
122#6393—22no—
123#6389—21no—
124#6389—21no—
125Dic7⋊C8—21no—
126Dic7⋊C8—21no—
127Dic7⋊C8—21no—
128Dic7⋊C8—21no—
129C8×Dic7—21no—
130C8×Dic7—21no—
131#6382—21no—
132#6382—21no—
133#6382—21no—
134#6382—21no—
135#6382—21no—
136#6382—21no—
137#6381—21no—
138#6381—21no—
139#6381—21no—
140#6381—21no—
141#6381—21no—
142#6381—21no—
143C4⋊(C7⋊C8)—21no—
144C4⋊(C7⋊C8)—21no—
145#6377—21no—
146#6377—21no—
147C4×C7⋊C8—21no—
148C4×C7⋊C8—21no—
149#3166—71no—
150#3077—71no—
151C2×#478D711yescharacteristic
152#2962—71no—
153#2090—71no—
154#2089—71no—
155#2063—71no—
156#2063—71no—
157#1998—71no—
158#1952—71no—
159#1951—71no—
160#1950—71no—
161#1931—71no—
162#1931—71no—
163C4×#100—71no—
164C24×C7—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—21no—
168C2×C7×D4—21no—
169C2×C7×D4—21no—
170C2×C7×D4C2×Q812yes—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—41no—
175C22×C4×C7—41no—
176C22×C4×C7—82no—
177C22×C4×C7#4111yescharacteristic
178C22×C4×C7#4111yescharacteristic
179C22×C4×C7C2411yescharacteristic
180C2×Dic14—21no—
181C2×Dic14—21no—
182C2×C7×C8—21no—
183C2×C7×C8—21no—
184C2×C7×C8—21no—
185C2×C7×C8—21no—
186C2×C7×C8C2×D411yescharacteristic
187C2×C7×C8C2×D411yescharacteristic
188C2×C7×C8C2×D411yescharacteristic
189C2×C7×C8C2×D411yescharacteristic
190C7×C4⋊C4—21no—
191C7×C4⋊C4—21no—
192C7×C4⋊C4—21no—
193C7×C4⋊C4—21no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—41no—
197C7×C4⋊C4—41no—
198C7×C4⋊C4—41no—
199C7×C4⋊C4—41no—
200C7×C22⋊C4—41no—
201C7×C22⋊C4—41no—
202C42×C7C2×D411yescharacteristic
203C42×C7C2×D411yescharacteristic
204C42×C7C2×D411yescharacteristic
205C42×C7C2×D411yescharacteristic
206C22⋊Dic7—21no—
207C22⋊Dic7—21no—
208C4⋊Dic7—21no—
209C4⋊Dic7—21no—
210C4⋊Dic7C2×D411yescharacteristic
211C4⋊Dic7C2×D411yescharacteristic
212C4⋊Dic7C2×D411yescharacteristic
213C4⋊Dic7C2×D411yescharacteristic
214Dic7⋊C4—21no—
215Dic7⋊C4—21no—
216Dic7⋊C4—21no—
217Dic7⋊C4—21no—
218C4×Dic7—21no—
219C4×Dic7—21no—
220#1136—21no—
221#1136—21no—
222#1136—21no—
223#1136—21no—
224#1136—21no—
225#1136—21no—
226#1136—21no—
227#1136—21no—
228#1136—21no—
229#1136C2×Q812yes—
230#1136C2×Q812yes—
231#1136#4112yes—
232C2×C7⋊C8—21no—
233C2×C7⋊C8—21no—
234C2×C7⋊C8—21no—
235C2×C7⋊C8—21no—
236C2×C7⋊C8—21no—
237C2×C7⋊C8—21no—
238#533—71no—
239C2×#125C2×D711yescharacteristic
240C2×C4×D4C2×D711yescharacteristic
241#501—141no—
242#501—141no—
243#499—141no—
244#499—141no—
245#478—21no—
246#478—21no—
247#478—21no—
248#478—21no—
249#478—141no—
250#478—141no—
251#476—141no—
252#474—141no—
253#446—141no—
254#446—141no—
255#446—141no—
256C8×Q8—141no—
257C2×#108—71no—
258C2×#108—71no—
259#428—71no—
260#428—71no—
261#428—71no—
262#428—71no—
263#428—71no—
264#428—71no—
265C2×#107C2×D711yescharacteristic
266C2×#106C2×D711yescharacteristic
267#424—71no—
268#424—71no—
269#423—71no—
270C2×C4⋊C8C2×D711yescharacteristic
271#418—71no—
272#418—71no—
273C2×#102C2×D711yescharacteristic
274C2×#102C2×D711yescharacteristic
275C2×#100—71no—
276C2×#100—71no—
277#405—71no—
278#405—71no—
279C4×M16—71no—
280C4×M16—71no—
281#343—71no—
282#343—71no—
283#343—71no—
284#343—71no—
285#343—71no—
286#343—71no—
287#341—71no—
288#341—71no—
289C23×C7—22no—
290C23×C7—41no—
291C23×C7—41no—
292C23×C7—81no—
293C23×C7—81no—
294C23×C7C2×#4111yescharacteristic
295C7×D4—22no—
296C7×D4—22no—
297C7×D4—41no—
298C7×D4—41no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
302C2×C4×C7—41no—
303C2×C4×C7—41no—
304C2×C4×C7—82no—
305C2×C4×C7—82no—
306C2×C4×C7—81no—
307C2×C4×C7—81no—
308C2×C4×C7—81no—
309C2×C4×C7#12111yescharacteristic
310C2×C4×C7#12111yescharacteristic
311C2×C4×C7#12111yescharacteristic
312C2×C4×C7#12111yescharacteristic
313C2×C4×C7C22×D411yescharacteristic
314C2×C4×C7C22×D411yescharacteristic
315C2×C4×C7C22×Q811yescharacteristic
316C2×C4×C7C2×#4111yescharacteristic
317C2×C4×C72−1+411yescharacteristic
318C2×C4×C72−1+411yescharacteristic
319C2×Dic7—21no—
320C2×Dic7—21no—
321C2×Dic7—21no—
322C2×Dic7—21no—
323Dic14—42no—
324Dic14—81no—
325C7×C8—21no—
326C7×C8—21no—
327C7×C8—21no—
328C7×C8—21no—
329C7⋊C8—22no—
330C7⋊C8—22no—
331C7⋊C8—22no—
332C7⋊C8—41no—
333C7⋊C8—41no—
334C7⋊C8—41no—
335C22×D4C22×D711yescharacteristic
336C23×C4—21no—
337C2×M16—71no—
338C2×M16—71no—
339C2×M16—71no—
340C2×M16—71no—
341C2×M16—71no—
342C2×M16—71no—
343C22×C8C22×D711yescharacteristic
344C22×C8C22×D711yescharacteristic
345C4⋊Q8—71no—
346C4⋊Q8—71no—
347#125—21no—
348#125—21no—
349#125—21no—
350#125—21no—
351#125—71no—
352#125—71no—
353C22⋊Q8—141no—
354C22⋊Q8—141no—
355C4×Q8—141no—
356C4×Q8—141no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361#117—71no—
362#117—71no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4C22×D711yescharacteristic
366C2×C4⋊C4C22×D711yescharacteristic
367C2×C4⋊C4C22×D711yescharacteristic
368C2×C22⋊C4—21no—
369C2×C42C22×D711yescharacteristic
370#108—142no—
371#108—142no—
372#107—21no—
373#107—21no—
374#107—141no—
375#107—141no—
376#107—141no—
377#107—141no—
378#107—141no—
379#107—141no—
380#106—21no—
381#106—21no—
382#106—141no—
383#106—141no—
384#106—141no—
385#106—141no—
386#106—141no—
387#106—141no—
388C4⋊C8—141no—
389C4⋊C8—141no—
390C4⋊C8—141no—
391C4⋊C8—141no—
392C4⋊C8—141no—
393C4⋊C8—141no—
394C4⋊C8C22⋊D711yescharacteristic
395C4⋊C8C22⋊D711yescharacteristic
396C4⋊C8C22⋊D711yescharacteristic
397C4⋊C8C22⋊D711yescharacteristic
398#102—21no—
399#102—21no—
400#102—21no—
401#102—21no—
402#102—141no—
403#102—141no—
404#102—141no—
405#102—141no—
406#100—74no—
407#100—142no—
408#97—141no—
409#97—141no—
410#97—141no—
411#97—141no—
412C4×C8—141no—
413C4×C8—141no—
414C4×C8—141no—
415C4×C8—141no—
416C22×C7—21no—
417C22×C7—21no—
418C22×C7—42no—
419C22×C7—82no—
420C22×C7—82no—
421C22×C7—81no—
422C22×C7—81no—
423C22×C7C2×#12111yescharacteristic
424C22×C7#53311yescharacteristic
425C22×C7#54111yescharacteristic
426C4×C7—21no—
427C4×C7—21no—
428C4×C7—21no—
429C4×C7—21no—
430C4×C7—81no—
431C4×C7—81no—
432C4×C7—81no—
433C4×C7#54711yescharacteristic
434C4×C7#54811yescharacteristic
435C4×C7D4×Q811yescharacteristic
436C4×C7D4×Q811yescharacteristic
437Dic7—41no—
438Dic7—41no—
439Dic7—41no—
440Dic7—41no—
441C24—21no—
442C2×Q8—141no—
443C2×Q8—141no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4Q8×D712yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—82no—
456C22×C4#115911yescharacteristic
457C22×C4#115911yescharacteristic
458C22×C4C23×D711yescharacteristic
459M16—72no—
460M16—72no—
461M16—72no—
462M16—141no—
463M16—141no—
464M16—141no—
465M16—141no—
466M16—141no—
467M16—141no—
468M16—141no—
469M16—141no—
470M16—141no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—141no—
476C2×C8—141no—
477C2×C8—141no—
478C2×C8—141no—
479C2×C8—141no—
480C2×C8—141no—
481C2×C8C2×C22⋊D711yescharacteristic
482C2×C8C2×C22⋊D711yescharacteristic
483C2×C8C2×C22⋊D711yescharacteristic
484C2×C8C2×C22⋊D711yescharacteristic
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—71no—
496C4⋊C4—71no—
497C4⋊C4—71no—
498C4⋊C4—71no—
499C4⋊C4—141no—
500C4⋊C4—141no—
501C4⋊C4—141no—
502C4⋊C4—141no—
503C4⋊C4—141no—
504C4⋊C4—141no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—141no—
508C22⋊C4—141no—
509C42—141no—
510C42—141no—
511C42D4×D711yescharacteristic
512C42D4×D711yescharacteristic
513C42C2×C22⋊D711yescharacteristic
514C42C2×C22⋊D711yescharacteristic
515C2×C7—21no—
516C2×C7—21no—
517C2×C7—82no—
518C2×C7#242911yescharacteristic
519C2×C7#306711yescharacteristic
520C2×C7#306811yescharacteristic
521C23—22no—
522C23—41no—
523C23—41no—
524C23—81no—
525C23—81no—
526C23C2×#115911yescharacteristic
527Q8—282no—
528Q8—561no—
529D4—22no—
530D4—22no—
531D4—41no—
532D4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—81no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—141no—
544C2×C4—141no—
545C2×C4—141no—
546C2×C4—141no—
547C2×C4#650111yescharacteristic
548C2×C4#650111yescharacteristic
549C2×C4#650111yescharacteristic
550C2×C4#650111yescharacteristic
551C2×C4C2×D4×D711yescharacteristic
552C2×C4C2×Q8×D711yescharacteristic
553C2×C4#655111yescharacteristic
554C2×C4D7×#4111yescharacteristic
555C2×C4#655411yescharacteristic
556C2×C4C22×C22⋊D711yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—142no—
562C8—142no—
563C8—142no—
564C8—281no—
565C8—281no—
566C8—281no—
567C7#2549311yescharacteristic, complemented, Sylow
568C22—21no—
569C22—21no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22—81no—
574C22—81no—
575C22#9031311yescharacteristic
576C22#9031611yescharacteristic
577C22C2×#650111yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—281no—
586C4—281no—
587C4—281no—
588C4—281no—
589C4#9032311yescharacteristic
590C4#9032411yescharacteristic
591C4Q8×C22⋊D711yescharacteristic
592C4#9051511yescharacteristic
593C2—21no—
594C2—21no—
595C2—82no—
596C2#1174020211yescharacteristic
597C2#1174137311yescharacteristic
598C2#1174140811yescharacteristic
subgroupG/H
centerC22C2×#6501
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#478C2
socleC22×C7C2×#121
prime radicalC22×C7×D4C23
hypercenterC2×#478D7
hypocenterC7#25493
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
2. #11740460C2semidirect
4. #11736453C2semidirect
5. #11729496C2semidirect
7. #11728380C2semidirect
8. #11728379C2semidirect
9. #11728327C2semidirect
10. #11728326C2semidirect
11. #11728228C2semidirect
116. #6407Q8semidirect
567. C7#25493semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4782
#117404602
#117397412
#117364532
#117294962
C4×#64072
#117283802
#117283792
#117283272
#117283262
#117282282
#117279512
#117279492
#254937