Finite Group Databasebeta

← #13405782

Subgroups — #13405782

Order 1792.

770 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#446C211yesmaximal, characteristic, complemented
2#11739946C211yesmaximal, characteristic
3#11739923C211yesmaximal, characteristic, complemented
4C2×#89618C211yesmaximal, characteristic
5#11728238C211yesmaximal, characteristic
6#11728237C211yesmaximal, characteristic
7#11728217C211yesmaximal, characteristic, complemented
8#11728216C211yesmaximal, characteristic, complemented
9#11728209C211yesmaximal, characteristic, complemented
10#11727582C211yesmaximal, characteristic, complemented
11#11727574C211yesmaximal, characteristic, complemented
12#11727572C211yesmaximal, characteristic
13#11727566C211yesmaximal, characteristic
14#11727524C211yesmaximal, characteristic, complemented
15#11727522C211yesmaximal, characteristic
16C2×C4×C7×Q8C2211yescharacteristic
17C2×C4×D28C2211yescharacteristic
18C2×#6432C2211yescharacteristic
19C7×#446—24no—
20C2×C7×C4⋊C8C2211yescharacteristic
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×C4⋊C8C2211yescharacteristic
23C2×C7×#97C2211yescharacteristic
24C2×C7×#97C2211yescharacteristic
25C2×C4×C7×C8C2211yescharacteristic
26#90003—21no—
27#90002—21no—
28C2×#6395C2211yescharacteristic
29C2×#6395C2211yescharacteristic
30C2×#6395C2211yescharacteristic
31C2×#6395C2211yescharacteristic
32C2×#6392C2211yescharacteristic
33C2×#6392C2211yescharacteristic
34C2×#6392C2211yescharacteristic
35C2×#6391C2211yescharacteristic
36#89764—21no—
37#89761—21no—
38#89761—21no—
39#89751—21no—
40#89751—21no—
41#89748—21no—
42#89711C2211yescharacteristic
43#89711C2211yescharacteristic
44#89708C2211yescharacteristic
45C4×C4⋊Dic7C2211yescharacteristic
46#89700C2211yescharacteristic
47#89700C2211yescharacteristic
48#89700C2211yescharacteristic
49#89700C2211yescharacteristic
50#89700C2211yescharacteristic
51#89700C2211yescharacteristic
52#89618—24no—
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#89346C2211yescharacteristic
61#25481—71nomaximal, Sylow
62C22×C7×Q8D411yescharacteristic
63C22×D28C2311yescharacteristic
64C22×C4×D7—21no—
65C22×Dic14—21no—
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C22×C7×C8C2311yescharacteristic
70C4×C7×Q8—22no—
71C4×C7×Q8—22no—
72C2×C7×C4⋊C4D411yescharacteristic
73C2×C7×C4⋊C4D411yescharacteristic
74C2×C7×C4⋊C4D411yescharacteristic
75C2×C42×C7C2311yescharacteristic
76C2×C42×C7C2311yescharacteristic
77C2×C42×C7C2311yescharacteristic
78C2×(C2×D7)⋊C4—21no—
79C2×(C2×D7)⋊C4—21no—
80C2×(C2×D7)⋊C4—21no—
81C2×(C2×D7)⋊C4—21no—
82C2×(C2×D7)⋊C4—21no—
83C2×C4⋊Dic7—21no—
84C2×C4⋊Dic7C2311yescharacteristic
85C2×C4⋊Dic7C2311yescharacteristic
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89C2×C4⋊Dic7C2311yescharacteristic
90C2×C4⋊Dic7C2311yescharacteristic
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×Dic7⋊C4—21no—
96C2×Dic7⋊C4—21no—
97C2×C4×Dic7—21no—
98C4×D28—22no—
99C4×D28—22no—
100#6432—22no—
101#6432—22no—
102C7×C4⋊C8—22no—
103C7×C4⋊C8—22no—
104C7×C4⋊C8D414yes—
105C7×#97—22no—
106C7×#97—22no—
107C4×C7×C8—22no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116C7⋊#95—21no—
117#6395—22no—
118#6395—22no—
119#6395—22no—
120#6395Q814yescomplemented
121#6392—22no—
122#6392—22no—
123#6392—22no—
124#6391—22no—
125C2×#474—71no—
126C2×#446D711yescharacteristic, complemented
127#2580—71no—
128#2567—71no—
129#2087—71no—
130#2086—71no—
131#2067—71no—
132#2065—71no—
133#1993—71no—
134#1949—71no—
135#1944—71no—
136#1942—71no—
137#1936—71no—
138#1934—71no—
139#1762—71no—
140C23×D7—21no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8—41no—
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2×D411yescharacteristic
147C22×C4×C7C2×D411yescharacteristic
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2411yescharacteristic
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C2×D28—21no—
159C2×D28—21no—
160C2×D28—21no—
161C2×D28—21no—
162C2×D28—21no—
163C2×D28C2×Q812yes—
164C2×C4×D7—42no—
165C2×C4×D7—81no—
166C2×C4×D7—81no—
167C2×Dic14—42no—
168C2×Dic14—81no—
169C2×Dic14—81no—
170C2×C7×C8—21no—
171C2×C7×C8—21no—
172C2×C7×C8—21no—
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C2×C7×C8—21no—
178C2×C7×C8—21no—
179C2×C7×C8C2×D412yes—
180C2×C7×C8C2×D412yes—
181C2×C7×C8C2×Q812yes—
182C7×C4⋊C4—22no—
183C7×C4⋊C4—22no—
184C7×C4⋊C4—22no—
185C42×C7—21no—
186C42×C7—21no—
187C42×C7—21no—
188C42×C7—21no—
189C42×C7C2×D412yes—
190C42×C7#4112yes—
191(C2×D7)⋊C4—42no—
192(C2×D7)⋊C4—42no—
193(C2×D7)⋊C4—42no—
194(C2×D7)⋊C4—81no—
195(C2×D7)⋊C4—81no—
196C4⋊Dic7—21no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7—21no—
200C4⋊Dic7—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7—21no—
204C4⋊Dic7—21no—
205C4⋊Dic7—21no—
206C4⋊Dic7—21no—
207C4⋊Dic7—21no—
208C4⋊Dic7—42no—
209C4⋊Dic7C2×Q812yes—
210C4⋊Dic7#4112yes—
211Dic7⋊C4—81no—
212Dic7⋊C4—81no—
213Dic7⋊C4—81no—
214Dic7⋊C4—81no—
215Dic7⋊C4—81no—
216Dic7⋊C4—81no—
217C4×Dic7—42no—
218C2×C4⋊Q8—71no—
219C2×C4×Q8C2×D711yescharacteristic
220C2×C4×D4—71no—
221#474—144no—
222#446—24no—
223C2×#107—71no—
224C2×#107—71no—
225C2×#107—71no—
226C2×#106—71no—
227C2×C4⋊C8C2×D711yescharacteristic
228C2×C4⋊C8C2×D711yescharacteristic
229C2×C4⋊C8C2×D711yescharacteristic
230C2×#102—71no—
231C2×#102—71no—
232C2×#102—71no—
233C2×#102—71no—
234C2×#97C2×D711yescharacteristic
235C2×#97C2×D711yescharacteristic
236C2×C4×C8C2×D711yescharacteristic
237#399—141no—
238#395—141no—
239#395—141no—
240#393—141no—
241#391—141no—
242#390—71no—
243#390—71no—
244#389—71no—
245#389—71no—
246#389—71no—
247#389—71no—
248#389—71no—
249#389—71no—
250#385—141no—
251#385—141no—
252#384—141no—
253#382—71no—
254C4×C4⋊C4—71no—
255#340—71no—
256#340—71no—
257#340—71no—
258#340—71no—
259#340—71no—
260#340—71no—
261#340—71no—
262#340—71no—
263C23×C7C22×D411yescharacteristic
264C22×D7—22no—
265C22×D7—41no—
266C22×D7—41no—
267C22×D7—41no—
268C22×D7—41no—
269C22×D7—41no—
270C22×D7—41no—
271C7×Q8—44no—
272C2×C4×C7—21no—
273C2×C4×C7—21no—
274C2×C4×C7—21no—
275C2×C4×C7—21no—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7#12112yes—
288C2×C4×C7#12112yes—
289C2×C4×C7#13712yes—
290C2×C4×C7C22×D411yescharacteristic
291C2×C4×C7C22×Q811yescharacteristic
292C2×C4×C7C2×#4111yescharacteristic
293C2×C4×C7C2×#4111yescharacteristic
294C2×C4×C72−1+411yescharacteristic
295C2×C4×C72−1+411yescharacteristic
296C2×Dic7—22no—
297C2×Dic7—22no—
298C2×Dic7—41no—
299C2×Dic7—41no—
300C2×Dic7—41no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309C2×Dic7—41no—
310C2×Dic7—41no—
311C2×Dic7—41no—
312C2×Dic7—41no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7—41no—
316C2×Dic7—41no—
317D28—22no—
318D28—22no—
319D28—41no—
320D28—41no—
321C4×D7—84no—
322Dic14—84no—
323C7×C8—22no—
324C7×C8—22no—
325C7×C8—22no—
326C7×C8—41no—
327C22×Q8—141no—
328C22×Q8D2811yescharacteristic
329C22×D4—71no—
330C23×C4—141no—
331C22×C8C22×D711yescharacteristic
332C22×C8C22×D711yescharacteristic
333C22×C8C22×D711yescharacteristic
334C22×C8C22×D711yescharacteristic
335C4⋊Q8—142no—
336C4⋊Q8—142no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×D4—142no—
340C4×D4—142no—
341C2×C4⋊C4—71no—
342C2×C4⋊C4—71no—
343C2×C4⋊C4—71no—
344C2×C4⋊C4—71no—
345C2×C4⋊C4—71no—
346C2×C4⋊C4—71no—
347C2×C4⋊C4—71no—
348C2×C4⋊C4—141no—
349C2×C4⋊C4—141no—
350C2×C4⋊C4—141no—
351C2×C4⋊C4—141no—
352C2×C4⋊C4—141no—
353C2×C4⋊C4—141no—
354C2×C4⋊C4—141no—
355C2×C4⋊C4D2811yescharacteristic
356C2×C4⋊C4D2811yescharacteristic
357C2×C4⋊C4D2811yescharacteristic
358C2×C22⋊C4—141no—
359C2×C22⋊C4—141no—
360C2×C22⋊C4—141no—
361C2×C22⋊C4—141no—
362C2×C22⋊C4—141no—
363C2×C42—141no—
364C2×C42C22×D711yescharacteristic
365C2×C42C22×D711yescharacteristic
366C2×C42C22×D711yescharacteristic
367#107—142no—
368#107—142no—
369#107—142no—
370#106—142no—
371C4⋊C8—22no—
372C4⋊C8—22no—
373C4⋊C8C22⋊D714yes—
374#102—74no—
375#102—142no—
376#102—142no—
377#102—142no—
378#97—22no—
379#97—22no—
380C4×C8—22no—
381#95—141no—
382#95—141no—
383#95—141no—
384#95—141no—
385#95—141no—
386#95—141no—
387#95—141no—
388#95—141no—
389#95—141no—
390C22×C7C2×#12111yescharacteristic
391C22×C7#54811yescharacteristic
392C22×C7D4×Q811yescharacteristic
393C22×C7C2×#13711yescharacteristic
394C22×C7#57511yescharacteristic
395C22×C7#57611yescharacteristic
396C22×C7#57611yescharacteristic
397C2×D7—42no—
398C2×D7—42no—
399C2×D7—42no—
400C2×D7—81no—
401C2×D7—81no—
402C2×D7—81no—
403C2×D7—81no—
404C4×C7—22no—
405C4×C7—22no—
406C4×C7—22no—
407C4×C7—41no—
408C4×C7—41no—
409C4×C7—41no—
410C4×C7#53311yescharacteristic
411C4×C7#54111yescharacteristic
412C4×C7#54711yescharacteristic
413C4×C7D4×Q811yescharacteristic
414Dic7—42no—
415Dic7—42no—
416Dic7—81no—
417Dic7—81no—
418Dic7—81no—
419Dic7—81no—
420Dic7—81no—
421C24—141no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—41no—
425C2×Q8—282no—
426C2×Q8—561no—
427C2×Q8—561no—
428C2×D4—72no—
429C2×D4—141no—
430C2×D4—141no—
431C2×D4—141no—
432C2×D4—141no—
433C2×D4—141no—
434C22×C4—141no—
435C22×C4—141no—
436C22×C4—141no—
437C22×C4—141no—
438C22×C4—141no—
439C22×C4—141no—
440C22×C4—141no—
441C22×C4—282no—
442C22×C4—561no—
443C22×C4—561no—
444C22×C4C2×D2811yescharacteristic
445C22×C4C2×D2811yescharacteristic
446C22×C4C2×D2811yescharacteristic
447C22×C4C2×D2811yescharacteristic
448C22×C4C2×D2811yescharacteristic
449C22×C4C2×D2811yescharacteristic
450C22×C4C23×D711yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8Q8×D712yes—
461C2×C8C2×C22⋊D712yes—
462C2×C8C2×C22⋊D712yes—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—72no—
467C4⋊C4—72no—
468C4⋊C4—141no—
469C4⋊C4—141no—
470C4⋊C4—141no—
471C4⋊C4—141no—
472C4⋊C4—141no—
473C4⋊C4—141no—
474C4⋊C4—141no—
475C4⋊C4—141no—
476C4⋊C4—141no—
477C4⋊C4—141no—
478C4⋊C4—141no—
479C4⋊C4—141no—
480C4⋊C4—282no—
481C4⋊C4—561no—
482C4⋊C4—561no—
483C4⋊C4—561no—
484C4⋊C4—561no—
485C4⋊C4—561no—
486C4⋊C4—561no—
487C22⋊C4—282no—
488C22⋊C4—282no—
489C22⋊C4—282no—
490C22⋊C4—561no—
491C22⋊C4—561no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—282no—
497C42#115712yes—
498C42C2×C22⋊D712yes—
499C2×C7#242911yescharacteristic
500C2×C7#305611yescharacteristic
501C2×C7#305811yescharacteristic
502C2×C7#337011yescharacteristic
503C2×C7#337511yescharacteristic
504C2×C7#338511yescharacteristic
505C2×C7#338911yescharacteristic
506D7—82no—
507C23—142no—
508C23—281no—
509C23—281no—
510C23—281no—
511C23—281no—
512C23—281no—
513C23—281no—
514C23C22×D2811yescharacteristic
515Q8—44no—
516Q8—564no—
517D4—142no—
518D4—142no—
519D4—281no—
520D4—281no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—142no—
537C2×C4—142no—
538C2×C4—281no—
539C2×C4—281no—
540C2×C4—281no—
541C2×C4—281no—
542C2×C4—281no—
543C2×C4—281no—
544C2×C4—281no—
545C2×C4—281no—
546C2×C4—281no—
547C2×C4—281no—
548C2×C4—281no—
549C2×C4—281no—
550C2×C4—281no—
551C2×C4—281no—
552C2×C4—281no—
553C2×C4—281no—
554C2×C4—281no—
555C2×C4—281no—
556C2×C4—281no—
557C2×C4—564no—
558C2×C4#647212yes—
559C2×C4#649312yes—
560C2×C4#649312yes—
561C2×C4C2×#115711yescharacteristic
562C2×C4C2×Q8×D711yescharacteristic
563C2×C4#655111yescharacteristic
564C2×C4D7×#4111yescharacteristic
565C2×C4#655411yescharacteristic
566C2×C4C22×C22⋊D711yescharacteristic
567C8—22no—
568C8—22no—
569C8—22no—
570C8—41no—
571C7#2548111yescharacteristic, complemented, Sylow
572C22—282no—
573C22—282no—
574C22—282no—
575C22—561no—
576C22—561no—
577C22—561no—
578C22—561no—
579C22Q8×D2811yescharacteristic
580C22#9026711yescharacteristic
581C22C2×#647211yescharacteristic
582C22#9043911yescharacteristic
583C22#9044311yescharacteristic
584C22#9044311yescharacteristic
585C22C2×#649311yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—282no—
593C4—282no—
594C4—561no—
595C4—561no—
596C4—561no—
597C4—561no—
598C4—561no—
599C4#9026911yescharacteristic
600C4#9027411yescharacteristic
601C4Q8×C22⋊D711yescharacteristic
602C4#9051511yescharacteristic
603C2—562no—
604C2#1173741611yescharacteristic
605C2#1173742111yescharacteristic
606C2#1173742411yescharacteristic
607C2#1173742911yescharacteristic
608C2#1173994111yescharacteristic
609C2#1174122111yescharacteristic
610C2#1174124411yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#446C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×#446D7
hypocenterC7#25481
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×C7×#446C2semidirect
3. #11739923C2semidirect
7. #11728217C2semidirect
8. #11728216C2semidirect
9. #11728209C2semidirect
10. #11727582C2semidirect
11. #11727574C2semidirect
14. #11727524C2semidirect
120. #6395Q8semidirect
126. C2×#446D7semidirect
571. C7#25481semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4462
#117399462
#117399232
C2×#896182
#117282382
#117282372
#117282172
#117282162
#117282092
#117275822
#117275742
#117275722
#117275662
#117275242
#117275222
#254817