Finite Group Databasebeta

← #13405678

Subgroups — #13405678

Order 1792.

774 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×C8×Q8C211yesmaximal, characteristic, complemented
2#11739946C211yesmaximal, characteristic
3#11739928C211yesmaximal, characteristic, complemented
4C2×#89619C211yesmaximal, characteristic
5#11728238C211yesmaximal, characteristic
6#11728237C211yesmaximal, characteristic
7#11728218C211yesmaximal, characteristic, complemented
8#11728217C211yesmaximal, characteristic, complemented
9#11728209C211yesmaximal, characteristic, complemented
10#11727532C211yesmaximal, characteristic, complemented
11#11727524C211yesmaximal, characteristic, complemented
12#11727523C211yesmaximal, characteristic, complemented
13#11727522C211yesmaximal, characteristic
14#11727522C211yesmaximal, characteristic
15C4×#6395C211yesmaximal, characteristic
16C2×C4×C7×Q8C2211yescharacteristic
17C2×C4×D28C2211yescharacteristic
18C2×#6433C2211yescharacteristic
19C7×C8×Q8—24no—
20C2×C7×C4⋊C8C2211yescharacteristic
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×C4⋊C8C2211yescharacteristic
23C2×C4×C7×C8C2211yescharacteristic
24C2×C4×C7×C8C2211yescharacteristic
25C2×C4×C7×C8C2211yescharacteristic
26#90003—21no—
27#90001—21no—
28C2×#6395C2211yescharacteristic
29C2×#6395C2211yescharacteristic
30C2×#6395C2211yescharacteristic
31C2×#6395C2211yescharacteristic
32C2×#6392C2211yescharacteristic
33C2×#6392C2211yescharacteristic
34C2×#6391C2211yescharacteristic
35C2×#6391C2211yescharacteristic
36#89764—21no—
37#89761—21no—
38#89761—21no—
39#89752—21no—
40#89744—21no—
41#89744—21no—
42#89711C2211yescharacteristic
43#89711C2211yescharacteristic
44#89708C2211yescharacteristic
45C4×C4⋊Dic7C2211yescharacteristic
46#89700C2211yescharacteristic
47#89700C2211yescharacteristic
48#89700C2211yescharacteristic
49#89700C2211yescharacteristic
50#89700C2211yescharacteristic
51#89700C2211yescharacteristic
52#89619—24no—
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#89346C2211yescharacteristic
61#25473—71nomaximal, Sylow
62C22×C7×Q8D411yescharacteristic
63C22×D28C2311yescharacteristic
64C22×C4×D7—21no—
65C22×C7×C8C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C4×C7×Q8—22no—
70C4×C7×Q8—22no—
71C2×C7×C4⋊C4D411yescharacteristic
72C2×C7×C4⋊C4D411yescharacteristic
73C2×C7×C4⋊C4D411yescharacteristic
74C2×C42×C7C2311yescharacteristic
75C2×C42×C7C2311yescharacteristic
76C2×C42×C7C2311yescharacteristic
77C2×(C2×D7)⋊C4—21no—
78C2×(C2×D7)⋊C4—21no—
79C2×(C2×D7)⋊C4—21no—
80C2×(C2×D7)⋊C4—21no—
81C2×(C2×D7)⋊C4—21no—
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4⋊Dic7C2311yescharacteristic
84C2×C4⋊Dic7C2311yescharacteristic
85C2×C4⋊Dic7C2311yescharacteristic
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89C2×Dic7⋊C4—21no—
90C2×Dic7⋊C4—21no—
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#6433—22no—
101#6433—22no—
102C7×C4⋊C8—22no—
103C7×C4⋊C8—22no—
104C7×C4⋊C8D414yes—
105C4×C7×C8—22no—
106C4×C7×C8—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#6391—22no—
124#6391—22no—
125C2×#478—71no—
126C2×C8×Q8D711yescharacteristic, complemented
127#2584—71no—
128#2580—71no—
129#2088—71no—
130#2087—71no—
131#2067—71no—
132#2065—71no—
133#1991—71no—
134#1949—71no—
135#1942—71no—
136#1941—71no—
137#1934—71no—
138#1934—71no—
139C4×#102—71no—
140C23×D7—21no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8—22no—
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×C7×C8—21no—
168C2×C7×C8—21no—
169C2×C7×C8—21no—
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×C8C2×D412yes—
177C2×C7×C8C2×D412yes—
178C2×C7×C8C2×Q812yes—
179C7×C4⋊C4—22no—
180C7×C4⋊C4—22no—
181C7×C4⋊C4—22no—
182C42×C7—21no—
183C42×C7—21no—
184C42×C7—21no—
185C42×C7—21no—
186C42×C7C2×D412yes—
187C42×C7#4112yes—
188(C2×D7)⋊C4—42no—
189(C2×D7)⋊C4—42no—
190(C2×D7)⋊C4—42no—
191(C2×D7)⋊C4—81no—
192(C2×D7)⋊C4—81no—
193C4⋊Dic7—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
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⋊Dic7C2×Q812yes—
206C4⋊Dic7#4112yes—
207Dic7⋊C4—42no—
208Dic7⋊C4—42no—
209Dic7⋊C4—42no—
210Dic7⋊C4—42no—
211Dic7⋊C4—81no—
212Dic7⋊C4—81no—
213Dic7⋊C4—81no—
214Dic7⋊C4—81no—
215C4×Dic7—81no—
216C2×#125—71no—
217C2×C4×Q8C2×D711yescharacteristic
218C2×C4×D4—71no—
219#478—144no—
220C8×Q8—24no—
221C2×#107—71no—
222C2×#107—71no—
223C2×#106—71no—
224C2×#106—71no—
225C2×C4⋊C8C2×D711yescharacteristic
226C2×C4⋊C8C2×D711yescharacteristic
227C2×C4⋊C8C2×D711yescharacteristic
228C2×#102—71no—
229C2×#102—71no—
230C2×#102—71no—
231C2×#102—71no—
232C2×C4×C8C2×D711yescharacteristic
233C2×C4×C8C2×D711yescharacteristic
234C2×C4×C8C2×D711yescharacteristic
235#399—141no—
236#398—141no—
237#395—141no—
238#393—141no—
239#390—71no—
240#390—71no—
241#389—71no—
242#389—71no—
243#389—71no—
244#389—71no—
245#389—71no—
246#389—71no—
247#389—141no—
248#389—141no—
249#385—141no—
250#385—141no—
251#382—71no—
252C4×C4⋊C4—71no—
253#340—71no—
254#340—71no—
255#340—71no—
256#340—71no—
257#340—71no—
258#340—71no—
259#340—71no—
260#340—71no—
261C23×C7C22×D411yescharacteristic
262C22×D7—22no—
263C22×D7—41no—
264C22×D7—41no—
265C22×D7—41no—
266C22×D7—41no—
267C22×D7—41no—
268C22×D7—41no—
269C7×Q8—28no—
270C2×C4×C7—21no—
271C2×C4×C7—21no—
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#12112yes—
285C2×C4×C7#12112yes—
286C2×C4×C7#13512yes—
287C2×C4×C7#13512yes—
288C2×C4×C7C22×D411yescharacteristic
289C2×C4×C7C22×Q811yescharacteristic
290C2×C4×C7C2×#4111yescharacteristic
291C2×C4×C7C2×#4111yescharacteristic
292C2×C4×C72−1+411yescharacteristic
293C2×C4×C72−1+411yescharacteristic
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—41no—
297C2×Dic7—41no—
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—
315D28—22no—
316D28—22no—
317D28—41no—
318D28—41no—
319C4×D7—84no—
320C7×C8—22no—
321C7×C8—22no—
322C7×C8—22no—
323C7×C8—41no—
324C22×Q8D2811yescharacteristic
325C22×D4—71no—
326C23×C4—141no—
327C22×C8C22×D711yescharacteristic
328C22×C8C22×D711yescharacteristic
329C22×C8C22×D711yescharacteristic
330C22×C8C22×D711yescharacteristic
331#125—142no—
332#125—142no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×D4—142no—
336C4×D4—142no—
337C2×C4⋊C4—71no—
338C2×C4⋊C4—71no—
339C2×C4⋊C4—71no—
340C2×C4⋊C4—71no—
341C2×C4⋊C4—71no—
342C2×C4⋊C4—71no—
343C2×C4⋊C4—71no—
344C2×C4⋊C4—141no—
345C2×C4⋊C4—141no—
346C2×C4⋊C4—141no—
347C2×C4⋊C4—141no—
348C2×C4⋊C4—141no—
349C2×C4⋊C4—141no—
350C2×C4⋊C4—141no—
351C2×C4⋊C4—141no—
352C2×C4⋊C4D2811yescharacteristic
353C2×C4⋊C4D2811yescharacteristic
354C2×C4⋊C4D2811yescharacteristic
355C2×C22⋊C4—141no—
356C2×C22⋊C4—141no—
357C2×C22⋊C4—141no—
358C2×C22⋊C4—141no—
359C2×C22⋊C4—141no—
360C2×C42—141no—
361C2×C42C22×D711yescharacteristic
362C2×C42C22×D711yescharacteristic
363C2×C42C22×D711yescharacteristic
364#107—142no—
365#107—142no—
366#106—142no—
367#106—142no—
368C4⋊C8—22no—
369C4⋊C8—22no—
370C4⋊C8C22⋊D714yes—
371#102—74no—
372#102—142no—
373#102—142no—
374#102—142no—
375C4×C8—22no—
376C4×C8—22no—
377C4×C8—22no—
378#95—141no—
379#95—141no—
380#95—141no—
381#95—141no—
382#95—141no—
383#95—141no—
384#95—141no—
385#95—141no—
386#95—141no—
387C22×C7C2×#12111yescharacteristic
388C22×C7#54811yescharacteristic
389C22×C7D4×Q811yescharacteristic
390C22×C7C2×#13511yescharacteristic
391C22×C7C2×#13511yescharacteristic
392C22×C7#57611yescharacteristic
393C22×C7#57711yescharacteristic
394C2×D7—42no—
395C2×D7—42no—
396C2×D7—42no—
397C2×D7—81no—
398C2×D7—81no—
399C2×D7—81no—
400C2×D7—81no—
401C4×C7—22no—
402C4×C7—22no—
403C4×C7—22no—
404C4×C7—22no—
405C4×C7—41no—
406C4×C7—41no—
407C4×C7#53311yescharacteristic
408C4×C7#54111yescharacteristic
409C4×C7#54711yescharacteristic
410C4×C7D4×Q811yescharacteristic
411Dic7—42no—
412Dic7—42no—
413Dic7—81no—
414Dic7—81no—
415Dic7—81no—
416Dic7—81no—
417Dic7—81no—
418C24—141no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×D4—72no—
423C2×D4—141no—
424C2×D4—141no—
425C2×D4—141no—
426C2×D4—141no—
427C2×D4—141no—
428C22×C4—141no—
429C22×C4—141no—
430C22×C4—141no—
431C22×C4—141no—
432C22×C4—141no—
433C22×C4—141no—
434C22×C4—141no—
435C22×C4—282no—
436C22×C4—561no—
437C22×C4—561no—
438C22×C4C2×D2811yescharacteristic
439C22×C4C2×D2811yescharacteristic
440C22×C4C2×D2811yescharacteristic
441C22×C4C2×D2811yescharacteristic
442C22×C4C2×D2811yescharacteristic
443C22×C4C2×D2811yescharacteristic
444C22×C4C23×D711yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8Q8×D712yes—
455C2×C8C2×C22⋊D712yes—
456C2×C8C2×C22⋊D712yes—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—72no—
461C4⋊C4—72no—
462C4⋊C4—141no—
463C4⋊C4—141no—
464C4⋊C4—141no—
465C4⋊C4—141no—
466C4⋊C4—141no—
467C4⋊C4—141no—
468C4⋊C4—141no—
469C4⋊C4—141no—
470C4⋊C4—141no—
471C4⋊C4—141no—
472C4⋊C4—141no—
473C4⋊C4—141no—
474C4⋊C4—282no—
475C4⋊C4—282no—
476C4⋊C4—282no—
477C4⋊C4—282no—
478C4⋊C4—561no—
479C4⋊C4—561no—
480C4⋊C4—561no—
481C4⋊C4—561no—
482C22⋊C4—282no—
483C22⋊C4—282no—
484C22⋊C4—282no—
485C22⋊C4—561no—
486C22⋊C4—561no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—561no—
492C42#115712yes—
493C42C2×C22⋊D712yes—
494C2×C7#242911yescharacteristic
495C2×C7#305011yescharacteristic
496C2×C7#306211yescharacteristic
497C2×C7#336111yescharacteristic
498C2×C7#336511yescharacteristic
499C2×C7#338011yescharacteristic
500C2×C7#338111yescharacteristic
501D7—82no—
502C23—142no—
503C23—281no—
504C23—281no—
505C23—281no—
506C23—281no—
507C23—281no—
508C23—281no—
509C23C22×D2811yescharacteristic
510Q8—28no—
511D4—142no—
512D4—142no—
513D4—281no—
514D4—281no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
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—142no—
530C2×C4—142no—
531C2×C4—281no—
532C2×C4—281no—
533C2×C4—281no—
534C2×C4—281no—
535C2×C4—281no—
536C2×C4—281no—
537C2×C4—281no—
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—564no—
551C2×C4#646712yes—
552C2×C4#646712yes—
553C2×C4#649312yes—
554C2×C4#649312yes—
555C2×C4C2×#115711yescharacteristic
556C2×C4C2×Q8×D711yescharacteristic
557C2×C4#655111yescharacteristic
558C2×C4D7×#4111yescharacteristic
559C2×C4#655411yescharacteristic
560C2×C4C22×C22⋊D711yescharacteristic
561C8—22no—
562C8—22no—
563C8—22no—
564C8—41no—
565C7#2547311yescharacteristic, complemented, Sylow
566C22—282no—
567C22—282no—
568C22—282no—
569C22—561no—
570C22—561no—
571C22—561no—
572C22—561no—
573C22Q8×D2811yescharacteristic
574C22#9026711yescharacteristic
575C22C2×#646711yescharacteristic
576C22C2×#646711yescharacteristic
577C22#9044211yescharacteristic
578C22#9044311yescharacteristic
579C22C2×#649311yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—282no—
587C4—282no—
588C4—561no—
589C4—561no—
590C4—561no—
591C4—561no—
592C4—561no—
593C4#9026911yescharacteristic
594C4#9027411yescharacteristic
595C4Q8×C22⋊D711yescharacteristic
596C4#9051511yescharacteristic
597C2—562no—
598C2#1173737211yescharacteristic
599C2#1173737511yescharacteristic
600C2#1173737611yescharacteristic
601C2#1173738011yescharacteristic
602C2#1173994111yescharacteristic
603C2#1174118711yescharacteristic
604C2#1174124711yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×C8×Q8C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×C8×Q8D7
hypocenterC7#25473
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C7×C8×Q8C2semidirect
3. #11739928C2semidirect
7. #11728218C2semidirect
8. #11728217C2semidirect
9. #11728209C2semidirect
10. #11727532C2semidirect
11. #11727524C2semidirect
12. #11727523C2semidirect
120. #6395Q8semidirect
126. C2×C8×Q8D7semidirect
565. C7#25473semidirect

Maximal subgroups

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

subgroupindex
C2×C7×C8×Q82
#117399462
#117399282
C2×#896192
#117282382
#117282372
#117282182
#117282172
#117282092
#117275322
#117275242
#117275232
#117275222
C4×#63952
#254737