Finite Group Databasebeta

← #13375643

Subgroups — #13375643

Order 1792.

846 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×#89619C211yesmaximal, characteristic
2#11731215C211yesmaximal, characteristic
3#11731104C211yesmaximal, characteristic, complemented
4C7×C8×C4⋊C4C211yesmaximal, characteristic, complemented
5#11728209C211yesmaximal, characteristic, complemented
6#11727532C211yesmaximal, characteristic, complemented
7#11727524C211yesmaximal, characteristic, complemented
8#11727523C211yesmaximal, characteristic, complemented
9C4×#6395C211yesmaximal, characteristic
10C4×#6395C211yesmaximal, characteristic
11C4×#6395C211yesmaximal, characteristic
12#11726425C211yesmaximal, characteristic
13#11726424C211yesmaximal, characteristic
14#11726378C211yesmaximal, characteristic, complemented
15#11726377C211yesmaximal, characteristic, complemented
16C2×C4×D28C2211yescharacteristic
17C2×C4×D28C2211yescharacteristic
18C2×C4×D28C2211yescharacteristic
19C2×#6433C2211yescharacteristic
20C2×C7×C4⋊C8C2211yescharacteristic
21C2×C4×C7×C8C2211yescharacteristic
22C2×C4×C7×C8C2211yescharacteristic
23C2×C4×C7×C8C2211yescharacteristic
24C4×C7×C4⋊C4C2211yescharacteristic
25C2×#6395C2211yescharacteristic
26C2×#6395C2211yescharacteristic
27C2×#6395C2211yescharacteristic
28C2×#6395C2211yescharacteristic
29C2×#6392C2211yescharacteristic
30C2×#6392C2211yescharacteristic
31C2×#6391C2211yescharacteristic
32C2×#6391C2211yescharacteristic
33#89761—21no—
34#89761—21no—
35#89750—21no—
36#89744—21no—
37#89708C2211yescharacteristic
38C4×C4⋊Dic7C2211yescharacteristic
39C4×C4⋊Dic7C2211yescharacteristic
40C4×C4⋊Dic7C2211yescharacteristic
41#89700C2211yescharacteristic
42#89700C2211yescharacteristic
43#89700C2211yescharacteristic
44#89700C2211yescharacteristic
45#89619C418yescomplemented
46#89439—21no—
47D7×#95—21no—
48#89424—21no—
49#89421—21no—
50C7×#336C2211yescharacteristic
51C7×#336C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#22966—71nomaximal, Sylow
61C22×D28C2311yescharacteristic
62C22×C4×D7—21no—
63C22×C4×D7—21no—
64C22×C4×D7—21no—
65C22×C7×C8C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C2×C7×C4⋊C4D411yescharacteristic
70C2×C7×C4⋊C4D411yescharacteristic
71C2×C42×C7C2311yescharacteristic
72C2×C42×C7C2311yescharacteristic
73C2×C42×C7C2311yescharacteristic
74C2×(C2×D7)⋊C4—21no—
75C2×(C2×D7)⋊C4—21no—
76C2×(C2×D7)⋊C4—21no—
77C2×C4⋊Dic7C2311yescharacteristic
78C2×C4⋊Dic7C2311yescharacteristic
79C2×C4⋊Dic7C2311yescharacteristic
80C2×C4⋊Dic7C2311yescharacteristic
81C2×C4⋊Dic7C2311yescharacteristic
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4⋊Dic7C2311yescharacteristic
84C2×Dic7⋊C4—21no—
85C2×Dic7⋊C4—21no—
86C2×Dic7⋊C4—21no—
87C2×Dic7⋊C4—21no—
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—21no—
90C2×C4×Dic7—21no—
91C2×C4×Dic7—21no—
92C2×C4×Dic7—21no—
93C4×D28—22no—
94C4×D28—22no—
95C4×D28—22no—
96C4×D28—41no—
97C4×D28—41no—
98C4×D28C2×C414yes—
99#6433—22no—
100#6433C2×C414yescomplemented
101C7×C4⋊C8C2×C414yescomplemented
102C4×C7×C8—22no—
103C4×C7×C8—41no—
104C4×C7×C8—41no—
105C7×#95D411yescharacteristic
106C7×#95D411yescharacteristic
107C7⋊#95—21no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116#6395—22no—
117#6395C2×C414yes—
118#6395C2×C414yes—
119#6395Q814yes—
120#6392—41no—
121#6392C2×C414yescomplemented
122#6391—41no—
123#6391C2×C414yescomplemented
124C2×#478—71no—
125#2370—71no—
126#2349—71no—
127#1991—71no—
128#1949—71no—
129#1942—71no—
130#1941—71no—
131#1921—71no—
132#1920—71no—
133#1864—71no—
134#1862—71no—
135C8×C4⋊C4D711yescharacteristic, complemented
136C4×#102—71no—
137C4×#102—71no—
138C4×#102—71no—
139C23×D7—21no—
140C22×C4×C7C2×D411yescharacteristic
141C22×C4×C7C2×D411yescharacteristic
142C22×C4×C7C2×D411yescharacteristic
143C22×C4×C7C2×D411yescharacteristic
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2411yescharacteristic
147C22×Dic7—21no—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C2×D28—21no—
155C2×D28—21no—
156C2×D28—21no—
157C2×D28C22×C412yes—
158C2×D28C2×Q812yes—
159C2×D28#4112yes—
160C2×C4×D7—24no—
161C2×C4×D7—42no—
162C2×C4×D7—42no—
163C2×C4×D7—42no—
164C2×C4×D7—42no—
165C2×C4×D7—81no—
166C2×C4×D7—81no—
167C2×C4×D7—81no—
168C2×C4×D7—81no—
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×C8—21no—
177C2×C7×C8—21no—
178C2×C7×C8C22×C412yes—
179C2×C7×C8C22×C412yes—
180C2×C7×C8C2×Q812yes—
181C7×C4⋊C4—22no—
182C7×C4⋊C4—22no—
183C42×C7—21no—
184C42×C7—21no—
185C42×C7—21no—
186C42×C7—21no—
187C42×C7C22×C412yes—
188C42×C7#4112yes—
189(C2×D7)⋊C4—24no—
190(C2×D7)⋊C4—42no—
191(C2×D7)⋊C4—42no—
192C4⋊Dic7—21no—
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⋊Dic7C22×C412yes—
203C4⋊Dic7C22×C412yes—
204C4⋊Dic7C22×C412yes—
205C4⋊Dic7C2×Q812yes—
206Dic7⋊C4—24no—
207Dic7⋊C4—24no—
208Dic7⋊C4—42no—
209Dic7⋊C4—81no—
210Dic7⋊C4—81no—
211Dic7⋊C4—81no—
212C4×Dic7—42no—
213C4×Dic7—81no—
214C4×Dic7—81no—
215C2×#125—71no—
216C2×C4×D4—71no—
217C2×C4×D4—71no—
218C2×C4×D4—71no—
219#478—78no—
220C2×#107—71no—
221C2×#107—71no—
222C2×#106—71no—
223C2×#106—71no—
224C2×C4⋊C8C2×D711yescharacteristic
225C2×#102—71no—
226C2×#102—71no—
227C2×#102—71no—
228C2×#102—71no—
229C2×C4×C8C2×D711yescharacteristic
230C2×C4×C8C2×D711yescharacteristic
231C2×C4×C8C2×D711yescharacteristic
232#389—71no—
233#389—71no—
234#389—71no—
235#389—71no—
236#389—141no—
237#387—141no—
238#387—141no—
239#385—141no—
240#385—141no—
241#382—71no—
242#380—141no—
243C4×C4⋊C4—71no—
244C4×C4⋊C4—71no—
245C4×C4⋊C4—71no—
246C4×C4⋊C4—141no—
247C4×C4⋊C4C2×D711yescharacteristic
248C2×#95—141no—
249#340—71no—
250#340—71no—
251#340—71no—
252#340—71no—
253#340—71no—
254#340—71no—
255#340—71no—
256#340—71no—
257#336C2×D711yescharacteristic
258#336C2×D711yescharacteristic
259C23×C7C22×D411yescharacteristic
260C22×D7—22no—
261C22×D7—22no—
262C22×D7—22no—
263C22×D7—41no—
264C22×D7—41no—
265C22×D7—41no—
266C22×D7—41no—
267C2×C4×C7—21no—
268C2×C4×C7—21no—
269C2×C4×C7—21no—
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×C7C4×D412yes—
282C2×C4×C7C4×D412yes—
283C2×C4×C7#13512yes—
284C2×C4×C7#13512yes—
285C2×C4×C7C23×C411yescharacteristic
286C2×C4×C7C22×Q811yescharacteristic
287C2×C4×C7C2×#4111yescharacteristic
288C2×C4×C7C2×#4111yescharacteristic
289C2×C4×C7H(5,𝔽2)11yescharacteristic
290C2×C4×C72−1+411yescharacteristic
291C2×Dic7—22no—
292C2×Dic7—22no—
293C2×Dic7—22no—
294C2×Dic7—22no—
295C2×Dic7—41no—
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—
312D28—22no—
313D28—22no—
314D28—22no—
315D28C4×Q814yes—
316C4×D7—84no—
317C4×D7—84no—
318C4×D7—84no—
319C7×C8—22no—
320C7×C8—22no—
321C7×C8—22no—
322C7×C8—41no—
323C22×D4—71no—
324C23×C4—141no—
325C23×C4—141no—
326C23×C4—141no—
327C22×C8C22×D711yescharacteristic
328C22×C8C22×D711yescharacteristic
329C22×C8C22×D711yescharacteristic
330C22×C8C22×D711yescharacteristic
331#125—74no—
332#125—142no—
333C4×D4—74no—
334C4×D4—142no—
335C4×D4—142no—
336C4×D4—142no—
337C4×D4—281no—
338C4×D4—281no—
339C2×C4⋊C4—71no—
340C2×C4⋊C4—71no—
341C2×C4⋊C4—71no—
342C2×C4⋊C4—71no—
343C2×C4⋊C4—71no—
344C2×C4⋊C4—71no—
345C2×C4⋊C4—71no—
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×C22⋊C4—141no—
355C2×C22⋊C4—141no—
356C2×C22⋊C4—141no—
357C2×C42—141no—
358C2×C42—141no—
359C2×C42—141no—
360C2×C42C22×D711yescharacteristic
361C2×C42C22×D711yescharacteristic
362C2×C42C22×D711yescharacteristic
363#107—74no—
364#107—281no—
365#106—74no—
366#106—281no—
367C4⋊C8C4×D714yescomplemented
368#102—74no—
369#102—74no—
370#102—74no—
371#102—142no—
372C4×C8—22no—
373C4×C8—41no—
374C4×C8—41no—
375#95—141no—
376#95—141no—
377#95—141no—
378#95—141no—
379#95—141no—
380#95—141no—
381#95—141no—
382#95—141no—
383#95—141no—
384#95D2811yescharacteristic
385#95D2811yescharacteristic
386C22×C7C2×C4×D411yescharacteristic
387C22×C7#54611yescharacteristic
388C22×C7D4×Q811yescharacteristic
389C22×C7C2×#13511yescharacteristic
390C22×C7C2×#13511yescharacteristic
391C22×C7#57611yescharacteristic
392C22×C7#57711yescharacteristic
393C2×D7—24no—
394C2×D7—42no—
395C2×D7—42no—
396C2×D7—42no—
397C2×D7—42no—
398C2×D7—42no—
399C2×D7—42no—
400C4×C7—22no—
401C4×C7—22no—
402C4×C7—22no—
403C4×C7—22no—
404C4×C7—41no—
405C4×C7—41no—
406C4×C7C2×C4×Q811yescharacteristic
407C4×C7#52011yescharacteristic
408C4×C7#55211yescharacteristic
409C4×C7#55411yescharacteristic
410Dic7—42no—
411Dic7—42no—
412Dic7—42no—
413Dic7—42no—
414Dic7—81no—
415Dic7—81no—
416Dic7—81no—
417C24—141no—
418C2×D4—72no—
419C2×D4—72no—
420C2×D4—72no—
421C2×D4—141no—
422C2×D4—141no—
423C2×D4—141no—
424C22×C4—141no—
425C22×C4—141no—
426C22×C4—141no—
427C22×C4—141no—
428C22×C4—144no—
429C22×C4—141no—
430C22×C4—141no—
431C22×C4—141no—
432C22×C4—282no—
433C22×C4—282no—
434C22×C4—282no—
435C22×C4—282no—
436C22×C4—561no—
437C22×C4—561no—
438C22×C4—561no—
439C22×C4—561no—
440C22×C4C2×D2811yescharacteristic
441C22×C4C2×D2811yescharacteristic
442C22×C4C2×D2811yescharacteristic
443C22×C4C2×D2811yescharacteristic
444C22×C4C2×D2811yescharacteristic
445C22×C4C2×D2811yescharacteristic
446C22×C4C23×D711yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8C2×C4×D712yes—
457C2×C8C2×C4×D712yes—
458C2×C8Q8×D712yes—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—72no—
462C4⋊C4—72no—
463C4⋊C4—72no—
464C4⋊C4—72no—
465C4⋊C4—144no—
466C4⋊C4—144no—
467C4⋊C4—141no—
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—282no—
478C4⋊C4—561no—
479C4⋊C4—561no—
480C4⋊C4—561no—
481C22⋊C4—144no—
482C22⋊C4—282no—
483C22⋊C4—282no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—282no—
489C42—561no—
490C42—561no—
491C42C2×C4×D712yes—
492C42#115712yes—
493C2×C7#236011yescharacteristic
494C2×C7C4×#13511yescharacteristic
495C2×C7#294611yescharacteristic
496C2×C7#329611yescharacteristic
497C2×C7#329711yescharacteristic
498C2×C7#338011yescharacteristic
499C2×C7#338111yescharacteristic
500D7—44no—
501C23—142no—
502C23—142no—
503C23—142no—
504C23—281no—
505C23—281no—
506C23—281no—
507C23—281no—
508C23C22×D2811yescharacteristic
509D4—74no—
510D4—142no—
511D4—142no—
512D4—142no—
513C2×C4—21no—
514C2×C4—21no—
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—142no—
528C2×C4—142no—
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—564no—
549C2×C4—564no—
550C2×C4—564no—
551C2×C4C4×D2812yes—
552C2×C4C4×D2812yes—
553C2×C4#646712yes—
554C2×C4#646712yes—
555C2×C4C22×C4×D711yescharacteristic
556C2×C4C2×#115711yescharacteristic
557C2×C4#654811yescharacteristic
558C2×C4C2×Q8×D711yescharacteristic
559C2×C4D7×#4111yescharacteristic
560C2×C4#655411yescharacteristic
561C8—22no—
562C8—22no—
563C8—22no—
564C8—41no—
565C7#2296611yescharacteristic, complemented, Sylow
566C22—144no—
567C22—282no—
568C22—282no—
569C22—282no—
570C22—282no—
571C22—282no—
572C22—282no—
573C22C2×C4×D2811yescharacteristic
574C22#9024511yescharacteristic
575C22Q8×D2811yescharacteristic
576C22C2×#646711yescharacteristic
577C22C2×#646711yescharacteristic
578C22#9044211yescharacteristic
579C22#9044311yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—282no—
587C4—282no—
588C4—282no—
589C4—282no—
590C4—561no—
591C4—561no—
592C4—561no—
593C4#9020211yescharacteristic
594C4#9022011yescharacteristic
595C4#9023711yescharacteristic
596C4C4×Q8×D711yescharacteristic
597C2—284no—
598C2#1173121811yescharacteristic
599C2C4×#646711yescharacteristic
600C2#1173600511yescharacteristic
601C2#1173688511yescharacteristic
602C2#1173688611yescharacteristic
603C2#1173737511yescharacteristic
604C2#1173737611yescharacteristic
subgroupG/H
centerC23C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×C8×C4⋊C4C2
socleC23×C7C22×D4
prime radicalC22×D28C23
cosocleC22×C4×C7C24
hypercenterC8×C4⋊C4D7
hypocenterC7#22966
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #11731104C2semidirect
4. C7×C8×C4⋊C4C2semidirect
5. #11728209C2semidirect
6. #11727532C2semidirect
7. #11727524C2semidirect
8. #11727523C2semidirect
14. #11726378C2semidirect
15. #11726377C2semidirect
45. #89619C4semidirect
100. #6433C2×C4semidirect
101. C7×C4⋊C8C2×C4semidirect
121. #6392C2×C4semidirect
123. #6391C2×C4semidirect
135. C8×C4⋊C4D7semidirect
367. C4⋊C8C4×D7semidirect
565. C7#22966semidirect

Maximal subgroups

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

subgroupindex
C2×#896192
#117312152
#117311042
C7×C8×C4⋊C42
#117282092
#117275322
#117275242
#117275232
C4×#63952
#117264252
#117264242
#117263782
#117263772
#229667