Finite Group Databasebeta

← #13276470

Subgroups — #13276470

Order 1792.

1630 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89744C212yesmaximal
2C2×C4×Dic7⋊C4C211yesmaximal, characteristic
3C2×#89419C212yesmaximal
4C2×#89422C211yesmaximal, characteristic
5C2×#89421C211yesmaximal, characteristic
6C7×C4⋊#95C211yesmaximal, characteristic
7#11729322C212yesmaximal
8#11729289C211yesmaximal, characteristic
9#11727174C212yesmaximal
10Dic7⋊#95C211yesmaximal, characteristic
11Dic7⋊#95C211yesmaximal, characteristic
12C22×C7×C4⋊C4C2212yes—
13C22×C42×C7C2211yescharacteristic
14C22×C4⋊Dic7C2212yes—
15C22×Dic7⋊C4C2212yes—
16C22×Dic7⋊C4C2212yes—
17C22×Dic7⋊C4C2212yes—
18C22×Dic7⋊C4C2212yes—
19C22×Dic7⋊C4C2211yescharacteristic
20C22×Dic7⋊C4C2211yescharacteristic
21C22×C4×Dic7C2212yes—
22C22×C4×Dic7C2211yescharacteristic
23C22×C4×Dic7C2211yescharacteristic
24C2×C7×#95C2211yescharacteristic
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2211yescharacteristic
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2211yescharacteristic
35#89744—28no—
36C4×Dic7⋊C4C418yescomplemented
37#89422—24no—
38#89421—24no—
39#89419—28no—
40#13954—71nomaximal, Sylow
41C23×C4×C7C2312yes—
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×Dic7C2312yes—
47C23×Dic7C2312yes—
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C2×C7×C4⋊C4—24no—
53C2×C7×C4⋊C4—24no—
54C2×C7×C4⋊C4—42no—
55C2×C42×C7—42no—
56C2×C42×C7C2×C414yes—
57C2×C4⋊Dic7—24no—
58C2×C4⋊Dic7—24no—
59C2×C4⋊Dic7—42no—
60C2×Dic7⋊C4—24no—
61C2×Dic7⋊C4—24no—
62C2×Dic7⋊C4—24no—
63C2×Dic7⋊C4—24no—
64C2×Dic7⋊C4—24no—
65C2×Dic7⋊C4—24no—
66C2×Dic7⋊C4—24no—
67C2×Dic7⋊C4—24no—
68C2×Dic7⋊C4—24no—
69C2×Dic7⋊C4—24no—
70C2×Dic7⋊C4—42no—
71C2×Dic7⋊C4—42no—
72C2×Dic7⋊C4C2×C414yes—
73C2×Dic7⋊C4C2×C414yes—
74C2×Dic7⋊C4D414yes—
75C2×Dic7⋊C4D414yes—
76C2×Dic7⋊C4Q814yes—
77C2×Dic7⋊C4Q814yes—
78C2×C4×Dic7—24no—
79C2×C4×Dic7—24no—
80C2×C4×Dic7—24no—
81C2×C4×Dic7—42no—
82C2×C4×Dic7C2×C414yes—
83C2×C4×Dic7C2×C414yes—
84C2×C4×Dic7D414yes—
85C2×C4×Dic7Q814yes—
86C7×#95—24no—
87C7×#95—22no—
88C7×#95—22no—
89C7⋊#95—22no—
90C7⋊#95—22no—
91C7⋊#95—24no—
92C7⋊#95—24no—
93C7⋊#95—24no—
94C7⋊#95—24no—
95C7⋊#95C2×C414yes—
96C7⋊#95C2×C414yes—
97C2×#389—72no—
98C2×#389—72no—
99C2×#382—71no—
100C2×C4×C4⋊C4—71no—
101C2×C4×C4⋊C4—71no—
102#1444—72no—
103#1444—72no—
104C4⋊#95—71no—
105C4⋊#95—71no—
106C4⋊#95—71no—
107C4⋊#95D711yescharacteristic
108C24×C7C2411yescharacteristic
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7C22×C412yes—
129C22×C4×C7C22×C412yes—
130C22×C4×C7C22×C412yes—
131C22×C4×C7C2×D412yes—
132C22×C4×C7C2×D412yes—
133C22×C4×C7C2×D412yes—
134C22×C4×C7C2×Q812yes—
135C22×C4×C7C2×Q812yes—
136C22×C4×C7C2×Q812yes—
137C22×C4×C7#4114yes—
138C22×Dic7—22no—
139C22×Dic7—22no—
140C22×Dic7—22no—
141C22×Dic7—22no—
142C22×Dic7—22no—
143C22×Dic7—22no—
144C22×Dic7—22no—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7C22×C412yes—
158C22×Dic7C22×C412yes—
159C22×Dic7C22×C412yes—
160C22×Dic7C22×C412yes—
161C22×Dic7C2×D412yes—
162C22×Dic7C2×D412yes—
163C22×Dic7C2×D412yes—
164C22×Dic7C2×D412yes—
165C22×Dic7C2×D412yes—
166C22×Dic7C2×D412yes—
167C22×Dic7C2×Q812yes—
168C22×Dic7C2×Q812yes—
169C22×Dic7C2×Q812yes—
170C22×Dic7C2×Q812yes—
171C22×Dic7C2×Q812yes—
172C22×Dic7C2×Q812yes—
173C22×Dic7#4114yes—
174C7×C4⋊C4—48no—
175C42×C7—44no—
176C4⋊Dic7—48no—
177Dic7⋊C4—216no—
178Dic7⋊C4—48no—
179Dic7⋊C4—48no—
180Dic7⋊C4—48no—
181Dic7⋊C4C4⋊C4116yescomplemented
182Dic7⋊C4C4⋊C4116yescomplemented
183C4×Dic7—44no—
184C4×Dic7—48no—
185C4×Dic7C4⋊C4116yescomplemented
186C22×C4⋊C4—71no—
187C22×C4⋊C4—71no—
188C22×C4⋊C4—72no—
189C22×C4⋊C4—72no—
190C22×C4⋊C4—72no—
191C22×C4⋊C4—72no—
192C22×C4⋊C4—72no—
193C22×C4⋊C4C2×D712yes—
194C22×C42—71no—
195C22×C42—71no—
196C22×C42—72no—
197C22×C42C2×D711yescharacteristic
198#389—148no—
199#389—148no—
200#382—144no—
201C4×C4⋊C4—78no—
202C4×C4⋊C4—144no—
203C2×#95—71no—
204C2×#95—71no—
205C2×#95—71no—
206C2×#95—71no—
207C2×#95—72no—
208C2×#95—72no—
209C2×#95—72no—
210C2×#95—72no—
211C2×#95C2×D711yescharacteristic
212C2×#95C2×D711yescharacteristic
213C2×#95C2×D712yes—
214C23×C7C23×C411yescharacteristic
215C23×C7C22×D411yescharacteristic
216C23×C7C22×D411yescharacteristic
217C23×C7C22×D411yescharacteristic
218C23×C7C22×Q811yescharacteristic
219C23×C7C22×Q811yescharacteristic
220C23×C7C22×Q811yescharacteristic
221C23×C7C2×#4112yes—
222C23×C7C2×#4112yes—
223C23×C7H(5,𝔽2)12yes—
224C23×C72−1+412yes—
225C2×C4×C7—22no—
226C2×C4×C7—22no—
227C2×C4×C7—22no—
228C2×C4×C7—22no—
229C2×C4×C7—22no—
230C2×C4×C7—22no—
231C2×C4×C7—24no—
232C2×C4×C7—24no—
233C2×C4×C7—24no—
234C2×C4×C7—24no—
235C2×C4×C7—24no—
236C2×C4×C7—24no—
237C2×C4×C7—24no—
238C2×C4×C7—24no—
239C2×C4×C7—24no—
240C2×C4×C7—42no—
241C2×C4×C7—42no—
242C2×C4×C7—42no—
243C2×C4×C7—42no—
244C2×C4×C7—42no—
245C2×C4×C7—42no—
246C2×C4×C7—42no—
247C2×C4×C7—42no—
248C2×C4×C7—42no—
249C2×C4×C7—42no—
250C2×C4×C7—42no—
251C2×C4×C7C2×C4⋊C414yes—
252C2×C4×C7C2×C4⋊C414yes—
253C2×C4×C7C2×C4⋊C414yes—
254C2×Dic7—22no—
255C2×Dic7—22no—
256C2×Dic7—22no—
257C2×Dic7—22no—
258C2×Dic7—22no—
259C2×Dic7—22no—
260C2×Dic7—24no—
261C2×Dic7—24no—
262C2×Dic7—24no—
263C2×Dic7—24no—
264C2×Dic7—24no—
265C2×Dic7—24no—
266C2×Dic7—24no—
267C2×Dic7—24no—
268C2×Dic7—24no—
269C2×Dic7—42no—
270C2×Dic7—42no—
271C2×Dic7—42no—
272C2×Dic7—42no—
273C2×Dic7—42no—
274C2×Dic7—42no—
275C2×Dic7—42no—
276C2×Dic7—42no—
277C2×Dic7—42no—
278C2×Dic7—42no—
279C2×Dic7—42no—
280C2×Dic7C2×C4⋊C414yes—
281C2×Dic7C2×C4⋊C414yes—
282C2×Dic7C2×C4⋊C414yes—
283C2×Dic7C2×C4⋊C414yes—
284C2×Dic7C2×C4⋊C414yes—
285C2×Dic7C2×C4⋊C414yes—
286C2×Dic7#12714yes—
287C2×Dic7C4⋊Q814yes—
288C2×Dic7C4⋊Q814yes—
289C2×Dic7C4⋊Q814yes—
290C23×C4—71no—
291C23×C4—71no—
292C23×C4—71no—
293C23×C4—71no—
294C23×C4—72no—
295C23×C4—72no—
296C23×C4C22×D712yes—
297C23×C4C22×D712yes—
298C23×C4C22×D711yescharacteristic
299C23×C4C22×D711yescharacteristic
300C23×C4C22×D711yescharacteristic
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—74no—
305C2×C4⋊C4—74no—
306C2×C4⋊C4—74no—
307C2×C4⋊C4—74no—
308C2×C4⋊C4—74no—
309C2×C4⋊C4—74no—
310C2×C4⋊C4—144no—
311C2×C4⋊C4—144no—
312C2×C4⋊C4—144no—
313C2×C4⋊C4—144no—
314C2×C4⋊C4—144no—
315C2×C4⋊C4—144no—
316C2×C4⋊C4—144no—
317C2×C4⋊C4—144no—
318C2×C4⋊C4—144no—
319C2×C4⋊C4—144no—
320C2×C4⋊C4—144no—
321C2×C4⋊C4—144no—
322C2×C4⋊C4—282no—
323C2×C4⋊C4—282no—
324C2×C4⋊C4—282no—
325C2×C42—42no—
326C2×C42—74no—
327C2×C42—74no—
328C2×C42—74no—
329C2×C42—74no—
330C2×C42—144no—
331C2×C42—144no—
332C2×C42—144no—
333C2×C42—282no—
334C2×C42C4×D714yes—
335#95—22no—
336#95—22no—
337#95—24no—
338#95—74no—
339#95—74no—
340#95—144no—
341#95—144no—
342#95—144no—
343#95—142no—
344#95—142no—
345#95—144no—
346C22×C7C22×C4⋊C411yescharacteristic
347C22×C7C22×C4⋊C411yescharacteristic
348C22×C7C22×C4⋊C411yescharacteristic
349C22×C7C4×#4111yescharacteristic
350C22×C7C4×#4111yescharacteristic
351C22×C7#51811yescharacteristic
352C22×C7#51911yescharacteristic
353C22×C7#52512yes—
354C22×C7C2×#12711yescharacteristic
355C22×C7C2×C4⋊Q811yescharacteristic
356C22×C7C2×C4⋊Q811yescharacteristic
357C22×C7C2×C4⋊Q811yescharacteristic
358C22×C7#53312yes—
359C22×C7#53712yes—
360C22×C7#54412yes—
361C22×C7#54612yes—
362C22×C7#54612yes—
363C22×C7#54812yes—
364C22×C7#54812yes—
365C22×C7#55412yes—
366C22×C7#55412yes—
367C22×C7#55712yes—
368C22×C7#55712yes—
369C4×C7—24no—
370C4×C7—24no—
371C4×C7—24no—
372C4×C7—44no—
373C4×C7—82no—
374Dic7—24no—
375Dic7—24no—
376Dic7—24no—
377Dic7—44no—
378Dic7—82no—
379Dic7#38418yes—
380C24C23×D711yescharacteristic
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—72no—
401C22×C4—72no—
402C22×C4—72no—
403C22×C4—72no—
404C22×C4—72no—
405C22×C4—72no—
406C22×C4—72no—
407C22×C4—72no—
408C22×C4—72no—
409C22×C4—72no—
410C22×C4—72no—
411C22×C4—72no—
412C22×C4—72no—
413C22×C4—72no—
414C22×C4—72no—
415C22×C4—72no—
416C22×C4—74no—
417C22×C4—142no—
418C22×C4—142no—
419C22×C4—142no—
420C22×C4—142no—
421C22×C4—142no—
422C22×C4—142no—
423C22×C4—142no—
424C22×C4—142no—
425C22×C4—142no—
426C22×C4—142no—
427C22×C4—142no—
428C22×C4—142no—
429C22×C4—142no—
430C22×C4—142no—
431C22×C4—142no—
432C22×C4—142no—
433C22×C4—142no—
434C22×C4—142no—
435C22×C4—142no—
436C22×C4C2×C4×D712yes—
437C22×C4C2×C4×D712yes—
438C22×C4C2×C4×D712yes—
439C22×C4#115714yes—
440C22×C4D4×D712yes—
441C22×C4D4×D712yes—
442C22×C4D4×D712yes—
443C22×C4Q8×D712yes—
444C22×C4Q8×D712yes—
445C22×C4Q8×D712yes—
446C4⋊C4—48no—
447C4⋊C4—716no—
448C4⋊C4—716no—
449C4⋊C4—1416no—
450C4⋊C4—288no—
451C4⋊C4—288no—
452C4⋊C4—288no—
453C4⋊C4—288no—
454C42—44no—
455C42—716no—
456C42—284no—
457C42—288no—
458C2×C7C2×#38411yescharacteristic
459C2×C7#229611yescharacteristic
460C2×C7#231611yescharacteristic
461C2×C7#234911yescharacteristic
462C2×C7#234911yescharacteristic
463C2×C7#235111yescharacteristic
464C2×C7#235111yescharacteristic
465C2×C7#254012yes—
466C2×C7#255012yes—
467C2×C7#255012yes—
468C2×C7#258412yes—
469C23C22×C4×D711yescharacteristic
470C23C2×#115712yes—
471C23C2×D4×D711yescharacteristic
472C23C2×D4×D711yescharacteristic
473C23C2×D4×D711yescharacteristic
474C23#654812yes—
475C23C2×Q8×D711yescharacteristic
476C23C2×Q8×D711yescharacteristic
477C23C2×Q8×D711yescharacteristic
478C23D7×#4112yes—
479C23#655412yes—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—74no—
507C2×C4—74no—
508C2×C4—74no—
509C2×C4—74no—
510C2×C4—74no—
511C2×C4—74no—
512C2×C4—74no—
513C2×C4—74no—
514C2×C4—74no—
515C2×C4—74no—
516C2×C4—142no—
517C2×C4—142no—
518C2×C4—142no—
519C2×C4—142no—
520C2×C4—144no—
521C2×C4—144no—
522C2×C4—142no—
523C2×C4—142no—
524C2×C4—144no—
525C2×C4—144no—
526C2×C4—144no—
527C2×C4—144no—
528C2×C4—144no—
529C2×C4—144no—
530C2×C4—144no—
531C2×C4—282no—
532C2×C4—282no—
533C2×C4—282no—
534C2×C4—282no—
535C2×C4—282no—
536C2×C4—282no—
537C2×C4—282no—
538C2×C4—282no—
539C2×C4—282no—
540C2×C4—282no—
541C2×C4—282no—
542C2×C4D7×C4⋊C414yes—
543C2×C4D7×C4⋊C414yes—
544C2×C4D7×C4⋊C414yes—
545C7#1395411yescharacteristic, complemented, Sylow
546C22C4×#115711yescharacteristic
547C22#9017711yescharacteristic
548C22#9018112yes—
549C22C2×D7×C4⋊C411yescharacteristic
550C22C2×D7×C4⋊C411yescharacteristic
551C22C2×D7×C4⋊C411yescharacteristic
552C22#9020212yes—
553C22#9020711yescharacteristic
554C22#9021311yescharacteristic
555C22#9023812yes—
556C22#9024312yes—
557C22#9025812yes—
558C22#9026912yes—
559C22#9028812yes—
560C22#9030112yes—
561C22#9031412yes—
562C22#9032712yes—
563C22#9036812yes—
564C22#9037612yes—
565C22D7×#12711yescharacteristic
566C22D7×C4⋊Q811yescharacteristic
567C22D7×C4⋊Q811yescharacteristic
568C22D7×C4⋊Q811yescharacteristic
569C4—24no—
570C4—24no—
571C4—24no—
572C4—44no—
573C4—78no—
574C4—82no—
575C4—144no—
576C4—144no—
577C4—144no—
578C4—284no—
579C4—562no—
580C2#1173081411yescharacteristic
581C2#1173108211yescharacteristic
582C2#1173120011yescharacteristic
583C2#1173131411yescharacteristic
584C2#1173145611yescharacteristic
585C2#1173160211yescharacteristic
586C2D7×#38411yescharacteristic
587C2#1173350812yes—
588C2#1173352512yes—
589C2#1173379212yes—
590C2#1173398212yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, prime radical, cosocleC24×C7C24
hypercenterC4⋊#95D7
hypocenterC7#13954
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
36. C4×Dic7⋊C4C4semidirect
181. Dic7⋊C4C4⋊C4semidirect
182. Dic7⋊C4C4⋊C4semidirect
185. C4×Dic7C4⋊C4semidirect
545. C7#13954semidirect

Maximal subgroups

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

subgroupindex
C2×#897442
C2×C4×Dic7⋊C42
C2×#894192
C2×#894222
C2×#894212
C7×C4⋊#952
#117293222
#117292892
#117271742
Dic7⋊#952
#139547