Finite Group Databasebeta

← #13282520

Subgroups — #13282520

Order 1792.

1398 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×#89701C211yesmaximal, characteristic
2C2×#89418C212yesmaximal
3C7×C4⋊#95C211yesmaximal, characteristic
4#11729322C212yesmaximal
5#11729318C212yesmaximal
6#11729289C211yesmaximal, characteristic
7#11727174C212yesmaximal
8#11727165C212yesmaximal
9#11727161C212yesmaximal
10C23×Dic14C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C42×C7C2211yescharacteristic
14C22×C4⋊Dic7C2211yescharacteristic
15C22×C4⋊Dic7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×Dic7⋊C4C2212yes—
18C22×Dic7⋊C4C2212yes—
19C22×C4×Dic7C2212yes—
20C2×C7×#95C2212yes—
21C2×C7×#95C2212yes—
22C2×C7⋊#95C2212yes—
23C2×C7⋊#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31#89701C418yescomplemented
32#89418—28no—
33#14467—71nomaximal, Sylow
34C23×C4×C7C2312yes—
35C23×C4×C7C2312yes—
36C23×C4×C7C2311yescharacteristic
37C23×C4×C7C2311yescharacteristic
38C23×C4×C7C2311yescharacteristic
39C23×Dic7C2312yes—
40C23×Dic7C2312yes—
41C23×Dic7C2312yes—
42C23×Dic7C2312yes—
43C22×Dic14—41no—
44C22×Dic14—41no—
45C22×Dic14—41no—
46C22×Dic14—41no—
47C22×Dic14C2×C414yes—
48C22×Dic14D414yes—
49C22×Dic14Q814yes—
50C2×C7×C4⋊C4—22no—
51C2×C7×C4⋊C4—41no—
52C2×C7×C4⋊C4—41no—
53C2×C7×C4⋊C4—41no—
54C2×C7×C4⋊C4—41no—
55C2×C7×C4⋊C4Q814yescomplemented
56C2×C42×C7—41no—
57C2×C42×C7—41no—
58C2×C42×C7C2×C414yes—
59C2×C4⋊Dic7—22no—
60C2×C4⋊Dic7—41no—
61C2×C4⋊Dic7—41no—
62C2×C4⋊Dic7—41no—
63C2×C4⋊Dic7—41no—
64C2×C4⋊Dic7—41no—
65C2×C4⋊Dic7—41no—
66C2×C4⋊Dic7C2×C414yes—
67C2×C4⋊Dic7Q814yescomplemented
68C2×Dic7⋊C4—24no—
69C2×Dic7⋊C4—42no—
70C2×Dic7⋊C4—42no—
71C2×Dic7⋊C4—42no—
72C2×Dic7⋊C4—42no—
73C2×Dic7⋊C4—42no—
74C2×C4×Dic7—24no—
75C2×C4×Dic7—42no—
76C2×C4×Dic7—42no—
77C7×#95—24no—
78C7×#95—24no—
79C7⋊#95—24no—
80C7⋊#95—24no—
81C7⋊#95—24no—
82C7⋊#95—24no—
83C7⋊#95—42no—
84C7⋊#95—42no—
85C7⋊#95—42no—
86C7⋊#95C2×C418yes—
87C7⋊#95C2×C418yes—
88C2×#391—71no—
89C2×#391—72no—
90#1444—72no—
91#1444—72no—
92#1441—72no—
93#1436—72no—
94#1436—72no—
95C4⋊#95—71no—
96C4⋊#95D711yescharacteristic
97C24×C7C2411yescharacteristic
98C22×C4×C7—21no—
99C22×C4×C7—21no—
100C22×C4×C7—21no—
101C22×C4×C7—21no—
102C22×C4×C7—21no—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—21no—
106C22×C4×C7—21no—
107C22×C4×C7—21no—
108C22×C4×C7—21no—
109C22×C4×C7—21no—
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×C7C22×C412yes—
124C22×C4×C7C22×C412yes—
125C22×C4×C7C22×C412yes—
126C22×C4×C7C2×D412yes—
127C22×C4×C7C2×Q814yes—
128C22×C4×C7C2×Q812yes—
129C22×C4×C7C2×Q812yes—
130C22×C4×C7C2×Q812yes—
131C22×C4×C7#4112yes—
132C22×C4×C7#4112yes—
133C22×Dic7—22no—
134C22×Dic7—22no—
135C22×Dic7—22no—
136C22×Dic7—22no—
137C22×Dic7—22no—
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×Dic7C22×C414yes—
157C22×Dic7C22×C414yes—
158C22×Dic7C2×D414yes—
159C22×Dic7C2×Q814yes—
160C22×Dic7C2×Q814yes—
161C2×Dic14—44no—
162C2×Dic14—44no—
163C2×Dic14—44no—
164C2×Dic14—44no—
165C2×Dic14—44no—
166C2×Dic14—44no—
167C2×Dic14C4⋊C4116yescomplemented
168C7×C4⋊C4—44no—
169C7×C4⋊C4—44no—
170C42×C7—44no—
171C4⋊Dic7—44no—
172C4⋊Dic7—44no—
173C4⋊Dic7—44no—
174Dic7⋊C4—48no—
175Dic7⋊C4—48no—
176C4×Dic7—48no—
177C23×Q8—71no—
178C22×C4⋊C4—71no—
179C22×C4⋊C4—71no—
180C22×C4⋊C4—72no—
181C22×C4⋊C4—71no—
182C22×C4⋊C4—72no—
183C22×C4⋊C4C2×D711yescharacteristic
184C22×C4⋊C4C2×D711yescharacteristic
185C22×C42—72no—
186C22×C42C2×D711yescharacteristic
187#391—78no—
188#391—148no—
189C2×#95—72no—
190C2×#95—72no—
191C2×#95—72no—
192C2×#95—72no—
193C2×#95—72no—
194C2×#95—72no—
195C2×#95—72no—
196C2×#95—72no—
197C2×#95—72no—
198C2×#95C2×D712yes—
199C2×#95C2×D712yes—
200C23×C7C23×C411yescharacteristic
201C23×C7C22×D411yescharacteristic
202C23×C7C22×Q811yescharacteristic
203C23×C7C22×Q811yescharacteristic
204C23×C7C22×Q811yescharacteristic
205C23×C7C2×#4111yescharacteristic
206C23×C7C2×#4111yescharacteristic
207C23×C7H(5,𝔽2)11yescharacteristic
208C23×C7H(5,𝔽2)11yescharacteristic
209C23×C7H(5,𝔽2)11yescharacteristic
210C23×C7H(5,𝔽2)11yescharacteristic
211C23×C7H(5,𝔽2)11yescharacteristic
212C23×C7H(5,𝔽2)11yescharacteristic
213C23×C72−1+411yescharacteristic
214C23×C72−1+411yescharacteristic
215C2×C4×C7—22no—
216C2×C4×C7—22no—
217C2×C4×C7—22no—
218C2×C4×C7—22no—
219C2×C4×C7—22no—
220C2×C4×C7—22no—
221C2×C4×C7—22no—
222C2×C4×C7—22no—
223C2×C4×C7—22no—
224C2×C4×C7—22no—
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—22no—
232C2×C4×C7—22no—
233C2×C4×C7—24no—
234C2×C4×C7—24no—
235C2×C4×C7—24no—
236C2×C4×C7—42no—
237C2×C4×C7—42no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
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×C7C2×C4⋊C414yes—
248C2×C4×C7C4×Q814yes—
249C2×C4×C7C4×Q814yes—
250C2×Dic7—24no—
251C2×Dic7—24no—
252C2×Dic7—24no—
253C2×Dic7—24no—
254C2×Dic7—24no—
255C2×Dic7—24no—
256C2×Dic7—24no—
257C2×Dic7—24no—
258C2×Dic7—24no—
259C2×Dic7—24no—
260C2×Dic7—24no—
261C2×Dic7—24no—
262C2×Dic7—42no—
263C2×Dic7—42no—
264C2×Dic7—42no—
265C2×Dic7—42no—
266C2×Dic7—42no—
267C2×Dic7—42no—
268C2×Dic7—42no—
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×Dic7C2×C4⋊C418yes—
278Dic14—416no—
279C22×Q8—74no—
280C22×Q8—74no—
281C22×Q8—74no—
282C22×Q8—281no—
283C22×Q8—281no—
284C22×Q8—281no—
285C22×Q8—281no—
286C23×C4—72no—
287C23×C4—72no—
288C23×C4—72no—
289C23×C4—72no—
290C23×C4C22×D712yes—
291C23×C4C22×D712yes—
292C23×C4C22×D711yescharacteristic
293C23×C4C22×D711yescharacteristic
294C23×C4C22×D711yescharacteristic
295C2×C4⋊C4—22no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—74no—
301C2×C4⋊C4—74no—
302C2×C4⋊C4—144no—
303C2×C4⋊C4—142no—
304C2×C4⋊C4—282no—
305C2×C4⋊C4—282no—
306C2×C4⋊C4—282no—
307C2×C4⋊C4—282no—
308C2×C4⋊C4—282no—
309C2×C4⋊C4—281no—
310C2×C4⋊C4—281no—
311C2×C4⋊C4—281no—
312C2×C4⋊C4—281no—
313C2×C4⋊C4—281no—
314C2×C4⋊C4—281no—
315C2×C4⋊C4Dic1414yescomplemented
316C2×C42—41no—
317C2×C42—41no—
318C2×C42—144no—
319C2×C42—282no—
320C2×C42—282no—
321C2×C42C4×D714yes—
322#95—24no—
323#95—24no—
324#95—78no—
325#95—78no—
326#95—144no—
327#95—144no—
328#95—144no—
329#95—144no—
330#95—282no—
331#95—282no—
332#95—282no—
333C22×C7C22×C4⋊C411yescharacteristic
334C22×C7C2×C4×Q811yescharacteristic
335C22×C7C2×C4×Q811yescharacteristic
336C22×C7#51811yescharacteristic
337C22×C7#51811yescharacteristic
338C22×C7#52011yescharacteristic
339C22×C7#52011yescharacteristic
340C22×C7#53411yescharacteristic
341C22×C7#53411yescharacteristic
342C22×C7#53811yescharacteristic
343C22×C7#53811yescharacteristic
344C22×C7#53911yescharacteristic
345C22×C7#53911yescharacteristic
346C22×C7#54311yescharacteristic
347C22×C7#54311yescharacteristic
348C22×C7#54311yescharacteristic
349C22×C7#54311yescharacteristic
350C22×C7#54411yescharacteristic
351C22×C7#54411yescharacteristic
352C22×C7D4×Q811yescharacteristic
353C22×C7D4×Q811yescharacteristic
354C22×C7#55011yescharacteristic
355C22×C7#55011yescharacteristic
356C22×C7#55411yescharacteristic
357C22×C7#55411yescharacteristic
358C22×C7#55511yescharacteristic
359C22×C7#55711yescharacteristic
360C22×C7#55711yescharacteristic
361C22×C7Q8211yescharacteristic
362C22×C7Q8211yescharacteristic
363C22×C7Q8211yescharacteristic
364C22×C7H(3,𝔽4)11yescharacteristic
365C22×C7#56211yescharacteristic
366C22×C7#56211yescharacteristic
367C22×C7#56311yescharacteristic
368C4×C7—24no—
369C4×C7—24no—
370C4×C7—24no—
371C4×C7—44no—
372C4×C7—82no—
373Dic7—28no—
374Dic7—44no—
375Dic7—44no—
376Dic7—82no—
377C24C23×D711yescharacteristic
378C2×Q8—716no—
379C2×Q8—284no—
380C2×Q8—284no—
381C2×Q8—284no—
382C2×Q8—284no—
383C2×Q8—284no—
384C2×Q8—284no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—74no—
411C22×C4—74no—
412C22×C4—74no—
413C22×C4—74no—
414C22×C4—74no—
415C22×C4—142no—
416C22×C4—142no—
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×C4—142no—
437C22×C4—142no—
438C22×C4C2×Dic1414yes—
439C22×C4C2×Dic1412yes—
440C22×C4C2×C4×D712yes—
441C22×C4C2×C4×D712yes—
442C22×C4C2×C4×D712yes—
443C22×C4#115712yes—
444C22×C4D4×D712yes—
445C22×C4#115912yes—
446C22×C4Q8×D712yes—
447C22×C4Q8×D712yes—
448C4⋊C4—44no—
449C4⋊C4—44no—
450C4⋊C4—284no—
451C4⋊C4—284no—
452C4⋊C4—284no—
453C4⋊C4—288no—
454C4⋊C4—288no—
455C42—44no—
456C42—288no—
457C2×C7#231511yescharacteristic
458C2×C7#232911yescharacteristic
459C2×C7#232911yescharacteristic
460C2×C7Q8×C4⋊C411yescharacteristic
461C2×C7Q8×C4⋊C411yescharacteristic
462C2×C7#236911yescharacteristic
463C2×C7#237911yescharacteristic
464C2×C7#273211yescharacteristic
465C2×C7#273211yescharacteristic
466C2×C7#273311yescharacteristic
467C2×C7#273411yescharacteristic
468C2×C7#280611yescharacteristic
469C2×C7#280611yescharacteristic
470C2×C7#280911yescharacteristic
471C2×C7#281111yescharacteristic
472C23C22×Dic1411yescharacteristic
473C23C22×C4×D711yescharacteristic
474C23C2×#115711yescharacteristic
475C23C2×D4×D711yescharacteristic
476C23C2×#115911yescharacteristic
477C23#654811yescharacteristic
478C23#654811yescharacteristic
479C23#654811yescharacteristic
480C23C2×Q8×D711yescharacteristic
481C23C2×Q8×D711yescharacteristic
482C23#655111yescharacteristic
483C23#655311yescharacteristic
484C23#655311yescharacteristic
485C23#655311yescharacteristic
486C23#655411yescharacteristic
487Q8—2816no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—78no—
521C2×C4—144no—
522C2×C4—144no—
523C2×C4—144no—
524C2×C4—144no—
525C2×C4—144no—
526C2×C4—144no—
527C2×C4—144no—
528C2×C4—144no—
529C2×C4—144no—
530C2×C4—144no—
531C2×C4—144no—
532C2×C4—144no—
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×C4—282no—
543C2×C4—282no—
544C2×C4—282no—
545C2×C4—282no—
546C2×C4—282no—
547C2×C4—282no—
548C2×C4C4×Dic1414yes—
549C2×C4#645014yes—
550C2×C4D7×C4⋊C414yes—
551C7#1446711yescharacteristic, complemented, Sylow
552C22C2×C4×Dic1411yescharacteristic
553C22#9017411yescharacteristic
554C22#9017711yescharacteristic
555C22#9018511yescharacteristic
556C22C2×#645011yescharacteristic
557C22#9019111yescharacteristic
558C22C2×D7×C4⋊C411yescharacteristic
559C22#9019511yescharacteristic
560C22#9020611yescharacteristic
561C22#9021211yescharacteristic
562C22#9021411yescharacteristic
563C22D4×Dic1411yescharacteristic
564C22#9023411yescharacteristic
565C22#9024411yescharacteristic
566C22#9025411yescharacteristic
567C22Q8×Dic1411yescharacteristic
568C22Q8×Dic1411yescharacteristic
569C22#9025811yescharacteristic
570C22#9027011yescharacteristic
571C22#9029311yescharacteristic
572C22#9029611yescharacteristic
573C22#9029611yescharacteristic
574C22#9030811yescharacteristic
575C22#9031411yescharacteristic
576C22#9032511yescharacteristic
577C22#9032511yescharacteristic
578C22#9032511yescharacteristic
579C22#9037411yescharacteristic
580C22#9037511yescharacteristic
581C22#9039011yescharacteristic
582C22#9039111yescharacteristic
583C22#9040911yescharacteristic
584C22#9041211yescharacteristic
585C22#9041311yescharacteristic
586C22#9041811yescharacteristic
587C4—24no—
588C4—24no—
589C4—24no—
590C4—44no—
591C4—82no—
592C4—148no—
593C4—284no—
594C4—284no—
595C4—562no—
596C2#1173077911yescharacteristic
597C2C4⋊C4×Dic1411yescharacteristic
598C2#1173110111yescharacteristic
599C2#1173131911yescharacteristic
600C2#1173145011yescharacteristic
601C2#1173167511yescharacteristic
602C2#1173176811yescharacteristic
603C2#1173357911yescharacteristic
604C2#1173358011yescharacteristic
605C2#1173362811yescharacteristic
606C2#1173363111yescharacteristic
607C2#1173384611yescharacteristic
608C2#1173384711yescharacteristic
609C2#1173404311yescharacteristic
610C2#1173404911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, prime radical, cosocleC24×C7C24
hypercenterC4⋊#95D7
hypocenterC7#14467
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
31. #89701C4semidirect
55. C2×C7×C4⋊C4Q8semidirect
67. C2×C4⋊Dic7Q8semidirect
167. C2×Dic14C4⋊C4semidirect
315. C2×C4⋊C4Dic14semidirect
551. C7#14467semidirect

Maximal subgroups

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

subgroupindex
C2×#897012
C2×#894182
C7×C4⋊#952
#117293222
#117293182
#117292892
#117271742
#117271652
#117271612
#144677