Finite Group Databasebeta

← #13277317

Subgroups — #13277317

Order 1792.

1470 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89748C211yesmaximal, characteristic
2C2×C4⋊C4×Dic7C211yesmaximal, characteristic
3C2×#89700C211yesmaximal, characteristic
4C2×#89424C212yesmaximal
5C7×C4⋊#95C211yesmaximal, characteristic
6#11729317C211yesmaximal, characteristic
7#11729317C211yesmaximal, characteristic
8C4×C7⋊#95C211yesmaximal, characteristic
9#11727175C212yesmaximal
10#11727163C212yesmaximal
11#11727159C212yesmaximal
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C22×C4⋊Dic7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×Dic7⋊C4C2212yes—
18C22×Dic7⋊C4C2212yes—
19C22×Dic7⋊C4C2212yes—
20C22×C4×Dic7C2212yes—
21C22×C4×Dic7C2211yescharacteristic
22C22×C4×Dic7C2211yescharacteristic
23C2×C7×#95C2212yes—
24C2×C7×#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2211yescharacteristic
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2211yescharacteristic
35#89748C418yescomplemented
36C4⋊C4×Dic7—24no—
37#89700—24no—
38#89424—28no—
39#14029—71nomaximal, Sylow
40C23×C4×C7C2312yes—
41C23×C4×C7C2312yes—
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×Dic7C2312yes—
46C23×Dic7C2312yes—
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C2×C7×C4⋊C4—22no—
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4C2×C414yes—
57C2×C42×C7—22no—
58C2×C42×C7—22no—
59C2×C42×C7—22no—
60C2×C4⋊Dic7—22no—
61C2×C4⋊Dic7—22no—
62C2×C4⋊Dic7—22no—
63C2×C4⋊Dic7—22no—
64C2×C4⋊Dic7C2×C414yes—
65C2×C4⋊Dic7D414yes—
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⋊C4—42no—
73C2×Dic7⋊C4C2×C418yes—
74C2×Dic7⋊C4C2×C418yes—
75C2×C4×Dic7—22no—
76C2×C4×Dic7—22no—
77C2×C4×Dic7—22no—
78C2×C4×Dic7—22no—
79C2×C4×Dic7—24no—
80C2×C4×Dic7—24no—
81C2×C4×Dic7—42no—
82C2×C4×Dic7C2×C414yes—
83C2×C4×Dic7Q814yes—
84C7×#95—24no—
85C7×#95—42no—
86C7⋊#95—24no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—22no—
91C7⋊#95—22no—
92C7⋊#95—24no—
93C7⋊#95—42no—
94C7⋊#95D414yes—
95C7⋊#95Q814yes—
96C2×#389—71no—
97C2×#387—72no—
98C2×#384—71no—
99C2×C4×C4⋊C4—71no—
100#1445—72no—
101#1441—72no—
102#1436—72no—
103C4⋊#95—71no—
104C4⋊#95—71no—
105C4⋊#95D711yescharacteristic
106C4×#95—71no—
107C24×C7C2411yescharacteristic
108C22×C4×C7—21no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—21no—
112C22×C4×C7—21no—
113C22×C4×C7—21no—
114C22×C4×C7—22no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
119C22×C4×C7—22no—
120C22×C4×C7—21no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—21no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7C22×C414yes—
134C22×C4×C7C22×C412yes—
135C22×C4×C7C2×D412yes—
136C22×C4×C7C2×D412yes—
137C22×C4×C7C2×Q812yes—
138C22×C4×C7C2×Q812yes—
139C22×C4×C7#4112yes—
140C22×C4×C7#4112yes—
141C22×C4×C7#4112yes—
142C22×C4×C7#4112yes—
143C22×Dic7—21no—
144C22×Dic7—21no—
145C22×Dic7—21no—
146C22×Dic7—21no—
147C22×Dic7—21no—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—22no—
162C22×Dic7—21no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—21no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—21no—
172C22×Dic7—22no—
173C22×Dic7C22×C414yes—
174C22×Dic7C22×C412yes—
175C22×Dic7C22×C412yes—
176C22×Dic7C2×D414yes—
177C22×Dic7C2×D412yes—
178C22×Dic7C2×D412yes—
179C22×Dic7C2×Q812yes—
180C22×Dic7C2×Q812yes—
181C22×Dic7C2×Q812yes—
182C22×Dic7C2×Q812yes—
183C22×Dic7#4112yes—
184C22×Dic7#4112yes—
185C7×C4⋊C4—28no—
186C7×C4⋊C4—44no—
187C42×C7—44no—
188C4⋊Dic7—28no—
189C4⋊Dic7—28no—
190Dic7⋊C4—216no—
191Dic7⋊C4—48no—
192Dic7⋊C4—48no—
193C4×Dic7—28no—
194C4×Dic7—28no—
195C4×Dic7—48no—
196C22×C4⋊C4—72no—
197C22×C4⋊C4—71no—
198C22×C4⋊C4—71no—
199C22×C4⋊C4—72no—
200C22×C4⋊C4—72no—
201C22×C4⋊C4C2×D711yescharacteristic
202C22×C4⋊C4C2×D711yescharacteristic
203C22×C42—71no—
204C22×C42—71no—
205C22×C42—72no—
206C22×C42C2×D711yescharacteristic
207#389—144no—
208#387—148no—
209#384—78no—
210C4×C4⋊C4—144no—
211C2×#95—71no—
212C2×#95—71no—
213C2×#95—71no—
214C2×#95—71no—
215C2×#95—72no—
216C2×#95—72no—
217C2×#95—72no—
218C2×#95—72no—
219C2×#95—72no—
220C2×#95—72no—
221C2×#95C2×D712yes—
222C2×#95C2×D712yes—
223C23×C7C23×C411yescharacteristic
224C23×C7C22×D411yescharacteristic
225C23×C7C22×D411yescharacteristic
226C23×C7C22×Q811yescharacteristic
227C23×C7C22×Q811yescharacteristic
228C23×C7C2×#4111yescharacteristic
229C23×C7C2×#4111yescharacteristic
230C23×C7C2×#4111yescharacteristic
231C23×C7C2×#4111yescharacteristic
232C23×C7C2×#4111yescharacteristic
233C23×C7C2×#4111yescharacteristic
234C23×C7H(5,𝔽2)11yescharacteristic
235C23×C7H(5,𝔽2)11yescharacteristic
236C23×C72−1+411yescharacteristic
237C23×C72−1+411yescharacteristic
238C2×C4×C7—24no—
239C2×C4×C7—24no—
240C2×C4×C7—24no—
241C2×C4×C7—22no—
242C2×C4×C7—22no—
243C2×C4×C7—22no—
244C2×C4×C7—22no—
245C2×C4×C7—22no—
246C2×C4×C7—22no—
247C2×C4×C7—41no—
248C2×C4×C7—41no—
249C2×C4×C7—41no—
250C2×C4×C7—41no—
251C2×C4×C7—42no—
252C2×C4×C7—41no—
253C2×C4×C7—42no—
254C2×C4×C7—42no—
255C2×C4×C7—41no—
256C2×C4×C7—41no—
257C2×C4×C7—41no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7#11714yes—
267C2×C4×C7C4×D414yes—
268C2×C4×C7C4×Q814yes—
269C2×C4×C7C22⋊Q814yes—
270C2×C4×C7#12314yes—
271C2×C4×C7#12514yes—
272C2×C4×C7#12614yes—
273C2×Dic7—22no—
274C2×Dic7—22no—
275C2×Dic7—22no—
276C2×Dic7—22no—
277C2×Dic7—22no—
278C2×Dic7—22no—
279C2×Dic7—22no—
280C2×Dic7—22no—
281C2×Dic7—22no—
282C2×Dic7—22no—
283C2×Dic7—22no—
284C2×Dic7—22no—
285C2×Dic7—22no—
286C2×Dic7—22no—
287C2×Dic7—22no—
288C2×Dic7—22no—
289C2×Dic7—22no—
290C2×Dic7—22no—
291C2×Dic7—24no—
292C2×Dic7—24no—
293C2×Dic7—24no—
294C2×Dic7—22no—
295C2×Dic7—24no—
296C2×Dic7—22no—
297C2×Dic7—22no—
298C2×Dic7—24no—
299C2×Dic7—24no—
300C2×Dic7—42no—
301C2×Dic7—42no—
302C2×Dic7—42no—
303C2×Dic7—42no—
304C2×Dic7—41no—
305C2×Dic7—42no—
306C2×Dic7—42no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309C2×Dic7—42no—
310C2×Dic7—41no—
311C2×Dic7—42no—
312C2×Dic7C4×D414yes—
313C2×Dic7C4×Q814yes—
314C2×Dic7C4⋊Q814yes—
315C23×C4—71no—
316C23×C4—71no—
317C23×C4—71no—
318C23×C4—72no—
319C23×C4—72no—
320C23×C4—71no—
321C23×C4C22×D712yes—
322C23×C4C22×D712yes—
323C23×C4C22×D711yescharacteristic
324C23×C4C22×D711yescharacteristic
325C23×C4C22×D711yescharacteristic
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—78no—
332C2×C4⋊C4—74no—
333C2×C4⋊C4—74no—
334C2×C4⋊C4—78no—
335C2×C4⋊C4—144no—
336C2×C4⋊C4—144no—
337C2×C4⋊C4—142no—
338C2×C4⋊C4—142no—
339C2×C4⋊C4—142no—
340C2×C4⋊C4—142no—
341C2×C4⋊C4—144no—
342C2×C4⋊C4—144no—
343C2×C4⋊C4—282no—
344C2×C4⋊C4—282no—
345C2×C4⋊C4—282no—
346C2×C4⋊C4C4×D714yes—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—74no—
351C2×C42—74no—
352C2×C42—142no—
353C2×C42—142no—
354C2×C42—142no—
355C2×C42—142no—
356C2×C42—144no—
357C2×C42—144no—
358C2×C42—282no—
359#95—24no—
360#95—42no—
361#95—74no—
362#95—74no—
363#95—142no—
364#95—142no—
365#95—144no—
366#95—144no—
367#95—144no—
368#95—144no—
369#95—144no—
370#95—282no—
371C22×C7C2×#11711yescharacteristic
372C22×C7C2×C4×D411yescharacteristic
373C22×C7C2×C4×D411yescharacteristic
374C22×C7C2×C4×Q811yescharacteristic
375C22×C7C2×C4×Q811yescharacteristic
376C22×C7#51811yescharacteristic
377C22×C7#51911yescharacteristic
378C22×C7C2×C22⋊Q811yescharacteristic
379C22×C7C2×#12311yescharacteristic
380C22×C7C2×#12511yescharacteristic
381C22×C7C2×#12611yescharacteristic
382C22×C7C2×C4⋊Q811yescharacteristic
383C22×C7#53211yescharacteristic
384C22×C7#53311yescharacteristic
385C22×C7#53311yescharacteristic
386C22×C7#54211yescharacteristic
387C22×C7#54211yescharacteristic
388C22×C7#54411yescharacteristic
389C22×C7#54411yescharacteristic
390C22×C7D4211yescharacteristic
391C22×C7#54711yescharacteristic
392C22×C7#54711yescharacteristic
393C22×C7#54711yescharacteristic
394C22×C7D4×Q811yescharacteristic
395C22×C7#55011yescharacteristic
396C22×C7#55011yescharacteristic
397C22×C7#55211yescharacteristic
398C22×C7#55211yescharacteristic
399C22×C7#55311yescharacteristic
400C22×C7#55311yescharacteristic
401C22×C7#55411yescharacteristic
402C22×C7#55411yescharacteristic
403C22×C7#55611yescharacteristic
404C22×C7#55711yescharacteristic
405C22×C7#55911yescharacteristic
406C4×C7—44no—
407C4×C7—42no—
408C4×C7—42no—
409C4×C7—82no—
410C4×C7#38718yescomplemented
411Dic7—24no—
412Dic7—24no—
413Dic7—24no—
414Dic7—44no—
415Dic7—44no—
416Dic7—42no—
417C24C23×D711yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—72no—
444C22×C4—72no—
445C22×C4—72no—
446C22×C4—72no—
447C22×C4—72no—
448C22×C4—72no—
449C22×C4—72no—
450C22×C4—72no—
451C22×C4—72no—
452C22×C4—74no—
453C22×C4—74no—
454C22×C4—72no—
455C22×C4—141no—
456C22×C4—141no—
457C22×C4—141no—
458C22×C4—141no—
459C22×C4—141no—
460C22×C4—141no—
461C22×C4—141no—
462C22×C4—141no—
463C22×C4—141no—
464C22×C4—141no—
465C22×C4—141no—
466C22×C4—141no—
467C22×C4—141no—
468C22×C4—142no—
469C22×C4—141no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4—142no—
474C22×C4—142no—
475C22×C4—141no—
476C22×C4—142no—
477C22×C4—141no—
478C22×C4—142no—
479C22×C4—141no—
480C22×C4—141no—
481C22×C4—142no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—142no—
485C22×C4C2×C4×D714yes—
486C22×C4C2×C4×D712yes—
487C22×C4#115712yes—
488C22×C4#115712yes—
489C22×C4D4×D712yes—
490C22×C4D4×D712yes—
491C22×C4#115912yes—
492C22×C4#115912yes—
493C22×C4Q8×D712yes—
494C22×C4Q8×D712yes—
495C4⋊C4—28no—
496C4⋊C4—44no—
497C4⋊C4—1416no—
498C4⋊C4—148no—
499C4⋊C4—148no—
500C4⋊C4—288no—
501C4⋊C4—288no—
502C42—44no—
503C42—148no—
504C42—148no—
505C42—288no—
506C2×C7C2×#38711yescharacteristic
507C2×C7C4×C4⋊Q811yescharacteristic
508C2×C7#233111yescharacteristic
509C2×C7#234411yescharacteristic
510C2×C7#234511yescharacteristic
511C2×C7#236511yescharacteristic
512C2×C7#236611yescharacteristic
513C2×C7#242211yescharacteristic
514C2×C7#242311yescharacteristic
515C2×C7#244011yescharacteristic
516C2×C7#244111yescharacteristic
517C2×C7#251111yescharacteristic
518C2×C7#251211yescharacteristic
519C2×C7#255211yescharacteristic
520C2×C7#257011yescharacteristic
521C23C22×C4×D711yescharacteristic
522C23C2×#115711yescharacteristic
523C23C2×#115711yescharacteristic
524C23C2×D4×D711yescharacteristic
525C23C2×D4×D711yescharacteristic
526C23C2×#115911yescharacteristic
527C23C2×#115911yescharacteristic
528C23#654811yescharacteristic
529C23C2×Q8×D711yescharacteristic
530C23C2×Q8×D711yescharacteristic
531C23#655111yescharacteristic
532C23D7×#4111yescharacteristic
533C23D7×#4111yescharacteristic
534C23#655311yescharacteristic
535C23#655411yescharacteristic
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—74no—
565C2×C4—74no—
566C2×C4—74no—
567C2×C4—142no—
568C2×C4—142no—
569C2×C4—142no—
570C2×C4—142no—
571C2×C4—142no—
572C2×C4—142no—
573C2×C4—142no—
574C2×C4—142no—
575C2×C4—142no—
576C2×C4—142no—
577C2×C4—142no—
578C2×C4—142no—
579C2×C4—142no—
580C2×C4—142no—
581C2×C4—142no—
582C2×C4—142no—
583C2×C4—142no—
584C2×C4—142no—
585C2×C4—142no—
586C2×C4—142no—
587C2×C4—144no—
588C2×C4—144no—
589C2×C4—142no—
590C2×C4—144no—
591C2×C4—144no—
592C2×C4—144no—
593C2×C4—144no—
594C2×C4—282no—
595C2×C4—282no—
596C2×C4—282no—
597C2×C4—282no—
598C2×C4—281no—
599C2×C4—281no—
600C2×C4—282no—
601C2×C4—281no—
602C2×C4—282no—
603C2×C4—282no—
604C2×C4—281no—
605C2×C4—282no—
606C2×C4#643514yes—
607C2×C4#644214yes—
608C2×C4(C22⋊D7)⋊C414yes—
609C2×C4#644614yes—
610C2×C4#645014yes—
611C2×C4#645214yes—
612C2×C4#645914yes—
613C7#1402911yescharacteristic, complemented, Sylow
614C22C2×#643511yescharacteristic
615C22C2×#644211yescharacteristic
616C22C2×(C22⋊D7)⋊C411yescharacteristic
617C22C2×#644611yescharacteristic
618C22C2×#645011yescharacteristic
619C22C2×#645211yescharacteristic
620C22#9019811yescharacteristic
621C22C2×#645911yescharacteristic
622C22#9020211yescharacteristic
623C22#9022011yescharacteristic
624C22#9022111yescharacteristic
625C22C4×D4×D711yescharacteristic
626C22#9023611yescharacteristic
627C22#9024211yescharacteristic
628C22#9024911yescharacteristic
629C22C4×Q8×D711yescharacteristic
630C22#9026311yescharacteristic
631C22#9027011yescharacteristic
632C22#9027211yescharacteristic
633C22#9028711yescharacteristic
634C22#9029011yescharacteristic
635C22#9029411yescharacteristic
636C22#9030011yescharacteristic
637C22#9031311yescharacteristic
638C22#9032211yescharacteristic
639C22#9032311yescharacteristic
640C22#9033411yescharacteristic
641C22#9036211yescharacteristic
642C22#9037211yescharacteristic
643C22#9037911yescharacteristic
644C22#9038011yescharacteristic
645C22#9040911yescharacteristic
646C22#9041211yescharacteristic
647C22D7×C4⋊Q811yescharacteristic
648C22#9042011yescharacteristic
649C4—42no—
650C4—42no—
651C4—44no—
652C4—82no—
653C4—144no—
654C4—144no—
655C4—144no—
656C4—284no—
657C4—282no—
658C4—284no—
659C4#8942418yescomplemented
660C2C2×#8942411yescharacteristic
661C2#1173121211yescharacteristic
662C2#1173121311yescharacteristic
663C2#1173133811yescharacteristic
664C2#1173133911yescharacteristic
665C2#1173163211yescharacteristic
666C2#1173178211yescharacteristic
667C2#1173341211yescharacteristic
668C2#1173341911yescharacteristic
669C2#1173344311yescharacteristic
670C2#1173366911yescharacteristic
671C2#1173375111yescharacteristic
672C2#1173378411yescharacteristic
673C2#1173393711yescharacteristic
674C2#1173396811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, prime radical, cosocleC24×C7C24
hypercenterC4⋊#95D7
hypocenterC7#14029
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
35. #89748C4semidirect
410. C4×C7#387semidirect
613. C7#14029semidirect
659. C4#89424semidirect

Maximal subgroups

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

subgroupindex
C2×#897482
C2×C4⋊C4×Dic72
C2×#897002
C2×#894242
C7×C4⋊#952
#117293172
C4×C7⋊#952
#117271752
#117271632
#117271592
#140297