Finite Group Databasebeta

← #13277025

Subgroups — #13277025

Order 1792.

1470 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#382C211yesmaximal, characteristic
2C2×#89745C211yesmaximal, characteristic
3C2×#89745C211yesmaximal, characteristic
4C2×C4⋊C4×Dic7C211yesmaximal, characteristic
5C2×#89700C211yesmaximal, characteristic
6#11729317C211yesmaximal, characteristic
7C4×C7⋊#95C211yesmaximal, characteristic
8#11727167C212yesmaximal
9#11727163C212yesmaximal
10#11727159C212yesmaximal
11Dic7⋊#95C212yesmaximal
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×Dic7C2211yescharacteristic
21C22×C4×Dic7C2212yes—
22C22×C4×Dic7C2211yescharacteristic
23C7×#382—24no—
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C4⋊C4×Dic7—24no—
37#89745—24no—
38#89745—24no—
39#89700C418yescomplemented
40#14006—71nomaximal, Sylow
41C23×C4×C7C2312yes—
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×Dic7C2312yes—
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2312yes—
51C23×Dic7C2311yescharacteristic
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4—22no—
57C2×C7×C4⋊C4D414yes—
58C2×C42×C7—22no—
59C2×C42×C7—22no—
60C2×C42×C7C2×C414yes—
61C2×C4⋊Dic7—22no—
62C2×C4⋊Dic7—22no—
63C2×C4⋊Dic7C2×C414yes—
64C2×C4⋊Dic7C2×C414yes—
65C2×C4⋊Dic7D414yes—
66C2×C4⋊Dic7Q814yes—
67C2×Dic7⋊C4—24no—
68C2×Dic7⋊C4—24no—
69C2×Dic7⋊C4—24no—
70C2×Dic7⋊C4—24no—
71C2×Dic7⋊C4—42no—
72C2×Dic7⋊C4—42no—
73C2×Dic7⋊C4—42no—
74C2×Dic7⋊C4—42no—
75C2×Dic7⋊C4C2×C418yes—
76C2×C4×Dic7—22no—
77C2×C4×Dic7—22no—
78C2×C4×Dic7—22no—
79C2×C4×Dic7—22no—
80C2×C4×Dic7—22no—
81C2×C4×Dic7—24no—
82C2×C4×Dic7—24no—
83C2×C4×Dic7—42no—
84C2×C4×Dic7Q814yes—
85C7×#95—24no—
86C7×#95—24no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—22no—
91C7⋊#95—22no—
92C7⋊#95—22no—
93C7⋊#95—24no—
94C7⋊#95—22no—
95C7⋊#95—42no—
96C7⋊#95C2×C418yes—
97C2×#389—71no—
98C2×#389—71no—
99C2×#389—71no—
100C2×#382D711yescharacteristic
101C2×C4×C4⋊C4—71no—
102#1442—72no—
103#1441—72no—
104#1436—72no—
105C4⋊#95—72no—
106C4⋊#95—71no—
107C4×#95—71no—
108C24×C7C2411yescharacteristic
109C22×C4×C7—22no—
110C22×C4×C7—21no—
111C22×C4×C7—21no—
112C22×C4×C7—21no—
113C22×C4×C7—21no—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—21no—
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×C7—22no—
134C22×C4×C7C22×C412yes—
135C22×C4×C7C22×C412yes—
136C22×C4×C7C22×C412yes—
137C22×C4×C7C2×D414yes—
138C22×C4×C7C2×D412yes—
139C22×C4×C7C2×D412yes—
140C22×C4×C7C2×Q812yes—
141C22×C4×C7C2×Q812yes—
142C22×C4×C7#4112yes—
143C22×C4×C7#4112yes—
144C22×Dic7—21no—
145C22×Dic7—22no—
146C22×Dic7—21no—
147C22×Dic7—22no—
148C22×Dic7—21no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—22no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7—22no—
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—21no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7C22×C414yes—
177C22×Dic7C22×C414yes—
178C22×Dic7C2×D414yes—
179C22×Dic7C2×Q812yes—
180C22×Dic7C2×Q814yes—
181C22×Dic7C2×Q812yes—
182C22×Dic7#4112yes—
183C22×Dic7#4112yes—
184C22×Dic7#4112yes—
185C22×Dic7#4112yes—
186C7×C4⋊C4—28no—
187C7×C4⋊C4—44no—
188C42×C7—28no—
189C4⋊Dic7—28no—
190C4⋊Dic7C4⋊C4116yescomplemented
191Dic7⋊C4—48no—
192Dic7⋊C4—48no—
193Dic7⋊C4—48no—
194C4×Dic7—28no—
195C4×Dic7—48no—
196C4×Dic7—44no—
197C22×C4⋊C4—71no—
198C22×C4⋊C4—71no—
199C22×C4⋊C4—72no—
200C22×C4⋊C4—72no—
201C22×C4⋊C4—72no—
202C22×C4⋊C4C2×D711yescharacteristic
203C22×C4⋊C4C2×D711yescharacteristic
204C22×C42—71no—
205C22×C42—71no—
206C22×C42—72no—
207C22×C42C2×D711yescharacteristic
208#389—78no—
209#389—144no—
210#389—144no—
211#382—24no—
212C4×C4⋊C4—144no—
213C2×#95—72no—
214C2×#95—71no—
215C2×#95—71no—
216C2×#95—71no—
217C2×#95—71no—
218C2×#95—72no—
219C2×#95—72no—
220C2×#95—72no—
221C2×#95—72no—
222C2×#95—72no—
223C2×#95C2×D712yes—
224C2×#95C2×D712yes—
225C23×C7C23×C411yescharacteristic
226C23×C7C22×D411yescharacteristic
227C23×C7C22×D411yescharacteristic
228C23×C7C22×Q811yescharacteristic
229C23×C7C22×Q811yescharacteristic
230C23×C7C2×#4111yescharacteristic
231C23×C7C2×#4111yescharacteristic
232C23×C7C2×#4111yescharacteristic
233C23×C7C2×#4111yescharacteristic
234C23×C7C2×#4111yescharacteristic
235C23×C7C2×#4111yescharacteristic
236C23×C7H(5,𝔽2)11yescharacteristic
237C23×C7H(5,𝔽2)11yescharacteristic
238C23×C72−1+411yescharacteristic
239C23×C72−1+411yescharacteristic
240C2×C4×C7—22no—
241C2×C4×C7—22no—
242C2×C4×C7—22no—
243C2×C4×C7—22no—
244C2×C4×C7—22no—
245C2×C4×C7—22no—
246C2×C4×C7—24no—
247C2×C4×C7—24no—
248C2×C4×C7—24no—
249C2×C4×C7—42no—
250C2×C4×C7—42no—
251C2×C4×C7—42no—
252C2×C4×C7—41no—
253C2×C4×C7—41no—
254C2×C4×C7—42no—
255C2×C4×C7—41no—
256C2×C4×C7—41no—
257C2×C4×C7—41no—
258C2×C4×C7—41no—
259C2×C4×C7—41no—
260C2×C4×C7—41no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—42no—
268C2×C4×C7C2×C4⋊C414yes—
269C2×C4×C7C4×D414yes—
270C2×C4×C7C4×Q814yes—
271C2×C4×C7#12114yes—
272C2×C4×C7C22⋊Q814yes—
273C2×C4×C7#12514yes—
274C2×C4×C7C4⋊Q814yes—
275C2×Dic7—24no—
276C2×Dic7—24no—
277C2×Dic7—22no—
278C2×Dic7—22no—
279C2×Dic7—22no—
280C2×Dic7—24no—
281C2×Dic7—24no—
282C2×Dic7—22no—
283C2×Dic7—22no—
284C2×Dic7—22no—
285C2×Dic7—24no—
286C2×Dic7—24no—
287C2×Dic7—24no—
288C2×Dic7—24no—
289C2×Dic7—24no—
290C2×Dic7—22no—
291C2×Dic7—22no—
292C2×Dic7—22no—
293C2×Dic7—22no—
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—22no—
297C2×Dic7—22no—
298C2×Dic7—22no—
299C2×Dic7—41no—
300C2×Dic7—41no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—42no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309C2×Dic7—42no—
310C2×Dic7—41no—
311C2×Dic7—42no—
312C2×Dic7—42no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7C2×C4⋊C418yes—
316C2×Dic7#12514yes—
317C23×C4—72no—
318C23×C4—71no—
319C23×C4—72no—
320C23×C4—71no—
321C23×C4—71no—
322C23×C4—71no—
323C23×C4C22×D712yes—
324C23×C4C22×D711yescharacteristic
325C23×C4C22×D711yescharacteristic
326C23×C4C22×D712yes—
327C23×C4C22×D711yescharacteristic
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—74no—
334C2×C4⋊C4—74no—
335C2×C4⋊C4—74no—
336C2×C4⋊C4—74no—
337C2×C4⋊C4—78no—
338C2×C4⋊C4—142no—
339C2×C4⋊C4—142no—
340C2×C4⋊C4—144no—
341C2×C4⋊C4—144no—
342C2×C4⋊C4—144no—
343C2×C4⋊C4—144no—
344C2×C4⋊C4—282no—
345C2×C4⋊C4—282no—
346C2×C4⋊C4—282no—
347C2×C4⋊C4—282no—
348C2×C4⋊C4C22⋊D714yes—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—74no—
352C2×C42—142no—
353C2×C42—142no—
354C2×C42—144no—
355C2×C42—144no—
356C2×C42—142no—
357C2×C42—142no—
358C2×C42—142no—
359C2×C42—282no—
360C2×C42C4×D714yes—
361#95—24no—
362#95—24no—
363#95—78no—
364#95—142no—
365#95—142no—
366#95—142no—
367#95—142no—
368#95—144no—
369#95—144no—
370#95—144no—
371#95—144no—
372#95—282no—
373C22×C7C22×C4⋊C411yescharacteristic
374C22×C7C2×C4×D411yescharacteristic
375C22×C7C2×C4×Q811yescharacteristic
376C22×C7C4×#4111yescharacteristic
377C22×C7C4×#4111yescharacteristic
378C22×C7#51811yescharacteristic
379C22×C7#51911yescharacteristic
380C22×C7C2×#12111yescharacteristic
381C22×C7C2×C22⋊Q811yescharacteristic
382C22×C7C2×#12511yescharacteristic
383C22×C7C2×#12511yescharacteristic
384C22×C7#52911yescharacteristic
385C22×C7#52911yescharacteristic
386C22×C7C2×C4⋊Q811yescharacteristic
387C22×C7#53311yescharacteristic
388C22×C7#54211yescharacteristic
389C22×C7#54211yescharacteristic
390C22×C7#54411yescharacteristic
391C22×C7#54411yescharacteristic
392C22×C7#54611yescharacteristic
393C22×C7#54611yescharacteristic
394C22×C7#54611yescharacteristic
395C22×C7#54711yescharacteristic
396C22×C7#54811yescharacteristic
397C22×C7#54811yescharacteristic
398C22×C7#54811yescharacteristic
399C22×C7#55011yescharacteristic
400C22×C7#55211yescharacteristic
401C22×C7#55311yescharacteristic
402C22×C7#55411yescharacteristic
403C22×C7#55411yescharacteristic
404C22×C7#55511yescharacteristic
405C22×C7#55611yescharacteristic
406C22×C7#55711yescharacteristic
407C22×C7#55711yescharacteristic
408C4×C7—42no—
409C4×C7—42no—
410C4×C7—44no—
411C4×C7—82no—
412C4×C7#38918yes—
413Dic7—28no—
414Dic7—24no—
415Dic7—44no—
416Dic7—42no—
417Dic7—42no—
418Dic7—42no—
419C24C23×D711yescharacteristic
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—74no—
446C22×C4—74no—
447C22×C4—72no—
448C22×C4—74no—
449C22×C4—72no—
450C22×C4—72no—
451C22×C4—74no—
452C22×C4—72no—
453C22×C4—72no—
454C22×C4—72no—
455C22×C4—141no—
456C22×C4—141no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—141no—
460C22×C4—142no—
461C22×C4—142no—
462C22×C4—141no—
463C22×C4—141no—
464C22×C4—142no—
465C22×C4—141no—
466C22×C4—141no—
467C22×C4—141no—
468C22×C4—141no—
469C22×C4—141no—
470C22×C4—141no—
471C22×C4—141no—
472C22×C4—141no—
473C22×C4—141no—
474C22×C4—142no—
475C22×C4—142no—
476C22×C4—141no—
477C22×C4—142no—
478C22×C4—142no—
479C22×C4—141no—
480C22×C4—141no—
481C22×C4—141no—
482C22×C4—141no—
483C22×C4—141no—
484C22×C4—141no—
485C22×C4—142no—
486C22×C4—141no—
487C22×C4C2×C4×D712yes—
488C22×C4C2×C4×D712yes—
489C22×C4C2×C4×D712yes—
490C22×C4#115712yes—
491C22×C4D4×D712yes—
492C22×C4#115912yes—
493C22×C4Q8×D712yes—
494C22×C4Q8×D712yes—
495C22×C4C2×C22⋊D714yes—
496C22×C4C2×C22⋊D712yes—
497C4⋊C4—28no—
498C4⋊C4—44no—
499C4⋊C4—716no—
500C4⋊C4—148no—
501C4⋊C4—288no—
502C4⋊C4—288no—
503C4⋊C4—288no—
504C42—28no—
505C42—148no—
506C42—288no—
507C42—284no—
508C2×C7C2×#38911yescharacteristic
509C2×C7C4×#12511yescharacteristic
510C2×C7#233111yescharacteristic
511C2×C7#234911yescharacteristic
512C2×C7#235111yescharacteristic
513C2×C7#236211yescharacteristic
514C2×C7#236311yescharacteristic
515C2×C7#242611yescharacteristic
516C2×C7#242711yescharacteristic
517C2×C7#243911yescharacteristic
518C2×C7#244211yescharacteristic
519C2×C7#250811yescharacteristic
520C2×C7#250911yescharacteristic
521C2×C7#255011yescharacteristic
522C2×C7#255211yescharacteristic
523C23C22×C4×D711yescharacteristic
524C23C2×#115711yescharacteristic
525C23C2×D4×D711yescharacteristic
526C23C2×#115911yescharacteristic
527C23C2×Q8×D711yescharacteristic
528C23C2×Q8×D711yescharacteristic
529C23D7×#4111yescharacteristic
530C23D7×#4111yescharacteristic
531C23D7×#4111yescharacteristic
532C23D7×#4111yescharacteristic
533C23#655311yescharacteristic
534C23#655311yescharacteristic
535C23#655411yescharacteristic
536C23#655411yescharacteristic
537C23C22×C22⋊D711yescharacteristic
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—74no—
567C2×C4—78no—
568C2×C4—142no—
569C2×C4—142no—
570C2×C4—144no—
571C2×C4—144no—
572C2×C4—142no—
573C2×C4—144no—
574C2×C4—144no—
575C2×C4—142no—
576C2×C4—142no—
577C2×C4—142no—
578C2×C4—144no—
579C2×C4—144no—
580C2×C4—142no—
581C2×C4—142no—
582C2×C4—142no—
583C2×C4—142no—
584C2×C4—142no—
585C2×C4—142no—
586C2×C4—144no—
587C2×C4—144no—
588C2×C4—144no—
589C2×C4—142no—
590C2×C4—142no—
591C2×C4—142no—
592C2×C4—281no—
593C2×C4—281no—
594C2×C4—281no—
595C2×C4—281no—
596C2×C4—282no—
597C2×C4—282no—
598C2×C4—281no—
599C2×C4—281no—
600C2×C4—281no—
601C2×C4—281no—
602C2×C4—281no—
603C2×C4—282no—
604C2×C4—281no—
605C2×C4—282no—
606C2×C4—281no—
607C2×C4—281no—
608C2×C4#645014yes—
609C2×C4#645214yes—
610C2×C4D7×C4⋊C414yes—
611C2×C4#645914yes—
612C2×C4C4×C22⋊D714yes—
613C2×C4#650214yes—
614C2×C4#650714yes—
615C7#1400611yescharacteristic, complemented, Sylow
616C22C2×#645011yescharacteristic
617C22C2×#645211yescharacteristic
618C22C2×D7×C4⋊C411yescharacteristic
619C22C2×#645911yescharacteristic
620C22#9020711yescharacteristic
621C22#9021211yescharacteristic
622C22#9021311yescharacteristic
623C22#9021311yescharacteristic
624C22#9022011yescharacteristic
625C22#9022111yescharacteristic
626C22#9022311yescharacteristic
627C22#9022411yescharacteristic
628C22#9036711yescharacteristic
629C22#9036711yescharacteristic
630C22#9036811yescharacteristic
631C22#9036811yescharacteristic
632C22#9037111yescharacteristic
633C22#9037111yescharacteristic
634C22#9037311yescharacteristic
635C22#9037311yescharacteristic
636C22#9037611yescharacteristic
637C22#9037611yescharacteristic
638C22D7×#12511yescharacteristic
639C22#9037911yescharacteristic
640C22#9038011yescharacteristic
641C22#9038011yescharacteristic
642C22#9038111yescharacteristic
643C22#9038111yescharacteristic
644C22C2×C4×C22⋊D711yescharacteristic
645C22C2×#650211yescharacteristic
646C22C2×#650711yescharacteristic
647C22#9051511yescharacteristic
648C22#9052011yescharacteristic
649C22#9052211yescharacteristic
650C22#9052511yescharacteristic
651C4—44no—
652C4—42no—
653C4—42no—
654C4—82no—
655C4—144no—
656C4—148no—
657C4—282no—
658C4—282no—
659C4—284no—
660C4—282no—
661C4#8974418yes—
662C2#1173159511yescharacteristic
663C2#1173159911yescharacteristic
664C2#1173160211yescharacteristic
665C2#1173160711yescharacteristic
666C2#1173160811yescharacteristic
667C2#1173161411yescharacteristic
668C2#1173161611yescharacteristic
669C2#1173167311yescharacteristic
670C2C2×#8974411yescharacteristic
671C2#1173968811yescharacteristic
672C2#1173968911yescharacteristic
673C2#1174044011yescharacteristic
674C2#1174044111yescharacteristic
675C2#1174048111yescharacteristic
676C2#1174048211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#382C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#382D7
hypocenterC7#14006
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
39. #89700C4semidirect
190. C4⋊Dic7C4⋊C4semidirect
615. C7#14006semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3822
C2×#897452
C2×C4⋊C4×Dic72
C2×#897002
#117293172
C4×C7⋊#952
#117271672
#117271632
#117271592
Dic7⋊#952
#140067