Finite Group Databasebeta

← #13364325

Subgroups — #13364325

Order 1792.

834 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89605C211yesmaximal, characteristic
2D7×#382C211yesmaximal, characteristic
3#11731197C211yesmaximal, characteristic
4C7×#1949C211yesmaximal, characteristic, complemented
5#11728386C211yesmaximal, characteristic
6#11728361C211yesmaximal, characteristic, complemented
7#11728333C211yesmaximal, characteristic
8#11728309C211yesmaximal, characteristic, complemented
9#11728209C211yesmaximal, characteristic, complemented
10#11727294C211yesmaximal, characteristic, complemented
11#11727222C211yesmaximal, characteristic, complemented
12#11726629C211yesmaximal, characteristic
13#11726628C211yesmaximal, characteristic
14#11726602C211yesmaximal, characteristic, complemented
15#11726602C211yesmaximal, characteristic, complemented
16C2×D7×C4⋊C4C2211yescharacteristic
17C2×D7×C4⋊C4C2211yescharacteristic
18C2×C42×D7C2211yescharacteristic
19C2×C7×#107C2211yescharacteristic
20C2×C7×#106C2211yescharacteristic
21C2×C7×C4⋊C8C2211yescharacteristic
22C7×#382C2211yescharacteristic
23C4×C7×C4⋊C4C2211yescharacteristic
24C2×(C2×D7)⋊C8C2211yescharacteristic
25C2×(C2×D7)⋊C8C2211yescharacteristic
26C2×#6392C2211yescharacteristic
27C2×#6391C2211yescharacteristic
28C2×C8×Dic7C2211yescharacteristic
29C2×C8×Dic7C2211yescharacteristic
30#89759C2211yescharacteristic
31#89759C2211yescharacteristic
32#89749C2211yescharacteristic
33#89749C2211yescharacteristic
34#89749C2211yescharacteristic
35#89749C2211yescharacteristic
36C2×#6382C2211yescharacteristic
37C2×#6382C2211yescharacteristic
38C2×#6381C2211yescharacteristic
39C2×#6381C2211yescharacteristic
40C4×(C2×D7)⋊C4—21no—
41#89708C2211yescharacteristic
42C4×C4⋊Dic7C2211yescharacteristic
43#89704—21no—
44C2×C4⋊(C7⋊C8)C2211yescharacteristic
45#89605C418yescomplemented
46#89436—21no—
47D7×#95—21no—
48D7×#95—21no—
49#89423—21no—
50#89422—21no—
51#89422—21no—
52C7×#340C2211yescharacteristic
53C7×#340C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#21983—71nomaximal, Sylow
61C22×C4×D7—21no—
62C22×C4×D7—21no—
63C22×C4×D7D411yescharacteristic
64C22×C4×D7D411yescharacteristic
65C22×C4×D7C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C42×C7—21no—
73C2×C42×C7C2311yescharacteristic
74C2×(C2×D7)⋊C4—21no—
75C2×(C2×D7)⋊C4—21no—
76C2×C4⋊Dic7C2311yescharacteristic
77C2×C4⋊Dic7C2311yescharacteristic
78C2×C4⋊Dic7C2311yescharacteristic
79C2×C4⋊Dic7C2311yescharacteristic
80C2×Dic7⋊C4—21no—
81C2×Dic7⋊C4—21no—
82C2×C4×Dic7—21no—
83C2×C4×Dic7D411yescharacteristic
84C2×C4×Dic7D411yescharacteristic
85C2×C4×Dic7C2311yescharacteristic
86C22×C7⋊C8C2311yescharacteristic
87C22×C7⋊C8C2311yescharacteristic
88D7×C4⋊C4—41no—
89D7×C4⋊C4—41no—
90D7×C4⋊C4—41no—
91D7×C4⋊C4—41no—
92C42×D7C2×C414yes—
93C42×D7Q814yes—
94C7×#107—41no—
95C7×#106—41no—
96C7×C4⋊C8C2×C414yescomplemented
97C7×#95—21no—
98C7×#95—21no—
99C7×#95—21no—
100C7⋊#95—21no—
101C7⋊#95—21no—
102C7⋊#95—21no—
103C7⋊#95—21no—
104C7⋊#95—21no—
105C7⋊#95—21no—
106C7⋊#95—21no—
107C7⋊#95—21no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113(C2×D7)⋊C8C2×C414yes—
114(C2×D7)⋊C8C2×C414yes—
115#6392—41no—
116#6391—41no—
117C8×Dic7C2×C414yescomplemented
118C8×Dic7C2×C414yescomplemented
119#6382—41no—
120#6382—41no—
121#6381—41no—
122#6381—41no—
123C4⋊(C7⋊C8)C2×C414yescomplemented
124C2×#431—71no—
125#2283—71no—
126C2×#382—71no—
127#1949—71no—
128#1949—71no—
129#1949—71no—
130#1949D711yescharacteristic, complemented
131#1853—71no—
132#1853—71no—
133#1852—71no—
134#1852—71no—
135#1846—71no—
136#1846—71no—
137#1835—71no—
138#1835—71no—
139C23×D7C2×D411yescharacteristic
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2411yescharacteristic
147C22×Dic7—21no—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7C2×D411yescharacteristic
152C22×Dic7C2×D411yescharacteristic
153C22×Dic7C2×D411yescharacteristic
154C2×C4×D7—22no—
155C2×C4×D7—22no—
156C2×C4×D7—21no—
157C2×C4×D7—21no—
158C2×C4×D7—21no—
159C2×C4×D7—21no—
160C2×C4×D7—41no—
161C2×C4×D7—41no—
162C2×C4×D7—42no—
163C2×C4×D7—42no—
164C2×C4×D7—42no—
165C2×C4×D7—42no—
166C2×C4×D7—42no—
167C2×C4×D7—42no—
168C2×C4×D7C4⋊C414yes—
169C2×C4×D7C4⋊C414yes—
170C2×C4×D7C22×C412yes—
171C2×C4×D7C2×Q812yes—
172C2×C7×C8—21no—
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8C22×C412yes—
177C2×C7×C8C22×C412yes—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4—21no—
186C42×C7—42no—
187C42×C7C22×C412yes—
188C42×C7C2×Q812yes—
189(C2×D7)⋊C4—42no—
190(C2×D7)⋊C4—42no—
191C4⋊Dic7—21no—
192C4⋊Dic7—21no—
193C4⋊Dic7—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199Dic7⋊C4—42no—
200Dic7⋊C4—42no—
201C4×Dic7—42no—
202C4×Dic7C4⋊C414yes—
203C4×Dic7C4⋊C414yes—
204C4×Dic7C22×C412yes—
205C4×Dic7C2×Q812yes—
206C2×C7⋊C8—21no—
207C2×C7⋊C8—21no—
208C2×C7⋊C8—21no—
209C2×C7⋊C8—21no—
210C2×C7⋊C8C22×C412yes—
211C2×C7⋊C8C22×C412yes—
212C22×C4⋊C4—71no—
213C22×C4⋊C4—71no—
214C22×C42—71no—
215#431—78no—
216C2×#107—71no—
217C2×#107—71no—
218C2×#107—71no—
219C2×#107C2×D711yescharacteristic
220C2×#106—71no—
221C2×#106—71no—
222C2×#106—71no—
223C2×#106C2×D711yescharacteristic
224C2×C4⋊C8—71no—
225C2×C4⋊C8C2×D711yescharacteristic
226C2×C22⋊C8—71no—
227C2×C22⋊C8—71no—
228C2×C4×C8—71no—
229C2×C4×C8—71no—
230#383—141no—
231#382—71no—
232#382—71no—
233#382—71no—
234#382—71no—
235#382—71no—
236#382—141no—
237#382—141no—
238#382C2×D711yescharacteristic
239#381—141no—
240#380—71no—
241#380—71no—
242C4×C4⋊C4—71no—
243C4×C4⋊C4C2×D711yescharacteristic
244C4×C22⋊C4—141no—
245#376—141no—
246C2×#95—141no—
247C2×#95—141no—
248#340—71no—
249#340—71no—
250#340—71no—
251#340—71no—
252#340—71no—
253#340—71no—
254#340C2×D711yescharacteristic
255#340C2×D711yescharacteristic
256C23×C7C22×D411yescharacteristic
257C22×D7—21no—
258C22×D7—21no—
259C22×D7—21no—
260C22×D7—21no—
261C22×D7C2×C4⋊C412yes—
262C22×D7#13512yes—
263C22×D7#13512yes—
264C2×C4×C7—21no—
265C2×C4×C7—21no—
266C2×C4×C7—21no—
267C2×C4×C7—21no—
268C2×C4×C7—41no—
269C2×C4×C7—41no—
270C2×C4×C7—41no—
271C2×C4×C7—41no—
272C2×C4×C7—41no—
273C2×C4×C7—41no—
274C2×C4×C7—41no—
275C2×C4×C7—41no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7C2×C4⋊C412yes—
281C2×C4×C7C2×C4⋊C412yes—
282C2×C4×C7C23×C411yescharacteristic
283C2×C4×C7C22×Q811yescharacteristic
284C2×C4×C7H(5,𝔽2)11yescharacteristic
285C2×C4×C7H(5,𝔽2)11yescharacteristic
286C2×C4×C72−1+411yescharacteristic
287C2×C4×C72−1+411yescharacteristic
288C2×Dic7—21no—
289C2×Dic7—21no—
290C2×Dic7—21no—
291C2×Dic7—21no—
292C2×Dic7—21no—
293C2×Dic7—21no—
294C2×Dic7—41no—
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×Dic7C2×C4⋊C412yes—
307C2×Dic7C2×C4⋊C412yes—
308C2×Dic7C2×C4⋊C412yes—
309C4×D7—28no—
310C4×D7—22no—
311C4×D7—22no—
312C4×D7—22no—
313C4×D7—22no—
314C4×D7—44no—
315C4×D7—84no—
316C4×D7—84no—
317C7×C8—22no—
318C7×C8—22no—
319C7⋊C8—22no—
320C7⋊C8—22no—
321C23×C4—71no—
322C23×C4—71no—
323C23×C4—71no—
324C23×C4—141no—
325C23×C4—141no—
326C22×C8—71no—
327C22×C8—71no—
328C22×C8C22×D711yescharacteristic
329C22×C8C22×D711yescharacteristic
330C2×C4⋊C4—71no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—71no—
333C2×C4⋊C4—71no—
334C2×C4⋊C4—141no—
335C2×C4⋊C4—141no—
336C2×C4⋊C4—281no—
337C2×C4⋊C4—281no—
338C2×C4⋊C4—281no—
339C2×C4⋊C4—281no—
340C2×C4⋊C4C22×D711yescharacteristic
341C2×C4⋊C4C22×D711yescharacteristic
342C2×C4⋊C4C22×D711yescharacteristic
343C2×C4⋊C4C22×D711yescharacteristic
344C2×C22⋊C4—141no—
345C2×C22⋊C4—141no—
346C2×C42—21no—
347C2×C42—71no—
348C2×C42—71no—
349C2×C42—71no—
350C2×C42—74no—
351C2×C42—74no—
352C2×C42—141no—
353C2×C42C22×D711yescharacteristic
354#107—41no—
355#107—281no—
356#107—281no—
357#107—281no—
358#106—41no—
359#106—281no—
360#106—281no—
361#106—281no—
362C4⋊C8—74no—
363C4⋊C8C4×D714yescomplemented
364C22⋊C8—74no—
365C22⋊C8—74no—
366C4×C8—74no—
367C4×C8—74no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—141no—
372#95—141no—
373#95—141no—
374#95—141no—
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—
384C22×C7C22×C4⋊C411yescharacteristic
385C22×C7#53511yescharacteristic
386C22×C7#53611yescharacteristic
387C22×C7C2×#13511yescharacteristic
388C22×C7C2×#13511yescharacteristic
389C22×C7#57511yescharacteristic
390C22×C7#57511yescharacteristic
391C2×D7—22no—
392C2×D7—22no—
393C2×D7—22no—
394C2×D7—22no—
395C2×D7—22no—
396C2×D7—22no—
397C2×D7#42714yes—
398C4×C7—22no—
399C4×C7—22no—
400C4×C7—81no—
401C4×C7—81no—
402C4×C7—81no—
403C4×C7—81no—
404C4×C7#52011yescharacteristic
405C4×C7#52011yescharacteristic
406C4×C7#54411yescharacteristic
407C4×C7#54411yescharacteristic
408Dic7—22no—
409Dic7—22no—
410Dic7—22no—
411Dic7—81no—
412Dic7—81no—
413Dic7—81no—
414Dic7—81no—
415C24—71no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—71no—
421C22×C4—71no—
422C22×C4—71no—
423C22×C4—74no—
424C22×C4—72no—
425C22×C4—72no—
426C22×C4—74no—
427C22×C4—142no—
428C22×C4—142no—
429C22×C4—141no—
430C22×C4—141no—
431C22×C4—141no—
432C22×C4—141no—
433C22×C4—141no—
434C22×C4—141no—
435C22×C4—141no—
436C22×C4—141no—
437C22×C4—281no—
438C22×C4—281no—
439C22×C4—282no—
440C22×C4—282no—
441C22×C4—282no—
442C22×C4—282no—
443C22×C4—282no—
444C22×C4—282no—
445C22×C4D4×D711yescharacteristic
446C22×C4D4×D711yescharacteristic
447C22×C4C23×D711yescharacteristic
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—72no—
453C2×C8—72no—
454C2×C8—141no—
455C2×C8—141no—
456C2×C8—141no—
457C2×C8—141no—
458C2×C8C2×C4×D712yes—
459C2×C8C2×C4×D712yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
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—282no—
477C4⋊C4—282no—
478C22⋊C4—282no—
479C22⋊C4—282no—
480C42—42no—
481C42—74no—
482C42—74no—
483C42—72no—
484C42—72no—
485C42—282no—
486C42C2×C4×D712yes—
487C42Q8×D712yes—
488C2×C7#231711yescharacteristic
489C2×C7C2×#42711yescharacteristic
490C2×C7#291111yescharacteristic
491C2×C7#321111yescharacteristic
492C2×C7#321111yescharacteristic
493C2×C7#323211yescharacteristic
494C2×C7#323211yescharacteristic
495D7—24no—
496C23—72no—
497C23—72no—
498C23—72no—
499C23—141no—
500C23—141no—
501C23—141no—
502C23—141no—
503C23C2×D4×D711yescharacteristic
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—72no—
521C2×C4—72no—
522C2×C4—72no—
523C2×C4—148no—
524C2×C4—141no—
525C2×C4—141no—
526C2×C4—141no—
527C2×C4—141no—
528C2×C4—141no—
529C2×C4—141no—
530C2×C4—142no—
531C2×C4—142no—
532C2×C4—142no—
533C2×C4—142no—
534C2×C4—284no—
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—564no—
548C2×C4—564no—
549C2×C4D7×C4⋊C412yes—
550C2×C4D7×C4⋊C412yes—
551C2×C4C22×C4×D711yescharacteristic
552C2×C4#654811yescharacteristic
553C2×C4C2×Q8×D711yescharacteristic
554C2×C4#655111yescharacteristic
555C2×C4#655311yescharacteristic
556C2×C4#655411yescharacteristic
557C8—22no—
558C8—22no—
559C8—142no—
560C8—142no—
561C7#2198311yescharacteristic, complemented, Sylow
562C22—74no—
563C22—142no—
564C22—142no—
565C22—142no—
566C22—142no—
567C22—142no—
568C22—142no—
569C22C2×D7×C4⋊C411yescharacteristic
570C22#9029811yescharacteristic
571C22#9031911yescharacteristic
572C22D7×#13511yescharacteristic
573C22D7×#13511yescharacteristic
574C22#9046411yescharacteristic
575C22#9046811yescharacteristic
576C4—22no—
577C4—22no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—142no—
583C4—142no—
584C4—142no—
585C4—561no—
586C4—561no—
587C4—561no—
588C4—561no—
589C4#9023711yescharacteristic
590C4#9026511yescharacteristic
591C4#9038011yescharacteristic
592C4#9042011yescharacteristic
593C2—144no—
594C2#1173341311yescharacteristic
595C2D7×#42711yescharacteristic
596C2#1173665311yescharacteristic
597C2#1173798611yescharacteristic
598C2#1173805011yescharacteristic
599C2#1173861811yescharacteristic
600C2#1173868211yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1949C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
cosocleC22×C4×C7C24
hypercenter#1949D7
hypocenterC7#21983
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. C7×#1949C2semidirect
6. #11728361C2semidirect
8. #11728309C2semidirect
9. #11728209C2semidirect
10. #11727294C2semidirect
11. #11727222C2semidirect
14. #11726602C2semidirect
15. #11726602C2semidirect
45. #89605C4semidirect
96. C7×C4⋊C8C2×C4semidirect
117. C8×Dic7C2×C4semidirect
118. C8×Dic7C2×C4semidirect
123. C4⋊(C7⋊C8)C2×C4semidirect
130. #1949D7semidirect
363. C4⋊C8C4×D7semidirect
561. C7#21983semidirect

Maximal subgroups

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

subgroupindex
C2×#896052
D7×#3822
#117311972
C7×#19492
#117283862
#117283612
#117283332
#117283092
#117282092
#117272942
#117272222
#117266292
#117266282
#117266022
#219837