Finite Group Databasebeta

← #13375576

Subgroups — #13375576

Order 1792.

788 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#446C211yesmaximal, characteristic, complemented
2#11739936C211yesmaximal, characteristic
3C2×#89611C211yesmaximal, characteristic
4#11729389C211yesmaximal, characteristic, complemented
5#11728232C211yesmaximal, characteristic
6#11728231C211yesmaximal, characteristic
7#11728221C211yesmaximal, characteristic, complemented
8#11728206C211yesmaximal, characteristic, complemented
9#11728205C211yesmaximal, characteristic, complemented
10#11727588C211yesmaximal, characteristic, complemented
11#11727588C211yesmaximal, characteristic, complemented
12#11727585C211yesmaximal, characteristic
13#11727562C211yesmaximal, characteristic
14#11727540C211yesmaximal, characteristic, complemented
15#11727507C211yesmaximal, characteristic
16C2×C4×C7×Q8C2211yescharacteristic
17C22×#1131C2211yescharacteristic
18C22×C8×D7C2211yescharacteristic
19C2×#6435C2211yescharacteristic
20C7×#446—24no—
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×C4⋊C8C2211yescharacteristic
23C2×C7×C4⋊C8C2211yescharacteristic
24C2×C7×#97C2211yescharacteristic
25C2×C7×#97C2211yescharacteristic
26C2×C4×C7×C8C2211yescharacteristic
27#90003C411yescharacteristic
28#90001C411yescharacteristic
29C2×(C2×D7)⋊C8C2211yescharacteristic
30C2×(C2×D7)⋊C8C2211yescharacteristic
31C2×#6389C2211yescharacteristic
32C2×Dic7⋊C8C2211yescharacteristic
33C2×Dic7⋊C8C2211yescharacteristic
34C2×Dic7⋊C8C2211yescharacteristic
35C2×Dic7⋊C8C2211yescharacteristic
36C2×C8×Dic7C2211yescharacteristic
37#89766C411yescharacteristic
38#89766C411yescharacteristic
39#89764C411yescharacteristic
40#89756C411yescharacteristic
41#89756C411yescharacteristic
42#89754C411yescharacteristic
43C4×(C2×D7)⋊C4C2211yescharacteristic
44C4×(C2×D7)⋊C4C2211yescharacteristic
45C4×C4⋊Dic7C2211yescharacteristic
46C4×Dic7⋊C4C2211yescharacteristic
47C4×Dic7⋊C4C2211yescharacteristic
48C2×C4⋊(C7⋊C8)C2211yescharacteristic
49C2×#6377C2211yescharacteristic
50#89611—24no—
51#89345C2211yescharacteristic
52#89345C2211yescharacteristic
53#89345C2211yescharacteristic
54#89345C2211yescharacteristic
55#89345C2211yescharacteristic
56#89345C2211yescharacteristic
57#89319C2211yescharacteristic
58#89319C2211yescharacteristic
59#89319C2211yescharacteristic
60#89319C2211yescharacteristic
61#22961—71nomaximal, Sylow
62C22×C7×Q8C2×C411yescharacteristic
63C22×C4×D7C2311yescharacteristic
64C22×C7×C8C2311yescharacteristic
65C22×C7×C8C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C4×C7×Q8—22no—
69C4×C7×Q8—22no—
70C2×C7×C4⋊C4C2×C411yescharacteristic
71C2×C7×C4⋊C4C2×C411yescharacteristic
72C2×C7×C4⋊C4C2×C411yescharacteristic
73C2×C42×C7C2311yescharacteristic
74C2×C42×C7C2311yescharacteristic
75C2×C42×C7C2311yescharacteristic
76C2×(C2×D7)⋊C4C2×C411yescharacteristic
77C2×(C2×D7)⋊C4C2×C411yescharacteristic
78C2×(C2×D7)⋊C4C2×C411yescharacteristic
79C2×(C2×D7)⋊C4C2×C411yescharacteristic
80C2×(C2×D7)⋊C4C2×C411yescharacteristic
81C2×(C2×D7)⋊C4C2×C411yescharacteristic
82C2×C4⋊Dic7C2×C411yescharacteristic
83C2×C4⋊Dic7C2×C411yescharacteristic
84C2×Dic7⋊C4C2×C411yescharacteristic
85C2×Dic7⋊C4C2×C411yescharacteristic
86C2×Dic7⋊C4C2×C411yescharacteristic
87C2×Dic7⋊C4C2×C411yescharacteristic
88C2×Dic7⋊C4C2×C411yescharacteristic
89C2×Dic7⋊C4C2×C411yescharacteristic
90C2×C4×Dic7C2311yescharacteristic
91C2×C4×Dic7C2311yescharacteristic
92C2×C4×Dic7C2311yescharacteristic
93C22×C7⋊C8C2311yescharacteristic
94C22×C7⋊C8C2311yescharacteristic
95C22×C7⋊C8C2311yescharacteristic
96C22×C7⋊C8C2311yescharacteristic
97C2×#1131—22no—
98C2×#1131—22no—
99C2×#1131—41no—
100C2×C8×D7—22no—
101C2×C8×D7—22no—
102C2×C8×D7—41no—
103#6435—22no—
104#6435—22no—
105C7×C4⋊C8—22no—
106C7×C4⋊C8—22no—
107C7×C4⋊C8D414yes—
108C7×#97—22no—
109C7×#97—22no—
110C4×C7×C8—22no—
111C7⋊#95C2×C411yescharacteristic
112C7⋊#95C2×C411yescharacteristic
113C7⋊#95C2×C411yescharacteristic
114C7⋊#95C2×C411yescharacteristic
115C7⋊#95C2×C411yescharacteristic
116C7⋊#95C2×C411yescharacteristic
117C7⋊#95C2×C411yescharacteristic
118C7⋊#95C2×C411yescharacteristic
119C7⋊#95C2×C411yescharacteristic
120C7⋊#95C2×C411yescharacteristic
121(C2×D7)⋊C8—22no—
122(C2×D7)⋊C8Q814yescomplemented
123#6389—41no—
124Dic7⋊C8—22no—
125Dic7⋊C8—22no—
126Dic7⋊C8—41no—
127Dic7⋊C8—41no—
128C8×Dic7—41no—
129C4⋊(C7⋊C8)—22no—
130#6377—22no—
131C2×#446D711yescharacteristic, complemented
132C2×#424—71no—
133#2396—71no—
134#1985—71no—
135#1940—71no—
136#1939—71no—
137#1939—71no—
138#1917—71no—
139#1917—71no—
140#1851—71no—
141#1850—71no—
142#1771—71no—
143#1753—71no—
144#1752—71no—
145#1750—71no—
146C23×D7C22×C411yescharacteristic
147C2×C7×Q8—22no—
148C2×C7×Q8—41no—
149C2×C7×Q8—41no—
150C22×C4×C7C22×C411yescharacteristic
151C22×C4×C7C22×C411yescharacteristic
152C22×C4×C7C22×C411yescharacteristic
153C22×C4×C7C22×C411yescharacteristic
154C22×C4×C7C22×C411yescharacteristic
155C22×C4×C7C22×C411yescharacteristic
156C22×C4×C7C2411yescharacteristic
157C22×Dic7C22×C411yescharacteristic
158C22×Dic7C22×C411yescharacteristic
159C22×Dic7C22×C411yescharacteristic
160C22×Dic7C22×C411yescharacteristic
161C22×Dic7C22×C411yescharacteristic
162C22×Dic7C22×C411yescharacteristic
163C22×Dic7C22×C411yescharacteristic
164C2×C4×D7—21no—
165C2×C4×D7—21no—
166C2×C4×D7—21no—
167C2×C4×D7—21no—
168C2×C4×D7C2×Q812yes—
169C2×C4×D7#4112yes—
170C2×C7×C8—21no—
171C2×C7×C8—21no—
172C2×C7×C8—21no—
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C2×C7×C8—21no—
178C2×C7×C8—21no—
179C2×C7×C8C2×D412yes—
180C2×C7×C8C2×D412yes—
181C2×C7×C8C2×Q812yes—
182C7×C4⋊C4—22no—
183C7×C4⋊C4—22no—
184C7×C4⋊C4—22no—
185C42×C7—21no—
186C42×C7—21no—
187C42×C7—21no—
188C42×C7—21no—
189C42×C7C2×D412yes—
190C42×C7#4112yes—
191(C2×D7)⋊C4—22no—
192(C2×D7)⋊C4—22no—
193(C2×D7)⋊C4—22no—
194(C2×D7)⋊C4—41no—
195(C2×D7)⋊C4—41no—
196(C2×D7)⋊C4—41no—
197C4⋊Dic7—22no—
198C4⋊Dic7—41no—
199Dic7⋊C4—22no—
200Dic7⋊C4—22no—
201Dic7⋊C4—22no—
202Dic7⋊C4—41no—
203Dic7⋊C4—41no—
204Dic7⋊C4—41no—
205C4×Dic7—21no—
206C4×Dic7—21no—
207C4×Dic7—21no—
208C4×Dic7—21no—
209C4×Dic7—21no—
210C4×Dic7—21no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8—21no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8—21no—
219C2×C7⋊C8—21no—
220C2×C7⋊C8—21no—
221C2×C7⋊C8—21no—
222C2×C7⋊C8C2×Q812yes—
223#1131—44no—
224C8×D7—44no—
225C22×M16—71no—
226C23×C8—71no—
227C2×C4×Q8C2×D711yescharacteristic
228C2×#117—71no—
229#446—24no—
230#424—144no—
231C2×C4⋊C8—71no—
232C2×C4⋊C8—71no—
233C2×C4⋊C8—71no—
234C2×C4⋊C8—71no—
235C2×C4⋊C8—71no—
236C2×C4⋊C8C2×D711yescharacteristic
237C2×C4⋊C8C2×D711yescharacteristic
238C2×C4⋊C8C2×D711yescharacteristic
239C2×C22⋊C8—71no—
240C2×C22⋊C8—71no—
241C2×#97—71no—
242C2×#97—71no—
243C2×#97C2×D711yescharacteristic
244C2×#97C2×D711yescharacteristic
245C2×C4×C8—71no—
246C2×C4×C8C2×D711yescharacteristic
247#400—71no—
248#399—71no—
249#398—71no—
250#398—71no—
251#396—71no—
252#396—71no—
253#395—71no—
254#393—71no—
255C4×C4⋊C4—71no—
256C4×C4⋊C4—71no—
257C4×C4⋊C4—71no—
258C4×C22⋊C4—71no—
259C4×C22⋊C4—71no—
260#336—71no—
261#336—71no—
262#336—71no—
263#336—71no—
264#336—71no—
265#336—71no—
266#336—71no—
267#336—71no—
268#336—71no—
269#336—71no—
270C23×C7C23×C411yescharacteristic
271C22×D7—21no—
272C22×D7—21no—
273C22×D7—21no—
274C22×D7—21no—
275C22×D7—21no—
276C22×D7—21no—
277C22×D7C4×Q812yes—
278C7×Q8—44no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—21no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—21no—
294C2×C4×C7—21no—
295C2×C4×C7C4×D412yes—
296C2×C4×C7C4×D412yes—
297C2×C4×C7C22×D411yescharacteristic
298C2×C4×C7C22×Q811yescharacteristic
299C2×C4×C7C2×#4111yescharacteristic
300C2×C4×C7C2×#4111yescharacteristic
301C2×C4×C7H(5,𝔽2)11yescharacteristic
302C2×C4×C72−1+411yescharacteristic
303C2×Dic7—21no—
304C2×Dic7—21no—
305C2×Dic7—21no—
306C2×Dic7—21no—
307C2×Dic7—21no—
308C2×Dic7—21no—
309C2×Dic7—21no—
310C2×Dic7—21no—
311C2×Dic7—21no—
312C2×Dic7—21no—
313C2×Dic7—21no—
314C2×Dic7—21no—
315C2×Dic7—21no—
316C2×Dic7—21no—
317C2×Dic7—21no—
318C2×Dic7—21no—
319C2×Dic7—21no—
320C2×Dic7—21no—
321C2×Dic7—21no—
322C2×Dic7C4×Q812yes—
323C2×Dic7#13112yes—
324C4×D7—22no—
325C4×D7—22no—
326C4×D7—22no—
327C4×D7—22no—
328C7×C8—22no—
329C7×C8—22no—
330C7×C8—22no—
331C7×C8—41no—
332C7⋊C8—22no—
333C7⋊C8—41no—
334C7⋊C8—41no—
335C7⋊C8—41no—
336C22×Q8C4×D711yescharacteristic
337C23×C4—71no—
338C2×M16—142no—
339C2×M16—142no—
340C2×M16—281no—
341C22×C8—71no—
342C22×C8—71no—
343C22×C8—71no—
344C22×C8—71no—
345C22×C8—142no—
346C22×C8—142no—
347C22×C8—281no—
348C22×C8C22×D711yescharacteristic
349C22×C8C22×D711yescharacteristic
350C22×C8C22×D711yescharacteristic
351C22×C8C22×D711yescharacteristic
352C4×Q8—22no—
353C4×Q8—22no—
354#117—142no—
355#117—142no—
356C2×C4⋊C4—71no—
357C2×C4⋊C4—71no—
358C2×C4⋊C4—71no—
359C2×C4⋊C4—71no—
360C2×C4⋊C4—71no—
361C2×C4⋊C4—71no—
362C2×C4⋊C4—71no—
363C2×C4⋊C4—71no—
364C2×C4⋊C4C4×D711yescharacteristic
365C2×C4⋊C4C4×D711yescharacteristic
366C2×C4⋊C4C4×D711yescharacteristic
367C2×C22⋊C4—71no—
368C2×C22⋊C4—71no—
369C2×C22⋊C4—71no—
370C2×C22⋊C4—71no—
371C2×C22⋊C4—71no—
372C2×C22⋊C4—71no—
373C2×C42—71no—
374C2×C42—71no—
375C2×C42—71no—
376C2×C42C22×D711yescharacteristic
377C2×C42C22×D711yescharacteristic
378C2×C42C22×D711yescharacteristic
379C4⋊C8—22no—
380C4⋊C8—22no—
381C4⋊C8—142no—
382C4⋊C8—142no—
383C4⋊C8—142no—
384C4⋊C8—281no—
385C4⋊C8—281no—
386C4⋊C8C22⋊D714yes—
387C22⋊C8—74no—
388C22⋊C8—142no—
389#97—22no—
390#97—22no—
391#97—142no—
392#97—281no—
393C4×C8—22no—
394C4×C8—281no—
395#95—71no—
396#95—71no—
397#95—71no—
398#95—71no—
399#95—71no—
400#95—71no—
401#95—71no—
402#95—71no—
403#95—71no—
404#95—71no—
405C22×C7C2×C4×D411yescharacteristic
406C22×C7C2×C4×Q811yescharacteristic
407C22×C7#52011yescharacteristic
408C22×C7C2×#13111yescharacteristic
409C22×C7#56811yescharacteristic
410C22×C7#56811yescharacteristic
411C22×C7#56811yescharacteristic
412C2×D7—22no—
413C2×D7—22no—
414C2×D7—22no—
415C2×D7—41no—
416C2×D7—41no—
417C2×D7—41no—
418C2×D7—41no—
419C4×C7—22no—
420C4×C7—22no—
421C4×C7—41no—
422C4×C7—41no—
423C4×C7—41no—
424C4×C7—41no—
425C4×C7#54611yescharacteristic
426C4×C7D4×Q811yescharacteristic
427C4×C7#55211yescharacteristic
428C4×C7#55411yescharacteristic
429Dic7—22no—
430Dic7—22no—
431Dic7—41no—
432Dic7—41no—
433Dic7—41no—
434Dic7—41no—
435Dic7—41no—
436C24—71no—
437C2×Q8—22no—
438C2×Q8—41no—
439C2×Q8—41no—
440C22×C4—71no—
441C22×C4—71no—
442C22×C4—72no—
443C22×C4—72no—
444C22×C4—71no—
445C22×C4—71no—
446C22×C4—71no—
447C22×C4—71no—
448C22×C4—71no—
449C22×C4—141no—
450C22×C4—141no—
451C22×C4—141no—
452C22×C4—141no—
453C22×C4C2×C4×D711yescharacteristic
454C22×C4C2×C4×D711yescharacteristic
455C22×C4C2×C4×D711yescharacteristic
456C22×C4C2×C4×D711yescharacteristic
457C22×C4C2×C4×D711yescharacteristic
458C22×C4C2×C4×D711yescharacteristic
459C22×C4C23×D711yescharacteristic
460M16—284no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—72no—
471C2×C8—141no—
472C2×C8—141no—
473C2×C8—141no—
474C2×C8—141no—
475C2×C8—141no—
476C2×C8—141no—
477C2×C8—141no—
478C2×C8—141no—
479C2×C8—141no—
480C2×C8—141no—
481C2×C8—141no—
482C2×C8—284no—
483C2×C8Q8×D712yes—
484C2×C8C2×C22⋊D712yes—
485C2×C8C2×C22⋊D712yes—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—142no—
490C4⋊C4—142no—
491C4⋊C4—142no—
492C4⋊C4—142no—
493C4⋊C4—281no—
494C4⋊C4—281no—
495C4⋊C4—281no—
496C4⋊C4—281no—
497C22⋊C4—142no—
498C22⋊C4—142no—
499C22⋊C4—142no—
500C22⋊C4—281no—
501C22⋊C4—281no—
502C22⋊C4—281no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—141no—
508C42—141no—
509C42—141no—
510C42—141no—
511C42—141no—
512C42—141no—
513C42#115712yes—
514C42C2×C22⋊D712yes—
515C2×C7#236011yescharacteristic
516C2×C7#293011yescharacteristic
517C2×C7#293511yescharacteristic
518C2×C7#296111yescharacteristic
519C2×C7#296211yescharacteristic
520C2×C7#299211yescharacteristic
521C2×C7#299511yescharacteristic
522D7—42no—
523C23—72no—
524C23—141no—
525C23—141no—
526C23—141no—
527C23—141no—
528C23—141no—
529C23—141no—
530C23C22×C4×D711yescharacteristic
531Q8—44no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—72no—
549C2×C4—72no—
550C2×C4—141no—
551C2×C4—141no—
552C2×C4—141no—
553C2×C4—141no—
554C2×C4—142no—
555C2×C4—142no—
556C2×C4—142no—
557C2×C4—142no—
558C2×C4—141no—
559C2×C4—141no—
560C2×C4—141no—
561C2×C4—141no—
562C2×C4—141no—
563C2×C4—141no—
564C2×C4—141no—
565C2×C4—141no—
566C2×C4—141no—
567C2×C4—141no—
568C2×C4—141no—
569C2×C4—141no—
570C2×C4—141no—
571C2×C4—141no—
572C2×C4—141no—
573C2×C4C4×C22⋊D712yes—
574C2×C4C4×C22⋊D712yes—
575C2×C4C2×#115711yescharacteristic
576C2×C4C2×Q8×D711yescharacteristic
577C2×C4#655111yescharacteristic
578C2×C4D7×#4111yescharacteristic
579C2×C4#655311yescharacteristic
580C2×C4C22×C22⋊D711yescharacteristic
581C8—22no—
582C8—22no—
583C8—22no—
584C8—41no—
585C8—142no—
586C8—281no—
587C8—281no—
588C8—281no—
589C7#2296111yescharacteristic, complemented, Sylow
590C22—142no—
591C22—142no—
592C22—142no—
593C22—281no—
594C22—281no—
595C22—281no—
596C22—281no—
597C22C4×Q8×D711yescharacteristic
598C22#9026511yescharacteristic
599C22#9043611yescharacteristic
600C22#9043611yescharacteristic
601C22D7×#13111yescharacteristic
602C22#9044111yescharacteristic
603C22C2×C4×C22⋊D711yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—142no—
611C4—142no—
612C4—281no—
613C4—281no—
614C4—281no—
615C4—281no—
616C4—281no—
617C4#9027011yescharacteristic
618C4#9027211yescharacteristic
619C4Q8×C22⋊D711yescharacteristic
620C4#9052011yescharacteristic
621C2—282no—
622C2#1173739111yescharacteristic
623C2#1173739411yescharacteristic
624C2#1173740411yescharacteristic
625C2#1173740611yescharacteristic
626C2#1173993511yescharacteristic
627C2#1174120111yescharacteristic
628C2#1174123311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D7
commutator, socleC23×C7C23×C4
FittingC2×C7×#446C2
prime radicalC23×D7C22×C4
cosocleC22×C4×C7C24
hypercenterC2×#446D7
hypocenterC7#22961
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×C7×#446C2semidirect
4. #11729389C2semidirect
7. #11728221C2semidirect
8. #11728206C2semidirect
9. #11728205C2semidirect
10. #11727588C2semidirect
11. #11727588C2semidirect
14. #11727540C2semidirect
122. (C2×D7)⋊C8Q8semidirect
131. C2×#446D7semidirect
589. C7#22961semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4462
#117399362
C2×#896112
#117293892
#117282322
#117282312
#117282212
#117282062
#117282052
#117275882
#117275852
#117275622
#117275402
#117275072
#229617