Finite Group Databasebeta

← #13373183

Subgroups — #13373183

Order 1792.

894 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×D4×C4⋊C4C211yesmaximal, characteristic
2C2×#89790C211yesmaximal, characteristic
3#11731088C211yesmaximal, characteristic, complemented
4#11729366C211yesmaximal, characteristic
5#11729366C211yesmaximal, characteristic
6#11729363C211yesmaximal, characteristic
7C4×#6406C211yesmaximal, characteristic
8#11729359C211yesmaximal, characteristic
9#11727370C211yesmaximal, characteristic, complemented
10#11727368C211yesmaximal, characteristic, complemented
11#11727357C211yesmaximal, characteristic, complemented
12#11727354C211yesmaximal, characteristic, complemented
13#11727342C211yesmaximal, characteristic, complemented
14#11727329C211yesmaximal, characteristic, complemented
15#11727232C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×C7×C4⋊C4—21no—
20C22×#1142C2211yescharacteristic
21C2×C4×Dic14C2211yescharacteristic
22C7×#389C2211yescharacteristic
23C7×#389C2211yescharacteristic
24C7×#385—21no—
25C7×#385—21no—
26C7×#384C2211yescharacteristic
27C7×#380—21no—
28C4×C7×C4⋊C4C2211yescharacteristic
29C2×#6406C2211yescharacteristic
30C2×#6406C2211yescharacteristic
31C2×#6406C2211yescharacteristic
32#89790C418yescomplemented
33#89750—21no—
34#89750—21no—
35C2×#6384C2211yescharacteristic
36C2×#6384C2211yescharacteristic
37C2×#6384C2211yescharacteristic
38C2×#6381C2211yescharacteristic
39#89708C2211yescharacteristic
40C4×C4⋊Dic7C2211yescharacteristic
41C4×C4⋊Dic7C2211yescharacteristic
42#89701C2211yescharacteristic
43#89701C2211yescharacteristic
44C2×C4⋊(C7⋊C8)C2211yescharacteristic
45C2×#6377C2211yescharacteristic
46C2×#6377C2211yescharacteristic
47C2×C4×C7⋊C8C2211yescharacteristic
48#89423—21no—
49#89420—21no—
50#89324C2211yescharacteristic
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89319C2211yescharacteristic
59#89319C2211yescharacteristic
60#22778—71nomaximal, Sylow
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—21no—
63C23×C4×C7—21no—
64C23×C4×C7—21no—
65C22×Dic14C2311yescharacteristic
66C4×C7×D4—22no—
67C4×C7×D4—22no—
68C4×C7×D4—22no—
69C4×C7×D4—41no—
70C4×C7×D4—41no—
71C4×C7×D4C2×C414yes—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4—21no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—44no—
77C2×C7×C4⋊C4D411yescharacteristic
78C2×C7×C4⋊C4D411yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4—21no—
85C2×C42×C7C2311yescharacteristic
86C2×C42×C7C2311yescharacteristic
87C2×C42×C7C2311yescharacteristic
88C2×#1142—22no—
89C2×#1142—22no—
90C2×#1142C2×C414yes—
91C2×C4⋊Dic7C2311yescharacteristic
92C2×C4⋊Dic7C2311yescharacteristic
93C2×C4⋊Dic7C2311yescharacteristic
94C2×Dic7⋊C4—21no—
95C2×C4×Dic7—21no—
96C2×C4×Dic7—21no—
97C2×C4×Dic7—21no—
98C22×C7⋊C8C2311yescharacteristic
99C22×C7⋊C8C2311yescharacteristic
100C22×C7⋊C8C2311yescharacteristic
101C22×C7⋊C8C2311yescharacteristic
102C4×Dic14—22no—
103C4×Dic14C2×C414yescomplemented
104C7×#95—21no—
105C7×#95—21no—
106C7×#95D411yescharacteristic
107C7×#95D411yescharacteristic
108#6406—22no—
109#6406—22no—
110#6406C2×C414yes—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118C7⋊#95—21no—
119#6384—41no—
120#6384—41no—
121#6384C2×C414yescomplemented
122#6381C2×C414yescomplemented
123C4⋊(C7⋊C8)—22no—
124#6377—41no—
125#6377C2×C414yescomplemented
126C4×C7⋊C8—41no—
127C2×#440—71no—
128#2356—71no—
129D4×C4⋊C4D711yescharacteristic
130#1935—71no—
131#1933—71no—
132#1921—71no—
133#1918—71no—
134#1877—71no—
135#1877—71no—
136#1836—71no—
137#1804—71no—
138#1803—71no—
139#1771—71no—
140#1762—71no—
141C4×#102—71no—
142C24×C7—21no—
143C2×C7×D4—21no—
144C2×C7×D4—21no—
145C2×C7×D4—21no—
146C2×C7×D4C22×C412yes—
147C2×C7×D4#4112yes—
148C2×C7×D4#4112yes—
149C22×C4×C7—21no—
150C22×C4×C7—24no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—42no—
154C22×C4×C7—42no—
155C22×C4×C7—42no—
156C22×C4×C7—42no—
157C22×C4×C7—42no—
158C22×C4×C7—42no—
159C22×C4×C7—81no—
160C22×C4×C7—81no—
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2411yescharacteristic
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C2×Dic14—21no—
173C2×Dic14—21no—
174C2×Dic14—21no—
175C2×Dic14—21no—
176C2×Dic14—21no—
177C2×Dic14C22×C412yes—
178C7×C4⋊C4—22no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—41no—
185C7×C4⋊C4—42no—
186C7×C4⋊C4—42no—
187C7×C4⋊C4—42no—
188C7×C4⋊C4—81no—
189C7×C4⋊C4C22×C412yes—
190C7×C22⋊C4—24no—
191C7×C22⋊C4—42no—
192C7×C22⋊C4—42no—
193C42×C7—21no—
194C42×C7—21no—
195C42×C7—21no—
196C42×C7—21no—
197C42×C7C22×C412yes—
198C42×C7#4112yes—
199#1142—28no—
200C4⋊Dic7—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7—21no—
204C4⋊Dic7—21no—
205C4⋊Dic7C22×C412yes—
206Dic7⋊C4—24no—
207C4×Dic7—24no—
208C4×Dic7—42no—
209C4×Dic7—42no—
210C2×C7⋊C8—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⋊C8C22×C412yes—
221C2×C7⋊C8C22×C412yes—
222C22×SD16—71no—
223C2×C4×Q8—71no—
224C2×C4×D4C2×D711yescharacteristic
225C2×C4×D4C2×D711yescharacteristic
226C2×C4×D4C2×D711yescharacteristic
227C22×C4⋊C4—21no—
228#440—78no—
229C2×#107—71no—
230C2×C4⋊C8—71no—
231C2×#103—71no—
232C2×#103—71no—
233C2×#103—71no—
234C2×#102—71no—
235C2×#102—71no—
236C2×#102—71no—
237C2×#97—71no—
238C2×#97—71no—
239C2×C4×C8—71no—
240#391—71no—
241#391—71no—
242#389C2×D711yescharacteristic
243#389C2×D711yescharacteristic
244#387—141no—
245#387—141no—
246#385—21no—
247#385—21no—
248#384C2×D711yescharacteristic
249#383—141no—
250#382—71no—
251#380—21no—
252C4×C4⋊C4—71no—
253C4×C4⋊C4—71no—
254C4×C4⋊C4C2×D711yescharacteristic
255#376—141no—
256#340—71no—
257#340—71no—
258#340—71no—
259#340—71no—
260#340—71no—
261#340—71no—
262#340—71no—
263#340—71no—
264#336—71no—
265#336—71no—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—41no—
270C23×C7—41no—
271C23×C7—41no—
272C23×C7—41no—
273C23×C7C22×D411yescharacteristic
274C7×D4—22no—
275C7×D4—22no—
276C7×D4—22no—
277C7×D4#11714yes—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—22no—
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—48no—
295C2×C4×C7—41no—
296C2×C4×C7—41no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
302C2×C4×C7—41no—
303C2×C4×C7—84no—
304C2×C4×C7—84no—
305C2×C4×C7C4×D412yes—
306C2×C4×C7C4×D412yes—
307C2×C4×C7AGL(1,ℤ/8)12yes—
308C2×C4×C7C23×C411yescharacteristic
309C2×C4×C7C2×#4111yescharacteristic
310C2×C4×C7C2×#4111yescharacteristic
311C2×C4×C7C2×#4111yescharacteristic
312C2×C4×C7H(5,𝔽2)11yescharacteristic
313C2×C4×C72−1+411yescharacteristic
314C2×Dic7—22no—
315C2×Dic7—22no—
316C2×Dic7—41no—
317C2×Dic7—41no—
318C2×Dic7—41no—
319C2×Dic7—41no—
320C2×Dic7—41no—
321C2×Dic7—41no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326Dic14—22no—
327Dic14—22no—
328Dic14—41no—
329Dic14—41no—
330C7⋊C8—22no—
331C7⋊C8—22no—
332C7⋊C8—41no—
333C7⋊C8—41no—
334C22×Q8—71no—
335C22×D4C22×D711yescharacteristic
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—21no—
339C2×SD16—74no—
340C2×SD16—142no—
341C2×SD16—142no—
342C22×C8—71no—
343C22×C8—71no—
344C22×C8—71no—
345C22×C8—71no—
346C4×Q8—74no—
347C4×Q8—142no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—41no—
352C4×D4—41no—
353C4×D4C4×D714yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—71no—
360C2×C4⋊C4—71no—
361C2×C4⋊C4—71no—
362C2×C4⋊C4—141no—
363C2×C4⋊C4C22⋊D711yescharacteristic
364C2×C4⋊C4C22⋊D711yescharacteristic
365C2×C4⋊C4C22×D711yescharacteristic
366C2×C4⋊C4C22×D711yescharacteristic
367C2×C4⋊C4C22×D711yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C42—141no—
372C2×C42—141no—
373C2×C42—141no—
374C2×C42C22×D711yescharacteristic
375C2×C42C22×D711yescharacteristic
376C2×C42C22×D711yescharacteristic
377#107—74no—
378C4⋊C8—142no—
379#103—74no—
380#103—281no—
381#103—281no—
382#102—74no—
383#102—142no—
384#102—142no—
385#97—74no—
386#97—281no—
387C4×C8—281no—
388#95—21no—
389#95—21no—
390#95—141no—
391#95—141no—
392#95—141no—
393#95—141no—
394#95—141no—
395#95—141no—
396#95—141no—
397#95—141no—
398#95C22⋊D711yescharacteristic
399#95C22⋊D711yescharacteristic
400C22×C7—24no—
401C22×C7—42no—
402C22×C7—42no—
403C22×C7—42no—
404C22×C7—42no—
405C22×C7—42no—
406C22×C7—42no—
407C22×C7C2×C4×D411yescharacteristic
408C22×C7#54611yescharacteristic
409C22×C7#54811yescharacteristic
410C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
411C22×C7#57511yescharacteristic
412C22×C7#57711yescharacteristic
413C22×C7#57811yescharacteristic
414C4×C7—22no—
415C4×C7—22no—
416C4×C7—22no—
417C4×C7—42no—
418C4×C7—41no—
419C4×C7—41no—
420C4×C7—41no—
421C4×C7—81no—
422C4×C7—81no—
423C4×C7C2×#11711yescharacteristic
424C4×C7#52011yescharacteristic
425C4×C7#55211yescharacteristic
426C4×C7#55311yescharacteristic
427Dic7—42no—
428Dic7—42no—
429Dic7—81no—
430Dic7—81no—
431C24—21no—
432C2×Q8—72no—
433C2×Q8—141no—
434C2×Q8—141no—
435C2×Q8—141no—
436C2×Q8—141no—
437C2×Q8—141no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×C4×D712yes—
442C2×D4#115912yes—
443C2×D4#116112yes—
444C22×C4—21no—
445C22×C4—24no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4—141no—
457C22×C4—141no—
458C22×C4—141no—
459C22×C4—141no—
460C22×C4C2×C22⋊D711yescharacteristic
461C22×C4C2×C22⋊D711yescharacteristic
462C22×C4C2×C22⋊D711yescharacteristic
463C22×C4C2×C22⋊D711yescharacteristic
464C22×C4C2×C22⋊D711yescharacteristic
465C22×C4C2×C22⋊D711yescharacteristic
466C22×C4C23×D711yescharacteristic
467SD16—148no—
468C2×C8—72no—
469C2×C8—72no—
470C2×C8—141no—
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—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—72no—
491C4⋊C4—81no—
492C4⋊C4—144no—
493C4⋊C4—141no—
494C4⋊C4—141no—
495C4⋊C4—141no—
496C4⋊C4—141no—
497C4⋊C4—141no—
498C4⋊C4C2×C4×D712yes—
499C22⋊C4—24no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—144no—
507C42—282no—
508C42—282no—
509C42C2×C4×D712yes—
510C42#115712yes—
511C2×C7—44no—
512C2×C7#235211yescharacteristic
513C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
514C2×C7#294711yescharacteristic
515C2×C7#331011yescharacteristic
516C2×C7#331511yescharacteristic
517C2×C7#336711yescharacteristic
518C2×C7#337611yescharacteristic
519C23—22no—
520C23—22no—
521C23—22no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23C22×C22⋊D711yescharacteristic
527Q8—142no—
528Q8—142no—
529Q8—281no—
530Q8—281no—
531D4—22no—
532D4—22no—
533D4—22no—
534D4#645514yes—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—48no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—84no—
561C2×C4—84no—
562C2×C4—142no—
563C2×C4—142no—
564C2×C4—281no—
565C2×C4—281no—
566C2×C4—281no—
567C2×C4—281no—
568C2×C4—281no—
569C2×C4—281no—
570C2×C4—281no—
571C2×C4—281no—
572C2×C4—281no—
573C2×C4—281no—
574C2×C4C4×C22⋊D712yes—
575C2×C4C4×C22⋊D712yes—
576C2×C4#649512yes—
577C2×C4C22×C4×D711yescharacteristic
578C2×C4C2×#115711yescharacteristic
579C2×C4C2×#115911yescharacteristic
580C2×C4#654811yescharacteristic
581C2×C4C2×#116111yescharacteristic
582C2×C4#655111yescharacteristic
583C8—142no—
584C8—142no—
585C8—281no—
586C8—281no—
587C7#2277811yescharacteristic, complemented, Sylow
588C22—24no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22C2×C4×C22⋊D711yescharacteristic
596C22C2×#649511yescharacteristic
597C22#9049711yescharacteristic
598C22#9050811yescharacteristic
599C22#9051311yescharacteristic
600C22#9052711yescharacteristic
601C22#9052911yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—42no—
609C4—81no—
610C4—81no—
611C4—282no—
612C4—282no—
613C4—561no—
614C4—561no—
615C4C2×#645511yescharacteristic
616C4#9019511yescharacteristic
617C4#9020411yescharacteristic
618C4#9020511yescharacteristic
619C2—44no—
620C2#1173960611yescharacteristic
621C2C4×#649511yescharacteristic
622C2#1174001611yescharacteristic
623C2#1174092911yescharacteristic
624C2#1174095811yescharacteristic
625C2#1174100811yescharacteristic
626C2#1174109011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×D4×C4⋊C4C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
cosocleC22×C4×C7C24
hypercenterD4×C4⋊C4D7
hypocenterC7#22778
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #11731088C2semidirect
9. #11727370C2semidirect
10. #11727368C2semidirect
11. #11727357C2semidirect
12. #11727354C2semidirect
13. #11727342C2semidirect
14. #11727329C2semidirect
15. #11727232C2semidirect
32. #89790C4semidirect
103. C4×Dic14C2×C4semidirect
121. #6384C2×C4semidirect
122. #6381C2×C4semidirect
125. #6377C2×C4semidirect
587. C7#22778semidirect

Maximal subgroups

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

subgroupindex
C7×D4×C4⋊C42
C2×#897902
#117310882
#117293662
#117293632
C4×#64062
#117293592
#117273702
#117273682
#117273572
#117273542
#117273422
#117273292
#117272322
#227787