Finite Group Databasebeta

← #13397731

Subgroups — #13397731

Order 1792.

940 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×Q8×C22⋊C4C211yesmaximal, characteristic
2C2×#90000C211yesmaximal, characteristic
3C2×C4×#1144C211yesmaximal, characteristic, complemented
4#11730929C211yesmaximal, characteristic
5#11729886C211yesmaximal, characteristic
6#11729386C211yesmaximal, characteristic, complemented
7#11729382C211yesmaximal, characteristic, complemented
8#11729380C211yesmaximal, characteristic, complemented
9#11727444C211yesmaximal, characteristic, complemented
10#11727438C211yesmaximal, characteristic, complemented
11#11727435C211yesmaximal, characteristic, complemented
12#11727428C211yesmaximal, characteristic, complemented
13#11727281C211yesmaximal, characteristic
14#11727273C211yesmaximal, characteristic
15#11727205C211yesmaximal, characteristic
16C23×C7×Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C22×#1144C2211yescharacteristic
20C22×#1144C2211yescharacteristic
21C2×#6487C2211yescharacteristic
22C2×C4×Dic14C2211yescharacteristic
23C7×#391—21no—
24C7×#391—21no—
25C7×#391C2211yescharacteristic
26C7×#391C2211yescharacteristic
27C7×#380—21no—
28C7×#380C2211yescharacteristic
29C4×C7×C22⋊C4—21no—
30C4×C7×C22⋊C4C2211yescharacteristic
31#90000—24no—
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38#89984C2211yescharacteristic
39C2×C22⋊(C7⋊C8)C2211yescharacteristic
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41C4×#1144—24no—
42C2×#6384C2211yescharacteristic
43C2×#6384C2211yescharacteristic
44C2×#6381C2211yescharacteristic
45C2×#6381C2211yescharacteristic
46#89723—21no—
47#89721—21no—
48#89707C2211yescharacteristic
49#89701C2211yescharacteristic
50#89700C2211yescharacteristic
51C2×C4⋊(C7⋊C8)C2211yescharacteristic
52C2×C4×C7⋊C8C2211yescharacteristic
53#89429—21no—
54#89426—21no—
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89319C2211yescharacteristic
60#89319C2211yescharacteristic
61#24906—71nomaximal, Sylow
62C22×C7×Q8—22no—
63C22×C7×Q8—22no—
64C22×C7×Q8—21no—
65C22×C7×Q8—22no—
66C22×C7×Q8—22no—
67C22×C7×Q8—41no—
68C22×C7×Q8—41no—
69C22×C7×Q8C2311yescharacteristic
70C22×C7×Q8C2311yescharacteristic
71C23×C4×C7—21no—
72C23×C4×C7C2311yescharacteristic
73C22×Dic14C2311yescharacteristic
74C4×C7×Q8—22no—
75C4×C7×Q8—22no—
76C4×C7×Q8—41no—
77C4×C7×Q8—41no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4D411yescharacteristic
84C2×C7×C22⋊C4D411yescharacteristic
85C2×C42×C7—21no—
86C2×C42×C7—21no—
87C2×C42×C7C2311yescharacteristic
88C2×C42×C7C2311yescharacteristic
89C2×C22⋊Dic7—21no—
90C2×C22⋊Dic7—21no—
91C2×#1144—22no—
92C2×#1144—22no—
93C2×#1144—22no—
94C2×#1144—22no—
95C2×#1144—41no—
96C2×#1144D414yes—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7—21no—
99C2×C4⋊Dic7C2311yescharacteristic
100C2×C4⋊Dic7C2311yescharacteristic
101C2×C4⋊Dic7C2311yescharacteristic
102#6487—22no—
103#6487—41no—
104C2×Dic7⋊C4—21no—
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—21no—
107C2×C4×Dic7—21no—
108C22×C7⋊C8C2311yescharacteristic
109C22×C7⋊C8C2311yescharacteristic
110C22×C7⋊C8C2311yescharacteristic
111C22×C7⋊C8C2311yescharacteristic
112C4×Dic14—22no—
113C4×Dic14—41no—
114C7×#95—21no—
115C7×#95—21no—
116C7×#95—21no—
117C7×#95—21no—
118C7×#95—21no—
119C7×#95D411yescharacteristic
120C7×#95D411yescharacteristic
121#6409—22no—
122#6409—22no—
123#6409—22no—
124#6409—22no—
125#6409—22no—
126#6409—41no—
127C7⋊#95—21no—
128C7⋊#95—21no—
129C7⋊#95—21no—
130C7⋊#95—21no—
131C22⋊(C7⋊C8)—22no—
132C22⋊(C7⋊C8)—41no—
133#6384—22no—
134#6384—41no—
135#6381—22no—
136#6381—41no—
137C4⋊(C7⋊C8)—41no—
138C4×C7⋊C8—22no—
139C2×#451—71no—
140C2×C4×Q16—71no—
141#2423—71no—
142Q8×C22⋊C4D711yescharacteristic
143#2095—71no—
144#2076—71no—
145#2056—71no—
146#2036—71no—
147#1933—71no—
148#1923—71no—
149#1878—71no—
150#1878—71no—
151#1863—71no—
152#1803—71no—
153#1787—71no—
154C24×C7C2×D411yescharacteristic
155C2×C7×Q8—24no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—42no—
165C2×C7×Q8—42no—
166C2×C7×Q8—44no—
167C2×C7×Q8—44no—
168C2×C7×Q8—44no—
169C2×C7×Q8—44no—
170C2×C7×Q8C2×D412yes—
171C2×C7×Q8#4112yes—
172C2×C7×Q8#4112yes—
173C2×C7×Q8#4112yes—
174C22×C4×C7—21no—
175C22×C4×C7—24no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—42no—
186C22×C4×C7—42no—
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D411yescharacteristic
190C22×C4×C7C2×D411yescharacteristic
191C22×C4×C7C2×D411yescharacteristic
192C22×C4×C7C2411yescharacteristic
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—21no—
197C2×Dic14—21no—
198C2×Dic14—21no—
199C2×Dic14—21no—
200C2×Dic14—21no—
201C2×Dic14—21no—
202C2×Dic14C2×D412yes—
203C7×C4⋊C4—21no—
204C7×C4⋊C4—21no—
205C7×C4⋊C4—21no—
206C7×C4⋊C4—21no—
207C7×C4⋊C4—42no—
208C7×C4⋊C4—42no—
209C7×C22⋊C4—41no—
210C7×C22⋊C4—42no—
211C7×C22⋊C4Q1614yescomplemented
212C42×C7—21no—
213C42×C7—21no—
214C42×C7—21no—
215C42×C7—21no—
216C42×C7—42no—
217C42×C7—42no—
218C22⋊Dic7—42no—
219C22⋊Dic7—81no—
220#1144—28no—
221#1144—44no—
222C4⋊Dic7—21no—
223C4⋊Dic7—21no—
224C4⋊Dic7—21no—
225C4⋊Dic7—21no—
226C4⋊Dic7—21no—
227C4⋊Dic7—21no—
228C4⋊Dic7—42no—
229C4⋊Dic7—81no—
230Dic7⋊C4—42no—
231Dic7⋊C4—42no—
232Dic7⋊C4—81no—
233C4×Dic7—42no—
234C2×C7⋊C8—21no—
235C2×C7⋊C8—21no—
236C2×C7⋊C8—21no—
237C2×C7⋊C8—21no—
238C2×C7⋊C8—21no—
239C2×C7⋊C8—21no—
240C2×C7⋊C8—21no—
241C2×C7⋊C8—21no—
242C2×C7⋊C8—21no—
243C2×C7⋊C8—21no—
244C2×C7⋊C8—21no—
245C2×C7⋊C8C2×D412yes—
246C23×Q8C2×D711yescharacteristic
247C22×Q16—71no—
248C22×Q16—71no—
249C2×C22⋊Q8—71no—
250C2×C4×Q8—71no—
251C2×C4×Q8C2×D711yescharacteristic
252C2×C4×Q8C2×D711yescharacteristic
253#451—144no—
254C4×Q16—144no—
255C2×#107—71no—
256C2×#107—71no—
257C2×C4⋊C8—71no—
258C2×#103—71no—
259C2×#103—71no—
260C2×#103—71no—
261C2×#103—71no—
262C2×#103—71no—
263C2×#103—71no—
264C2×#103—71no—
265C2×#103—71no—
266C2×C22⋊C8—71no—
267C2×C22⋊C8—71no—
268C2×C4×C8—71no—
269#399—141no—
270#398—141no—
271#391—21no—
272#391—21no—
273#391—71no—
274#391C2×D711yescharacteristic
275#391C2×D711yescharacteristic
276#389—71no—
277#388—141no—
278#387—141no—
279#384—71no—
280#380—21no—
281#380—71no—
282#380C2×D711yescharacteristic
283C4×C22⋊C4—21no—
284C4×C22⋊C4C2×D711yescharacteristic
285#340—71no—
286#340—71no—
287#340—71no—
288#340—71no—
289#336—71no—
290#336—71no—
291C23×C7—21no—
292C23×C7—21no—
293C23×C7—21no—
294C23×C7—21no—
295C23×C7—21no—
296C23×C7—21no—
297C23×C7C2×Q1612yes—
298C23×C7C22×D411yescharacteristic
299C7×Q8—22no—
300C7×Q8—22no—
301C7×Q8—22no—
302C7×Q8—22no—
303C7×Q8—22no—
304C7×Q8—48no—
305C7×Q8—41no—
306C7×Q8—41no—
307C7×Q8#12314yes—
308C2×C4×C7—22no—
309C2×C4×C7—21no—
310C2×C4×C7—22no—
311C2×C4×C7—21no—
312C2×C4×C7—22no—
313C2×C4×C7—21no—
314C2×C4×C7—21no—
315C2×C4×C7—22no—
316C2×C4×C7—21no—
317C2×C4×C7—21no—
318C2×C4×C7—21no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—21no—
324C2×C4×C7—21no—
325C2×C4×C7—48no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7C2×Q1612yes—
339C2×C4×C7C2×Q1612yes—
340C2×C4×C7C22×D411yescharacteristic
341C2×C4×C7C2×#4111yescharacteristic
342C2×C4×C7C2×#4111yescharacteristic
343C2×C4×C7C2×#4111yescharacteristic
344C2×C4×C7H(5,𝔽2)11yescharacteristic
345C2×C4×C7H(5,𝔽2)11yescharacteristic
346C2×Dic7—22no—
347C2×Dic7—41no—
348C2×Dic7—41no—
349C2×Dic7—41no—
350C2×Dic7—41no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358Dic14—22no—
359Dic14—22no—
360Dic14—41no—
361Dic14—41no—
362C7⋊C8—22no—
363C7⋊C8—41no—
364C7⋊C8—41no—
365C7⋊C8—41no—
366C22×Q8—22no—
367C22×Q8—22no—
368C22×Q8—21no—
369C22×Q8—22no—
370C22×Q8—22no—
371C22×Q8—41no—
372C22×Q8—41no—
373C22×Q8—71no—
374C22×Q8C22×D711yescharacteristic
375C22×Q8C22×D711yescharacteristic
376C23×C4—21no—
377C23×C4C22×D711yescharacteristic
378C2×Q16—74no—
379C2×Q16—142no—
380C2×Q16—142no—
381C2×Q16—142no—
382C2×Q16—142no—
383C2×Q16—281no—
384C22×C8—71no—
385C22×C8—71no—
386C22×C8—71no—
387C22×C8—71no—
388C22⋊Q8—142no—
389C22⋊Q8—281no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—41no—
393C4×Q8—41no—
394C4×Q8—142no—
395C4×Q8—281no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—71no—
399C2×C4⋊C4—71no—
400C2×C4⋊C4—71no—
401C2×C4⋊C4—141no—
402C2×C4⋊C4—141no—
403C2×C4⋊C4—141no—
404C2×C4⋊C4—141no—
405C2×C4⋊C4—141no—
406C2×C4⋊C4C22×D711yescharacteristic
407C2×C4⋊C4C22×D711yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—141no—
410C2×C22⋊C4—141no—
411C2×C22⋊C4C22⋊D711yescharacteristic
412C2×C22⋊C4C22⋊D711yescharacteristic
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—141no—
416C2×C42C22×D711yescharacteristic
417C2×C42C22×D711yescharacteristic
418#107—142no—
419#107—281no—
420C4⋊C8—281no—
421#103—142no—
422#103—142no—
423#103—142no—
424#103—142no—
425#103—142no—
426#103—142no—
427#103—281no—
428#103—281no—
429C22⋊C8—142no—
430C22⋊C8—281no—
431C4×C8—142no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—141no—
438#95—141no—
439#95—141no—
440#95—141no—
441#95C22⋊D711yescharacteristic
442#95C22⋊D711yescharacteristic
443C22×C7—22no—
444C22×C7—22no—
445C22×C7—22no—
446C22×C7—41no—
447C22×C7—41no—
448C22×C7—41no—
449C22×C7—41no—
450C22×C7#52511yescharacteristic
451C22×C7D4211yescharacteristic
452C22×C7#54611yescharacteristic
453C22×C7C22×Q1611yescharacteristic
454C22×C7#57511yescharacteristic
455C22×C7#57711yescharacteristic
456C22×C7#57811yescharacteristic
457C4×C7—24no—
458C4×C7—22no—
459C4×C7—22no—
460C4×C7—41no—
461C4×C7—42no—
462C4×C7—41no—
463C4×C7—41no—
464C4×C7—81no—
465C4×C7—81no—
466C4×C7C2×#12311yescharacteristic
467C4×C7#53811yescharacteristic
468C4×C7#54611yescharacteristic
469C4×C7#55111yescharacteristic
470Dic7—42no—
471Dic7—81no—
472Dic7—81no—
473Dic7—81no—
474C24C2×C22⋊D711yescharacteristic
475C2×Q8—24no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—72no—
491C2×Q8—141no—
492C2×Q8—141no—
493C2×Q8—141no—
494C2×Q8—141no—
495C2×Q8—141no—
496C2×Q8#115712yes—
497C2×Q8#115712yes—
498C2×Q8D4×D712yes—
499C2×Q8#115912yes—
500C22×C4—21no—
501C22×C4—24no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—141no—
514C22×C4—141no—
515C22×C4—141no—
516C22×C4—141no—
517C22×C4C2×C22⋊D711yescharacteristic
518C22×C4C2×C22⋊D711yescharacteristic
519C22×C4C2×C22⋊D711yescharacteristic
520C22×C4C2×C22⋊D711yescharacteristic
521C22×C4C2×C22⋊D711yescharacteristic
522C22×C4C23×D711yescharacteristic
523Q16—148no—
524Q16—284no—
525C2×C8—72no—
526C2×C8—141no—
527C2×C8—141no—
528C2×C8—141no—
529C2×C8—141no—
530C2×C8—141no—
531C2×C8—141no—
532C2×C8—141no—
533C2×C8—141no—
534C2×C8—141no—
535C2×C8—141no—
536C2×C8—141no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—141no—
544C4⋊C4—141no—
545C4⋊C4—141no—
546C4⋊C4—141no—
547C4⋊C4—141no—
548C4⋊C4—141no—
549C4⋊C4—282no—
550C4⋊C4—282no—
551C4⋊C4—282no—
552C4⋊C4—561no—
553C4⋊C4—561no—
554C22⋊C4—41no—
555C22⋊C4—42no—
556C22⋊C4—282no—
557C22⋊C4—561no—
558C22⋊C4#114414yescomplemented
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—42no—
564C42—42no—
565C42—282no—
566C2×C7—42no—
567C2×C7#241811yescharacteristic
568C2×C7#310411yescharacteristic
569C2×C7#312111yescharacteristic
570C2×C7#327111yescharacteristic
571C2×C7D4×Q1611yescharacteristic
572C2×C7#329911yescharacteristic
573C2×C7#332711yescharacteristic
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23C2×#114412yes—
581C23C22×C22⋊D711yescharacteristic
582Q8—22no—
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—22no—
587Q8—48no—
588Q8—41no—
589Q8—41no—
590Q8—142no—
591Q8—142no—
592Q8—281no—
593Q8—281no—
594Q8#644614yes—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—48no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—142no—
626C2×C4—281no—
627C2×C4—281no—
628C2×C4—281no—
629C2×C4—281no—
630C2×C4—281no—
631C2×C4—281no—
632C2×C4—281no—
633C2×C4—281no—
634C2×C4—281no—
635C2×C4—281no—
636C2×C4—281no—
637C2×C4C2×#114412yes—
638C2×C4C2×#114412yes—
639C2×C4C2×#115711yescharacteristic
640C2×C4C2×#115711yescharacteristic
641C2×C4C2×D4×D711yescharacteristic
642C2×C4C2×#115911yescharacteristic
643C2×C4#654811yescharacteristic
644C2×C4#654811yescharacteristic
645C8—142no—
646C8—281no—
647C8—281no—
648C8—281no—
649C7#2490611yescharacteristic, complemented, Sylow
650C22—22no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22#9048211yescharacteristic
658C22D4×C22⋊D711yescharacteristic
659C22#9049711yescharacteristic
660C22C22×#114411yescharacteristic
661C22#9051311yescharacteristic
662C22#9052811yescharacteristic
663C22#9052911yescharacteristic
664C4—22no—
665C4—22no—
666C4—24no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4—42no—
671C4—81no—
672C4—81no—
673C4—282no—
674C4—561no—
675C4—561no—
676C4—561no—
677C4C2×#644611yescharacteristic
678C4#9018111yescharacteristic
679C4#9018511yescharacteristic
680C4#9018611yescharacteristic
681C2—42no—
682C2#1173957311yescharacteristic
683C2#1173989211yescharacteristic
684C2#1173999711yescharacteristic
685C2#1174098611yescharacteristic
686C2#1174099211yescharacteristic
687C2#1174099611yescharacteristic
688C2D4×#114411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×Q8×C22⋊C4C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
hypercenterQ8×C22⋊C4D7
hypocenterC7#24906
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#1144C2semidirect
6. #11729386C2semidirect
7. #11729382C2semidirect
8. #11729380C2semidirect
9. #11727444C2semidirect
10. #11727438C2semidirect
11. #11727435C2semidirect
12. #11727428C2semidirect
211. C7×C22⋊C4Q16semidirect
558. C22⋊C4#1144semidirect
649. C7#24906semidirect

Maximal subgroups

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

subgroupindex
C7×Q8×C22⋊C42
C2×#900002
C2×C4×#11442
#117309292
#117298862
#117293862
#117293822
#117293802
#117274442
#117274382
#117274352
#117274282
#117272812
#117272732
#117272052
#249067