Finite Group Databasebeta

← #13416912

Subgroups — #13416912

Order 1792.

828 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#89794C211yesmaximal, characteristic, complemented
3C2×C4×#1143C211yesmaximal, characteristic
4#11731122C211yesmaximal, characteristic
5#11729387C211yesmaximal, characteristic
6#11729387C211yesmaximal, characteristic
7#11729382C211yesmaximal, characteristic, complemented
8#11729382C211yesmaximal, characteristic, complemented
9#11727384C211yesmaximal, characteristic
10#11727380C211yesmaximal, characteristic
11#11727373C211yesmaximal, characteristic, complemented
12#11727360C211yesmaximal, characteristic, complemented
13#11727340C211yesmaximal, characteristic
14#11727324C211yesmaximal, characteristic, complemented
15#11727236C211yesmaximal, characteristic, complemented
16C2×C4×C7×Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C22×#1143C2211yescharacteristic
20C2×C4×D28C2211yescharacteristic
21C2×#6433C2211yescharacteristic
22C7×#389—21no—
23C7×#389—21no—
24C7×#389C2211yescharacteristic
25C7×#389C2211yescharacteristic
26C7×#384—21no—
27C7×#384C2211yescharacteristic
28C4×C7×C4⋊C4—21no—
29C4×C7×C4⋊C4C2211yescharacteristic
30C2×#6409C2211yescharacteristic
31C2×#6409C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C4×#1143—24no—
34#89794—24no—
35#89764—21no—
36#89761—21no—
37C2×#6383C2211yescharacteristic
38C2×#6383C2211yescharacteristic
39C2×#6383C2211yescharacteristic
40C2×#6382C2211yescharacteristic
41C2×#6382C2211yescharacteristic
42C2×#6381C2211yescharacteristic
43C2×#6381C2211yescharacteristic
44C2×#6381C2211yescharacteristic
45#89711C2211yescharacteristic
46#89711C2211yescharacteristic
47#89700C2211yescharacteristic
48#89700C2211yescharacteristic
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50C2×C4×C7⋊C8C2211yescharacteristic
51#89448—21no—
52#89439—21no—
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89319C2211yescharacteristic
58#89319C2211yescharacteristic
59#89319C2211yescharacteristic
60#89319C2211yescharacteristic
61#26379—71nomaximal, Sylow
62C22×C7×Q8C2311yescharacteristic
63C22×D28C2311yescharacteristic
64C22×C4×D7—21no—
65C4×C7×Q8—22no—
66C4×C7×Q8—22no—
67C4×C7×Q8—22no—
68C4×C7×Q8—22no—
69C4×C7×Q8—41no—
70C4×C7×Q8—41no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4—21no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4D411yescharacteristic
79C2×C7×C4⋊C4D411yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C42×C7—21no—
84C2×C42×C7—21no—
85C2×C42×C7—21no—
86C2×C42×C7C2311yescharacteristic
87C2×C42×C7C2311yescharacteristic
88C2×C42×C7C2311yescharacteristic
89C2×#1143—22no—
90C2×#1143—22no—
91C2×#1143Q814yes—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—21no—
95C2×(C2×D7)⋊C4—21no—
96C2×(C2×D7)⋊C4—21no—
97C2×C4⋊Dic7C2311yescharacteristic
98C2×C4⋊Dic7C2311yescharacteristic
99C2×C4⋊Dic7C2311yescharacteristic
100C2×Dic7⋊C4—21no—
101C2×Dic7⋊C4—21no—
102C2×Dic7⋊C4—21no—
103C2×Dic7⋊C4—21no—
104C22×C7⋊C8C2311yescharacteristic
105C22×C7⋊C8C2311yescharacteristic
106C22×C7⋊C8C2311yescharacteristic
107C22×C7⋊C8C2311yescharacteristic
108C4×D28—22no—
109C4×D28—41no—
110#6433—22no—
111#6433—41no—
112C7×#95—21no—
113C7×#95—21no—
114C7×#95D411yescharacteristic
115C7×#95D411yescharacteristic
116#6409—22no—
117#6409—22no—
118#6409D414yes—
119C7⋊#95—21no—
120C7⋊#95—21no—
121#6383—22no—
122#6383—22no—
123#6383—41no—
124#6382—22no—
125#6382—22no—
126#6381—22no—
127#6381—22no—
128#6381—41no—
129C4⋊(C7⋊C8)—22no—
130C4×C7⋊C8—22no—
131C2×#479—71no—
132C2×C4×SD16—71no—
133#2454—71no—
134Q8×C4⋊C4D711yescharacteristic, complemented
135#2093—71no—
136#2084—71no—
137#2067—71no—
138#2059—71no—
139#1942—71no—
140#1916—71no—
141#1880—71no—
142#1880—71no—
143#1864—71no—
144#1863—71no—
145#1863—71no—
146C23×D7—21no—
147C2×C7×Q8—21no—
148C2×C7×Q8—21no—
149C2×C7×Q8—21no—
150C2×C7×Q8C2×D412yes—
151C2×C7×Q8C2×Q812yes—
152C2×C7×Q8#4112yes—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2411yescharacteristic
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C2×D28—21no—
168C2×D28—21no—
169C2×D28—21no—
170C2×D28—21no—
171C2×D28—21no—
172C2×D28C2×Q812yes—
173C2×C4×D7—42no—
174C2×C4×D7—42no—
175C2×C4×D7—81no—
176C7×C4⋊C4—24no—
177C7×C4⋊C4—22no—
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—42no—
185C7×C4⋊C4—42no—
186C7×C4⋊C4—42no—
187C7×C4⋊C4—81no—
188C7×C4⋊C4—81no—
189C7×C4⋊C4—81no—
190C7×C4⋊C4#4112yes—
191C42×C7—24no—
192C42×C7—21no—
193C42×C7—21no—
194C42×C7—21no—
195C42×C7—21no—
196C42×C7—21no—
197C42×C7—21no—
198C42×C7—42no—
199C42×C7—42no—
200#1143—28no—
201(C2×D7)⋊C4—42no—
202(C2×D7)⋊C4—42no—
203(C2×D7)⋊C4—81no—
204(C2×D7)⋊C4—81no—
205(C2×D7)⋊C4—81no—
206C4⋊Dic7—21no—
207C4⋊Dic7—21no—
208C4⋊Dic7—21no—
209C4⋊Dic7—21no—
210C4⋊Dic7—21no—
211C4⋊Dic7C2×D412yes—
212Dic7⋊C4—42no—
213Dic7⋊C4—42no—
214Dic7⋊C4—81no—
215Dic7⋊C4—81no—
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⋊C8—21no—
223C2×C7⋊C8—21no—
224C2×C7⋊C8—21no—
225C2×C7⋊C8—21no—
226C2×C7⋊C8C2×D412yes—
227C2×C7⋊C8C2×Q812yes—
228C22×SD16—71no—
229C2×#125—71no—
230C2×C4×Q8C2×D711yescharacteristic
231C2×C4×Q8C2×D711yescharacteristic
232C2×C4×Q8C2×D711yescharacteristic
233C2×C4×D4—71no—
234#479—144no—
235C4×SD16—144no—
236C2×#107—71no—
237C2×#107—71no—
238C2×#107—71no—
239C2×#106—71no—
240C2×#106—71no—
241C2×C4⋊C8—71no—
242C2×#103—71no—
243C2×#103—71no—
244C2×#103—71no—
245C2×#102—71no—
246C2×#102—71no—
247C2×#102—71no—
248C2×C4×C8—71no—
249#399—141no—
250#396—141no—
251#390—71no—
252#390—71no—
253#389—21no—
254#389—21no—
255#389—71no—
256#389—71no—
257#389C2×D711yescharacteristic
258#389C2×D711yescharacteristic
259#385—141no—
260#384—21no—
261#384C2×D711yescharacteristic
262#380—141no—
263C4×C4⋊C4—21no—
264C4×C4⋊C4C2×D711yescharacteristic
265#340—71no—
266#340—71no—
267#340—71no—
268#340—71no—
269#336—71no—
270#336—71no—
271#336—71no—
272#336—71no—
273C23×C7C22×D411yescharacteristic
274C22×D7—22no—
275C22×D7—41no—
276C22×D7—41no—
277C22×D7—41no—
278C22×D7—41no—
279C22×D7—41no—
280C22×D7—41no—
281C7×Q8—22no—
282C7×Q8—22no—
283C7×Q8—22no—
284C7×Q8C22⋊Q814yes—
285C2×C4×C7—21no—
286C2×C4×C7—22no—
287C2×C4×C7—21no—
288C2×C4×C7—22no—
289C2×C4×C7—22no—
290C2×C4×C7—21no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—22no—
294C2×C4×C7—21no—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—21no—
302C2×C4×C7—21no—
303C2×C4×C7—21no—
304C2×C4×C7—21no—
305C2×C4×C7—41no—
306C2×C4×C7—41no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7—41no—
311C2×C4×C7—41no—
312C2×C4×C7—41no—
313C2×C4×C7#13512yes—
314C2×C4×C7#13712yes—
315C2×C4×C7C22×D411yescharacteristic
316C2×C4×C7C22×Q811yescharacteristic
317C2×C4×C7C2×#4111yescharacteristic
318C2×C4×C7C2×#4111yescharacteristic
319C2×C4×C7H(5,𝔽2)11yescharacteristic
320C2×C4×C72−1+411yescharacteristic
321C2×Dic7—22no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326C2×Dic7—41no—
327C2×Dic7—41no—
328C2×Dic7—41no—
329C2×Dic7—41no—
330D28—22no—
331D28—22no—
332D28—41no—
333D28—41no—
334C4×D7—84no—
335C7⋊C8—22no—
336C7⋊C8—22no—
337C7⋊C8—41no—
338C7⋊C8—41no—
339C22×Q8C22×D711yescharacteristic
340C22×D4—71no—
341C23×C4—141no—
342C2×SD16—74no—
343C2×SD16—142no—
344C2×SD16—142no—
345C22×C8—71no—
346C22×C8—71no—
347C22×C8—71no—
348C22×C8—71no—
349#125—142no—
350#125—281no—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×Q8—41no—
356C4×Q8—41no—
357C4×D4—142no—
358C4×D4—281no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—71no—
367C2×C4⋊C4—71no—
368C2×C4⋊C4—71no—
369C2×C4⋊C4—141no—
370C2×C4⋊C4—141no—
371C2×C4⋊C4—141no—
372C2×C4⋊C4—141no—
373C2×C4⋊C4C22⋊D711yescharacteristic
374C2×C4⋊C4C22⋊D711yescharacteristic
375C2×C4⋊C4C22×D711yescharacteristic
376C2×C4⋊C4C22×D711yescharacteristic
377C2×C4⋊C4C22×D711yescharacteristic
378C2×C22⋊C4—141no—
379C2×C22⋊C4—141no—
380C2×C22⋊C4—141no—
381C2×C22⋊C4—141no—
382C2×C22⋊C4—141no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42C22×D711yescharacteristic
387C2×C42C22×D711yescharacteristic
388C2×C42C22×D711yescharacteristic
389#107—142no—
390#107—142no—
391#107—281no—
392#106—142no—
393#106—142no—
394C4⋊C8—142no—
395#103—74no—
396#103—142no—
397#103—142no—
398#102—142no—
399#102—142no—
400#102—281no—
401C4×C8—142no—
402#95—21no—
403#95—21no—
404#95—141no—
405#95—141no—
406#95C22⋊D711yescharacteristic
407#95C22⋊D711yescharacteristic
408C22×C7#52511yescharacteristic
409C22×C7D4211yescharacteristic
410C22×C7D4×Q811yescharacteristic
411C22×C7C2×#13511yescharacteristic
412C22×C7C2×#13711yescharacteristic
413C22×C7#57611yescharacteristic
414C22×C7#57711yescharacteristic
415C2×D7—42no—
416C2×D7—42no—
417C2×D7—42no—
418C2×D7—81no—
419C2×D7—81no—
420C2×D7—81no—
421C2×D7—81no—
422C4×C7—22no—
423C4×C7—24no—
424C4×C7—22no—
425C4×C7—41no—
426C4×C7—42no—
427C4×C7—41no—
428C4×C7—41no—
429C4×C7—41no—
430C4×C7—81no—
431C4×C7—81no—
432C4×C7C2×C22⋊Q811yescharacteristic
433C4×C7#53911yescharacteristic
434C4×C7#54711yescharacteristic
435C4×C7#55411yescharacteristic
436Dic7—42no—
437Dic7—81no—
438Dic7—81no—
439C24—141no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8#115712yes—
444C2×Q8D4×D712yes—
445C2×Q8Q8×D712yes—
446C2×D4—72no—
447C2×D4—141no—
448C2×D4—141no—
449C2×D4—141no—
450C2×D4—141no—
451C2×D4—141no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—141no—
457C22×C4—141no—
458C22×C4—141no—
459C22×C4—282no—
460C22×C4—282no—
461C22×C4—561no—
462C22×C4C2×C22⋊D711yescharacteristic
463C22×C4C2×C22⋊D711yescharacteristic
464C22×C4C2×C22⋊D711yescharacteristic
465C22×C4C2×C22⋊D711yescharacteristic
466C22×C4C2×C22⋊D711yescharacteristic
467C22×C4C2×C22⋊D711yescharacteristic
468C22×C4C23×D711yescharacteristic
469SD16—148no—
470C2×C8—72no—
471C2×C8—72no—
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—
482C4⋊C4—24no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—72no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4—141no—
498C4⋊C4—141no—
499C4⋊C4—141no—
500C4⋊C4—141no—
501C4⋊C4—141no—
502C4⋊C4—282no—
503C4⋊C4—282no—
504C4⋊C4—561no—
505C4⋊C4—561no—
506C4⋊C4#115712yes—
507C22⋊C4—282no—
508C22⋊C4—282no—
509C22⋊C4—561no—
510C22⋊C4—561no—
511C22⋊C4—561no—
512C42—24no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—42no—
520C42—42no—
521C2×C7#244911yescharacteristic
522C2×C7#310811yescharacteristic
523C2×C7#311911yescharacteristic
524C2×C7#326611yescharacteristic
525C2×C7#328711yescharacteristic
526C2×C7#338111yescharacteristic
527C2×C7#338511yescharacteristic
528D7—82no—
529C23—142no—
530C23—281no—
531C23—281no—
532C23—281no—
533C23—281no—
534C23—281no—
535C23—281no—
536C23C22×C22⋊D711yescharacteristic
537Q8—22no—
538Q8—22no—
539Q8—22no—
540Q8#645914yes—
541D4—142no—
542D4—142no—
543D4—281no—
544D4—281no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—142no—
574C2×C4—281no—
575C2×C4—281no—
576C2×C4—281no—
577C2×C4—281no—
578C2×C4—281no—
579C2×C4—281no—
580C2×C4—281no—
581C2×C4—281no—
582C2×C4—564no—
583C2×C4#650512yes—
584C2×C4#651312yes—
585C2×C4C2×#115711yescharacteristic
586C2×C4C2×#115711yescharacteristic
587C2×C4C2×D4×D711yescharacteristic
588C2×C4#654811yescharacteristic
589C2×C4C2×Q8×D711yescharacteristic
590C2×C4#655111yescharacteristic
591C8—142no—
592C8—142no—
593C8—281no—
594C8—281no—
595C7#2637911yescharacteristic, complemented, Sylow
596C22—282no—
597C22—282no—
598C22—282no—
599C22—561no—
600C22—561no—
601C22—561no—
602C22—561no—
603C22#9048211yescharacteristic
604C22D4×C22⋊D711yescharacteristic
605C22C2×#650511yescharacteristic
606C22Q8×C22⋊D711yescharacteristic
607C22C2×#651311yescharacteristic
608C22#9052611yescharacteristic
609C22#9052811yescharacteristic
610C4—22no—
611C4—24no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—42no—
618C4—81no—
619C4—81no—
620C4—282no—
621C4—561no—
622C4—561no—
623C4#9019811yescharacteristic
624C4C2×#645911yescharacteristic
625C4#9020211yescharacteristic
626C4#9020611yescharacteristic
627C2—562no—
628C2#1173961811yescharacteristic
629C2#1173988811yescharacteristic
630C2#1174001311yescharacteristic
631C2#1174100411yescharacteristic
632C2#1174103011yescharacteristic
633C2#1174113811yescharacteristic
634C2#1174115111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×Q8×C4⋊C4C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterQ8×C4⋊C4D7
hypocenterC7#26379
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C7×Q8×C4⋊C4C2semidirect
2. C2×#89794C2semidirect
7. #11729382C2semidirect
8. #11729382C2semidirect
11. #11727373C2semidirect
12. #11727360C2semidirect
14. #11727324C2semidirect
15. #11727236C2semidirect
134. Q8×C4⋊C4D7semidirect
595. C7#26379semidirect

Maximal subgroups

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

subgroupindex
C7×Q8×C4⋊C42
C2×#897942
C2×C4×#11432
#117311222
#117293872
#117293822
#117273842
#117273802
#117273732
#117273602
#117273402
#117273242
#117272362
#263797