Finite Group Databasebeta

← #13414205

Subgroups — #13414205

Order 1792.

794 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2446C211yesmaximal, characteristic
2C2×#89862C211yesmaximal, characteristic
3C2×#89802C211yesmaximal, characteristic
4C4⋊C4×Dic14C211yesmaximal, characteristic
5#11729535C211yesmaximal, characteristic
6#11729383C211yesmaximal, characteristic
7#11727444C211yesmaximal, characteristic
8#11727444C211yesmaximal, characteristic
9#11727444C211yesmaximal, characteristic
10#11727439C211yesmaximal, characteristic
11#11727429C211yesmaximal, characteristic
12#11727424C211yesmaximal, characteristic
13#11727386C211yesmaximal, characteristic
14#11727378C211yesmaximal, characteristic
15#11727237C211yesmaximal, characteristic
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C22×#1144C2211yescharacteristic
19C22×#1144C2211yescharacteristic
20C2×C4×Dic14C2211yescharacteristic
21C2×C4×Dic14C2211yescharacteristic
22C2×C4×Dic14C2211yescharacteristic
23C7×#400—21no—
24C7×#398—21no—
25C7×#391C2211yescharacteristic
26C7×#391C2211yescharacteristic
27C7×#391C2211yescharacteristic
28C7×#389C2211yescharacteristic
29C7×#387—21no—
30C7×#387—21no—
31C4×C7×C4⋊C4C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38#89862—24no—
39#89802—24no—
40#89748—21no—
41C4⋊C4×Dic7—21no—
42C2×#6384C2211yescharacteristic
43C2×#6384C2211yescharacteristic
44C2×#6382C2211yescharacteristic
45C2×#6382C2211yescharacteristic
46#89707C2211yescharacteristic
47#89700C2211yescharacteristic
48#89700C2211yescharacteristic
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50C2×#6377C2211yescharacteristic
51#89419—21no—
52#89419—21no—
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89319C2211yescharacteristic
58#89319C2211yescharacteristic
59#89319C2211yescharacteristic
60#89319C2211yescharacteristic
61#26187—71nomaximal, Sylow
62C22×C7×Q8C2311yescharacteristic
63C22×C7×Q8C2311yescharacteristic
64C22×Dic14C2311yescharacteristic
65C7×C4⋊Q8—22no—
66C7×C4⋊Q8—41no—
67C4×C7×Q8—22no—
68C4×C7×Q8—41no—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4D411yescharacteristic
74C2×C7×C4⋊C4D411yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C4⋊C4C2311yescharacteristic
77C2×C42×C7—21no—
78C2×C42×C7C2311yescharacteristic
79C2×C42×C7C2311yescharacteristic
80C2×C42×C7C2311yescharacteristic
81C2×#1144—22no—
82C2×#1144—22no—
83C2×#1144—22no—
84C2×#1144—22no—
85C2×#1144—22no—
86C2×#1144D414yes—
87C2×C4⋊Dic7—21no—
88C2×C4⋊Dic7—21no—
89C2×C4⋊Dic7C2311yescharacteristic
90C2×C4⋊Dic7C2311yescharacteristic
91C2×C4⋊Dic7C2311yescharacteristic
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×Dic7⋊C4—21no—
96C2×Dic7⋊C4—21no—
97C2×C4×Dic7—21no—
98C2×C4×Dic7—21no—
99C2×C4×Dic7—21no—
100C22×C7⋊C8C2311yescharacteristic
101C22×C7⋊C8C2311yescharacteristic
102C22×C7⋊C8C2311yescharacteristic
103C22×C7⋊C8C2311yescharacteristic
104C4×Dic14—22no—
105C4×Dic14—22no—
106C4×Dic14—22no—
107C4×Dic14—22no—
108C4×Dic14—41no—
109C4×Dic14—41no—
110C7×#95—21no—
111C7×#95—21no—
112C7×#95—21no—
113C7×#95—21no—
114C7×#95—21no—
115C7×#95—21no—
116C7×#95—21no—
117C7×#95D411yescharacteristic
118C7×#95D411yescharacteristic
119#6409—22no—
120#6409—22no—
121#6409—22no—
122#6409—22no—
123#6409—22no—
124#6409—41no—
125C7⋊#95—21no—
126C7⋊#95—21no—
127#6384—22no—
128#6384—22no—
129#6382—22no—
130#6382—41no—
131C4⋊(C7⋊C8)—22no—
132#6377—22no—
133C2×#462—71no—
134C2×#441—71no—
135#2446D711yescharacteristic
136Q8×C4⋊C4—71no—
137#2096—71no—
138#2088—71no—
139#2072—71no—
140#2043—71no—
141#1935—71no—
142#1917—71no—
143#1878—71no—
144#1878—71no—
145#1878—71no—
146#1865—71no—
147#1865—71no—
148C2×C7×Q8—21no—
149C2×C7×Q8—21no—
150C2×C7×Q8—21no—
151C2×C7×Q8—21no—
152C2×C7×Q8—21no—
153C2×C7×Q8—21no—
154C2×C7×Q8—21no—
155C2×C7×Q8—21no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8C2×D412yes—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2×D411yescharacteristic
168C22×C4×C7C2×D411yescharacteristic
169C22×C4×C7C2×D411yescharacteristic
170C22×C4×C7C2411yescharacteristic
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C2×Dic14—21no—
176C2×Dic14—21no—
177C2×Dic14—21no—
178C2×Dic14C2×D412yes—
179C2×Dic14#4112yes—
180C2×Dic14#4112yes—
181C7×C4⋊C4—22no—
182C7×C4⋊C4—22no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4—21no—
186C7×C4⋊C4—21no—
187C7×C4⋊C4—42no—
188C7×C4⋊C4—42no—
189C7×C4⋊C4—42no—
190C7×C4⋊C4—42no—
191C42×C7—21no—
192C42×C7—21no—
193C42×C7—21no—
194C42×C7—21no—
195C42×C7—21no—
196C42×C7—21no—
197C42×C7—42no—
198#1144—28no—
199#1144—44no—
200C4⋊Dic7—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7—21no—
204C4⋊Dic7—21no—
205C4⋊Dic7—42no—
206C4⋊Dic7—81no—
207C4⋊Dic7#4112yes—
208Dic7⋊C4—24no—
209Dic7⋊C4—42no—
210Dic7⋊C4—42no—
211Dic7⋊C4—81no—
212Dic7⋊C4—81no—
213C4×Dic7—24no—
214C4×Dic7—42no—
215C4×Dic7—42no—
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⋊C8—21no—
227C2×C7⋊C8C2×D412yes—
228C22×Q16—71no—
229C22×Q16—71no—
230C2×C4⋊Q8C2×D711yescharacteristic
231C2×C4×Q8—71no—
232C2×C4×Q8—71no—
233C2×C4×Q8—71no—
234C2×C4×Q8C2×D711yescharacteristic
235#462—144no—
236#441—144no—
237C2×#106—71no—
238C2×#106—71no—
239C2×C4⋊C8—71no—
240C2×#103—71no—
241C2×#103—71no—
242C2×#103—71no—
243C2×#103—71no—
244C2×#103—71no—
245C2×#103—71no—
246C2×#103—71no—
247C2×#103—71no—
248C2×#97—71no—
249#400—21no—
250#398—21no—
251#391C2×D711yescharacteristic
252#391C2×D711yescharacteristic
253#391C2×D711yescharacteristic
254#389—71no—
255#389—71no—
256#389—141no—
257#389—141no—
258#389C2×D711yescharacteristic
259#387—21no—
260#387—21no—
261#384—71no—
262#384—141no—
263C4×C4⋊C4—141no—
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
274C7×Q8—22no—
275C7×Q8—22no—
276C7×Q8—41no—
277C7×Q8—41no—
278C7×Q8—41no—
279C7×Q8—41no—
280C7×Q8—41no—
281C7×Q8—41no—
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—22no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—21no—
294C2×C4×C7—21no—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
302C2×C4×C7—41no—
303C2×C4×C7—41no—
304C2×C4×C7—41no—
305C2×C4×C7—41no—
306C2×C4×C7—41no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7#13712yes—
311C2×C4×C7#13712yes—
312C2×C4×C7C22×D411yescharacteristic
313C2×C4×C7C2×#4111yescharacteristic
314C2×C4×C7C2×#4111yescharacteristic
315C2×C4×C7C2×#4111yescharacteristic
316C2×C4×C7H(5,𝔽2)11yescharacteristic
317C2×C4×C72−1+411yescharacteristic
318C2×Dic7—22no—
319C2×Dic7—22no—
320C2×Dic7—22no—
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—
330Dic14—22no—
331Dic14—22no—
332Dic14—22no—
333Dic14#12314yes—
334C7⋊C8—22no—
335C7⋊C8—41no—
336C7⋊C8—41no—
337C7⋊C8—41no—
338C22×Q8—71no—
339C22×Q8C22×D711yescharacteristic
340C22×Q8C22×D711yescharacteristic
341C2×Q16—74no—
342C2×Q16—142no—
343C2×Q16—142no—
344C2×Q16—142no—
345C2×Q16—142no—
346C2×Q16—142no—
347C22×C8—71no—
348C22×C8—71no—
349C22×C8—71no—
350C22×C8—71no—
351C4⋊Q8—22no—
352C4⋊Q8—41no—
353C4×Q8—22no—
354C4×Q8—41no—
355C4×Q8—142no—
356C4×Q8—142no—
357C4×Q8—142no—
358C4×Q8—142no—
359C4×Q8—281no—
360C4×Q8—281no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—71no—
366C2×C4⋊C4—71no—
367C2×C4⋊C4—71no—
368C2×C4⋊C4—141no—
369C2×C4⋊C4—141no—
370C2×C4⋊C4—141no—
371C2×C4⋊C4—141no—
372C2×C4⋊C4—141no—
373C2×C4⋊C4—141no—
374C2×C4⋊C4—141no—
375C2×C4⋊C4C22⋊D711yescharacteristic
376C2×C4⋊C4C22⋊D711yescharacteristic
377C2×C4⋊C4C22×D711yescharacteristic
378C2×C4⋊C4C22×D711yescharacteristic
379C2×C42—21no—
380C2×C42—141no—
381C2×C42—141no—
382C2×C42—141no—
383C2×C42C22×D711yescharacteristic
384C2×C42C22×D711yescharacteristic
385C2×C42C22×D711yescharacteristic
386#106—142no—
387#106—281no—
388C4⋊C8—142no—
389#103—142no—
390#103—142no—
391#103—142no—
392#103—142no—
393#103—142no—
394#103—142no—
395#103—142no—
396#103—281no—
397#97—142no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—141no—
406#95—141no—
407#95C22⋊D711yescharacteristic
408#95C22⋊D711yescharacteristic
409C22×C7#52511yescharacteristic
410C22×C7D4211yescharacteristic
411C22×C7#54811yescharacteristic
412C22×C7C2×#13711yescharacteristic
413C22×C7C2×#13711yescharacteristic
414C22×C7#57711yescharacteristic
415C22×C7#57811yescharacteristic
416C4×C7—22no—
417C4×C7—22no—
418C4×C7—41no—
419C4×C7—42no—
420C4×C7—41no—
421C4×C7—41no—
422C4×C7—41no—
423C4×C7—81no—
424C4×C7—81no—
425C4×C7—81no—
426C4×C7C2×#12311yescharacteristic
427C4×C7#53911yescharacteristic
428C4×C7#54711yescharacteristic
429C4×C7#55311yescharacteristic
430Dic7—24no—
431Dic7—42no—
432Dic7—81no—
433Dic7—81no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—72no—
446C2×Q8—72no—
447C2×Q8—72no—
448C2×Q8—141no—
449C2×Q8—141no—
450C2×Q8—141no—
451C2×Q8D4×D712yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
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
467Q16—148no—
468Q16—284no—
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—
480C2×C8—141no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—72no—
492C4⋊C4—144no—
493C4⋊C4—141no—
494C4⋊C4—141no—
495C4⋊C4—141no—
496C4⋊C4—141no—
497C4⋊C4—141no—
498C4⋊C4—282no—
499C4⋊C4—282no—
500C4⋊C4—282no—
501C4⋊C4—561no—
502C4⋊C4—561no—
503C4⋊C4—561no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—42no—
511C42—144no—
512C42—282no—
513C42—282no—
514C2×C7#244311yescharacteristic
515C2×C7#311311yescharacteristic
516C2×C7#312011yescharacteristic
517C2×C7#327011yescharacteristic
518C2×C7#327811yescharacteristic
519C2×C7#336911yescharacteristic
520C2×C7#337411yescharacteristic
521C23C22×C22⋊D711yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—74no—
531Q8—142no—
532Q8—142no—
533Q8—142no—
534C2×C4—21no—
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—41no—
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—41no—
561C2×C4—41no—
562C2×C4—142no—
563C2×C4—142no—
564C2×C4—142no—
565C2×C4—142no—
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×C4#650512yes—
575C2×C4#651412yes—
576C2×C4C2×D4×D711yescharacteristic
577C2×C4#654811yescharacteristic
578C2×C4D7×#4111yescharacteristic
579C2×C4D7×#4111yescharacteristic
580C2×C4D7×#4111yescharacteristic
581C2×C4#655411yescharacteristic
582C8—142no—
583C8—281no—
584C8—281no—
585C8—281no—
586C7#2618711yescharacteristic, complemented, Sylow
587C22D4×C22⋊D711yescharacteristic
588C22C2×#650511yescharacteristic
589C22C2×#651411yescharacteristic
590C22#9051911yescharacteristic
591C22#9052211yescharacteristic
592C22#9052811yescharacteristic
593C22#9052911yescharacteristic
594C4—22no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—144no—
605C4—282no—
606C4—561no—
607C4—561no—
608C4D7×#12311yescharacteristic
609C4#9034611yescharacteristic
610C4#9035111yescharacteristic
611C4#9035211yescharacteristic
612C2#1174034211yescharacteristic
613C2#1174081411yescharacteristic
614C2#1174089111yescharacteristic
615C2#1174099111yescharacteristic
616C2#1174101111yescharacteristic
617C2#1174112211yescharacteristic
618C2#1174114411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2446C2
socle, prime radicalC23×C7C22×D4
hypercenter#2446D7
hypocenterC7#26187
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2446

Complements

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

NH ≅ G/Ntype
586. C7#26187semidirect

Maximal subgroups

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

subgroupindex
C7×#24462
C2×#898622
C2×#898022
C4⋊C4×Dic142
#117295352
#117293832
#117274442
#117274392
#117274292
#117274242
#117273862
#117273782
#117272372
#261877