Finite Group Databasebeta

← C4×#90389 #13512907

Subgroups — C4×#90389 #13512907

Order 1792.

2518 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90389C211yesmaximal, characteristic
2C4×C7×#125C211yesmaximal, characteristic, complemented
3#11740468C211yesmaximal, characteristic, complemented
4#11733643C212yesmaximal, complemented
5#11733414C212yesmaximal, complemented
6#11732401C214yesmaximal, complemented
7#11732397C214yesmaximal, complemented
8#11731669C211yesmaximal, characteristic, complemented
9#11731598C211yesmaximal, characteristic, complemented
10C4×#6457C214yesmaximal, complemented
11C4×#6458C212yesmaximal, complemented
12C4×#6458C214yesmaximal, complemented
13C4×#6456C212yesmaximal, complemented
14C4×#6437C211yesmaximal, characteristic, complemented
15C4×#6435C211yesmaximal, characteristic, complemented
16C2×C7×#125C2211yescharacteristic
17#90389C4116yesdirect product factor
18C2×#6458C2212yes—
19C2×#6458C2214yes—
20C2×#6457C2214yes—
21C2×#6456C2212yes—
22C2×#6456C2212yes—
23C2×#6437C2211yescharacteristic
24C2×C4×D28C2212yes—
25C2×C4×D28C2214yes—
26C2×C4×D28C2214yes—
27C2×#6435C2211yescharacteristic
28C2×#6435C2211yescharacteristic
29C2×C42×D7C2211yescharacteristic
30C2×C42×D7C2214yes—
31C7×#389C2212yes—
32C7×#387C2214yes—
33C7×#382C2211yescharacteristic
34C4×C7×C4⋊C4C2214yes—
35C4×C7×C4⋊C4C2212yes—
36C43×C7C2211yescharacteristic
37#89762C2214yes—
38#89761C2214yes—
39#89760C2214yes—
40#89760C2212yes—
41#89759C2212yes—
42#89759C2214yes—
43#89757C2212yes—
44#89757C2214yes—
45#89753C2214yes—
46C4⋊C4×Dic7C2212yes—
47C4⋊C4×Dic7C2212yes—
48#89711C2212yes—
49#89711C2214yes—
50C4×(C2×D7)⋊C4C2212yes—
51C4×(C2×D7)⋊C4C2214yes—
52C4×(C2×D7)⋊C4C2214yes—
53C4×(C2×D7)⋊C4C2212yes—
54#89707C2211yescharacteristic
55#89704C2211yescharacteristic
56#89704C2211yescharacteristic
57C4×Dic7⋊C4C2212yes—
58C4×Dic7⋊C4C2212yes—
59C42×Dic7C2211yescharacteristic
60#89442C2214yes—
61#89442C2214yes—
62#89442C2214yes—
63#89441C2214yes—
64#89438C2214yes—
65#89438C2214yes—
66#89437C2214yes—
67#89437C2214yes—
68#89437C2214yes—
69#89437C2214yes—
70#89436C2214yes—
71#89427C2214yes—
72C4×#540—71nomaximal, Sylow
73C22×D28C2312yes—
74C22×D28C2314yes—
75C22×D28C2314yes—
76C22×C4×D7C2311yescharacteristic
77C22×C4×D7C2314yes—
78C22×C4×D7C2311yescharacteristic
79C22×C4×D7C2314yes—
80C22×C4×D7C2311yescharacteristic
81C22×C4×D7C2314yes—
82C7×#125C2×C418yescomplemented
83C2×C7×C4⋊C4C2312yes—
84C2×C7×C4⋊C4C2314yes—
85C2×C7×C4⋊C4C2312yes—
86C2×C7×C4⋊C4C2314yes—
87C2×C42×C7C2314yes—
88C2×C42×C7C2311yescharacteristic
89C2×C42×C7C2312yes—
90C2×C42×C7C2312yes—
91C2×C42×C7C2311yescharacteristic
92C2×C42×C7C2311yescharacteristic
93C2×(C2×D7)⋊C4C2312yes—
94C2×(C2×D7)⋊C4C2314yes—
95C2×(C2×D7)⋊C4C2314yes—
96C2×(C2×D7)⋊C4C2314yes—
97C2×(C2×D7)⋊C4C2314yes—
98C2×(C2×D7)⋊C4C2314yes—
99C2×(C2×D7)⋊C4C2314yes—
100C2×(C2×D7)⋊C4C2314yes—
101C2×(C2×D7)⋊C4C2312yes—
102C2×(C2×D7)⋊C4C2314yes—
103C2×(C2×D7)⋊C4C2314yes—
104C2×C4⋊Dic7C2312yes—
105C2×C4⋊Dic7C2314yes—
106C2×C4⋊Dic7C2314yes—
107C2×Dic7⋊C4C2312yes—
108C2×Dic7⋊C4C2312yes—
109C2×C4×Dic7C2312yes—
110C2×C4×Dic7C2311yescharacteristic
111C2×C4×Dic7C2311yescharacteristic
112C2×C4×Dic7C2311yescharacteristic
113C2×C4×Dic7C2314yes—
114C2×C4×Dic7C2314yes—
115C2×C4×Dic7C2312yes—
116C2×C4×Dic7C2311yescharacteristic
117C2×C4×Dic7C2311yescharacteristic
118#6458C2×C4132yescomplemented
119#6458C2×C4116yescomplemented
120#6457C2×C4132yescomplemented
121#6456—28no—
122#6456C2×C4116yescomplemented
123#6437C2×C418yescomplemented
124C4×D28—28no—
125C4×D28—48no—
126C4×D28—48no—
127#6435—24no—
128#6435C2×C418yescomplemented
129C42×D7—24no—
130C42×D7—48no—
131C7×#95C2314yes—
132C7×#95C2314yes—
133C7×#95C2314yes—
134C7⋊#95C2314yes—
135C7⋊#95C2314yes—
136C7⋊#95C2312yes—
137C7⋊#95C2314yes—
138C7⋊#95C2312yes—
139C7⋊#95C2312yes—
140C7⋊#95C2314yes—
141C7⋊#95C2312yes—
142C2×#540—71no—
143#2335—74no—
144#2333—74no—
145#2330—71no—
146#2328—71no—
147#2324—72no—
148#2319—72no—
149#2314—71no—
150C4×#127—71no—
151C4×#125D711yescharacteristic, complemented
152C4×#123—74no—
153C4×#121—72no—
154C4×#121—74no—
155C42×D4—72no—
156C4×#117—71no—
157C23×D7C2411yescharacteristic
158C23×D7C2414yes—
159C22×C4×C7C2414yes—
160C22×C4×C7C2412yes—
161C22×C4×C7C2414yes—
162C22×C4×C7C2412yes—
163C22×C4×C7C2411yescharacteristic
164C22×C4×C7C2411yescharacteristic
165C22×C4×C7C2411yescharacteristic
166C22×Dic7C2411yescharacteristic
167C22×Dic7C2411yescharacteristic
168C22×Dic7C2414yes—
169C22×Dic7C2412yes—
170C22×Dic7C2411yescharacteristic
171C22×Dic7C2412yes—
172C2×D28—24no—
173C2×D28—24no—
174C2×D28—44no—
175C2×D28—44no—
176C2×D28—44no—
177C2×D28—44no—
178C2×D28C22×C418yes—
179C2×D28C22×C4116yes—
180C2×D28C22×C4116yes—
181C2×C4×D7—22no—
182C2×C4×D7—22no—
183C2×C4×D7—22no—
184C2×C4×D7—22no—
185C2×C4×D7—28no—
186C2×C4×D7—28no—
187C2×C4×D7—24no—
188C2×C4×D7—28no—
189C2×C4×D7—28no—
190C2×C4×D7—44no—
191C2×C4×D7—44no—
192C2×C4×D7—44no—
193C2×C4×D7—44no—
194C2×C4×D7—42no—
195C2×C4×D7C22×C414yes—
196C2×C4×D7C22×C4116yes—
197C7×C4⋊C4—24no—
198C7×C4⋊C4—44no—
199C7×C4⋊C4C22×C418yes—
200C7×C4⋊C4C22×C4116yes—
201C42×C7—22no—
202C42×C7—28no—
203C42×C7—24no—
204C42×C7—42no—
205C42×C7C22×C414yes—
206C42×C7#4114yes—
207(C2×D7)⋊C4—28no—
208(C2×D7)⋊C4—24no—
209(C2×D7)⋊C4—28no—
210(C2×D7)⋊C4—44no—
211(C2×D7)⋊C4—44no—
212(C2×D7)⋊C4—44no—
213(C2×D7)⋊C4—44no—
214(C2×D7)⋊C4—44no—
215(C2×D7)⋊C4C22×C418yes—
216(C2×D7)⋊C4C22×C4116yes—
217(C2×D7)⋊C4C22×C4116yes—
218C4⋊Dic7—24no—
219C4⋊Dic7—44no—
220C4⋊Dic7—44no—
221Dic7⋊C4—24no—
222Dic7⋊C4C22×C418yes—
223C4×Dic7—22no—
224C4×Dic7—22no—
225C4×Dic7—22no—
226C4×Dic7—24no—
227C4×Dic7—44no—
228C4×Dic7—44no—
229C4×Dic7—42no—
230C4×Dic7C22×C414yes—
231C4×Dic7#4114yes—
232#540—716no—
233C2×#127—71no—
234C2×#125C2×D711yescharacteristic
235C2×#123—74no—
236C2×#121—72no—
237C2×#121—74no—
238C2×C4×D4—72no—
239C2×C4×D4—72no—
240C2×C4×D4—72no—
241C2×C4×D4—74no—
242C2×C4×D4—74no—
243C2×#117—71no—
244C2×#117—71no—
245C22×C42—71no—
246C22×C42—74no—
247#390—72no—
248#390—74no—
249#390—72no—
250#390—74no—
251#389—72no—
252#389—74no—
253#389C2×D712yes—
254#388—74no—
255#388—74no—
256#388—74no—
257#388—74no—
258#388—74no—
259#387—74no—
260#387—74no—
261#387C2×D714yes—
262#386—74no—
263#386—74no—
264#386—74no—
265#386—74no—
266#385—74no—
267#384—71no—
268#382C2×D711yescharacteristic
269#381—74no—
270#380—72no—
271#380—74no—
272C4×C4⋊C4—72no—
273C4×C4⋊C4—72no—
274C4×C4⋊C4—72no—
275C4×C4⋊C4—72no—
276C4×C4⋊C4C2×D712yes—
277C4×C4⋊C4C2×D714yes—
278C4×C22⋊C4—72no—
279C4×C22⋊C4—72no—
280C4×C22⋊C4—74no—
281C4×C22⋊C4—74no—
282C4×C22⋊C4—74no—
283C4×C22⋊C4—74no—
284#376—71no—
285#376—71no—
286C43—71no—
287C43C2×D711yescharacteristic
288C23×C7C2511yescharacteristic
289C22×D7—21no—
290C22×D7—24no—
291C22×D7—24no—
292C22×D7—21no—
293C22×D7—24no—
294C22×D7—22no—
295C22×D7—24no—
296C22×D7—24no—
297C22×D7—22no—
298C22×D7—24no—
299C22×D7C23×C412yes—
300C22×D7C23×C418yes—
301C2×C4×C7—24no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—24no—
306C2×C4×C7—22no—
307C2×C4×C7—24no—
308C2×C4×C7—24no—
309C2×C4×C7—22no—
310C2×C4×C7—24no—
311C2×C4×C7—22no—
312C2×C4×C7C23×C414yes—
313C2×C4×C7C23×C418yes—
314C2×C4×C7C23×C412yes—
315C2×C4×C7C2×#4112yes—
316C2×C4×C7C2×#4112yes—
317C2×C4×C7C2×#4112yes—
318C2×C4×C7C2×#4112yes—
319C2×C4×C7H(5,𝔽2)14yes—
320C2×Dic7—21no—
321C2×Dic7—21no—
322C2×Dic7—22no—
323C2×Dic7—22no—
324C2×Dic7—22no—
325C2×Dic7—22no—
326C2×Dic7—21no—
327C2×Dic7—21no—
328C2×Dic7—24no—
329C2×Dic7—24no—
330C2×Dic7—22no—
331C2×Dic7—24no—
332C2×Dic7—22no—
333C2×Dic7C23×C414yes—
334C2×Dic7C23×C412yes—
335C2×Dic7C2×#4114yes—
336D28—216no—
337D28—416no—
338D28—416no—
339C4×D7—28no—
340C4×D7—416no—
341C4×D7—416no—
342C4×D7—44no—
343C4×D7—44no—
344C4×D7—416no—
345C22×D4—72no—
346C22×D4—74no—
347C22×D4—74no—
348C23×C4—71no—
349C23×C4—74no—
350C23×C4—71no—
351C23×C4—74no—
352C23×C4—74no—
353C23×C4—71no—
354#127—78no—
355#125C4×D718yescomplemented
356#123—732no—
357#121—732no—
358#121—716no—
359C4×D4—716no—
360C4×D4—148no—
361C4×D4—148no—
362C4×D4—288no—
363C4×D4—288no—
364#117—78no—
365#117—144no—
366C2×C4⋊C4—72no—
367C2×C4⋊C4—72no—
368C2×C4⋊C4—72no—
369C2×C4⋊C4—74no—
370C2×C4⋊C4—74no—
371C2×C4⋊C4C22×D712yes—
372C2×C4⋊C4C22×D714yes—
373C2×C4⋊C4C22×D712yes—
374C2×C4⋊C4C22×D714yes—
375C2×C22⋊C4—72no—
376C2×C22⋊C4—74no—
377C2×C22⋊C4—74no—
378C2×C22⋊C4—72no—
379C2×C22⋊C4—74no—
380C2×C22⋊C4—74no—
381C2×C22⋊C4—74no—
382C2×C22⋊C4—74no—
383C2×C22⋊C4—74no—
384C2×C22⋊C4—74no—
385C2×C22⋊C4—74no—
386C2×C42—71no—
387C2×C42—71no—
388C2×C42—71no—
389C2×C42—71no—
390C2×C42—72no—
391C2×C42—71no—
392C2×C42—72no—
393C2×C42—74no—
394C2×C42—74no—
395C2×C42—144no—
396C2×C42—288no—
397C2×C42C22×D711yescharacteristic
398C2×C42C22×D712yes—
399C2×C42C22×D714yes—
400C2×C42C22×D712yes—
401C2×C42C22×D711yescharacteristic
402C2×C42C22×D711yescharacteristic
403#95—72no—
404#95—72no—
405#95—72no—
406#95—72no—
407#95—74no—
408#95—74no—
409#95—74no—
410#95—74no—
411#95C22×D714yes—
412#95C22×D714yes—
413#95C22×D714yes—
414C22×C7C24×C411yescharacteristic
415C22×C7C22×#4111yescharacteristic
416C22×C7C22×#4111yescharacteristic
417C22×C7C2×H(5,𝔽2)12yes—
418C22×C7#58512yes—
419C2×D7—22no—
420C2×D7—28no—
421C2×D7—28no—
422C2×D7—24no—
423C2×D7—28no—
424C2×D7—44no—
425C2×D7—41no—
426C2×D7—41no—
427C2×D7—44no—
428C2×D7—44no—
429C2×D7—42no—
430C2×D7—44no—
431C4×C7—28no—
432C4×C7—24no—
433C4×C7—22no—
434C4×C7—44no—
435C4×C7—42no—
436C4×C7C4×#4114yes—
437C4×C7#54014yescomplemented
438Dic7—22no—
439Dic7—24no—
440Dic7—24no—
441Dic7—41no—
442Dic7—44no—
443Dic7—41no—
444C24—74no—
445C24—71no—
446C2×D4—78no—
447C2×D4—716no—
448C2×D4—716no—
449C2×D4—144no—
450C2×D4—144no—
451C2×D4—284no—
452C2×D4—284no—
453C2×D4—284no—
454C2×D4—284no—
455C22×C4—72no—
456C22×C4—72no—
457C22×C4—71no—
458C22×C4—74no—
459C22×C4—716no—
460C22×C4—71no—
461C22×C4—71no—
462C22×C4—74no—
463C22×C4—148no—
464C22×C4—142no—
465C22×C4—142no—
466C22×C4—142no—
467C22×C4—142no—
468C22×C4—148no—
469C22×C4—148no—
470C22×C4—144no—
471C22×C4—148no—
472C22×C4—284no—
473C22×C4—284no—
474C22×C4—282no—
475C22×C4—284no—
476C22×C4—284no—
477C22×C4C23×D714yes—
478C22×C4C23×D712yes—
479C22×C4C23×D714yes—
480C22×C4C23×D712yes—
481C22×C4C23×D711yescharacteristic
482C22×C4C23×D711yescharacteristic
483C22×C4C23×D711yescharacteristic
484C4⋊C4—24no—
485C4⋊C4—44no—
486C4⋊C4—78no—
487C4⋊C4—144no—
488C4⋊C4—144no—
489C4⋊C4—284no—
490C4⋊C4—284no—
491C4⋊C4C2×C4×D718yes—
492C4⋊C4C2×C4×D7116yes—
493C22⋊C4—78no—
494C22⋊C4—716no—
495C22⋊C4—716no—
496C22⋊C4—144no—
497C22⋊C4—148no—
498C22⋊C4—148no—
499C22⋊C4—284no—
500C22⋊C4—284no—
501C22⋊C4—284no—
502C22⋊C4—284no—
503C22⋊C4—284no—
504C42—22no—
505C42—28no—
506C42—24no—
507C42—42no—
508C42—74no—
509C42—74no—
510C42—142no—
511C42—142no—
512C42—142no—
513C42—144no—
514C42—282no—
515C42—284no—
516C42—284no—
517C42C2×C4×D714yes—
518C42#116114yes—
519C2×C7C2×C4×#4111yescharacteristic
520C2×C7C4×H(5,𝔽2)12yes—
521C2×C7C2×#54011yescharacteristic
522C2×C7#345511yescharacteristic
523C2×C7#346012yes—
524D7—42no—
525D7—48no—
526C23—72no—
527C23—78no—
528C23—144no—
529C23—141no—
530C23—141no—
531C23—144no—
532C23—144no—
533C23—142no—
534C23—144no—
535C23—144no—
536C23—142no—
537C23—144no—
538C23C24×D711yescharacteristic
539D4—1416no—
540D4—2816no—
541D4—2816no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—74no—
554C2×C4—72no—
555C2×C4—74no—
556C2×C4—141no—
557C2×C4—141no—
558C2×C4—142no—
559C2×C4—142no—
560C2×C4—142no—
561C2×C4—142no—
562C2×C4—148no—
563C2×C4—141no—
564C2×C4—141no—
565C2×C4—144no—
566C2×C4—144no—
567C2×C4—142no—
568C2×C4—144no—
569C2×C4—142no—
570C2×C4—2816no—
571C2×C4—284no—
572C2×C4—2816no—
573C2×C4—284no—
574C2×C4—2816no—
575C2×C4C22×C4×D714yes—
576C2×C4C22×C4×D718yes—
577C2×C4C22×C4×D712yes—
578C2×C4C2×#116112yes—
579C2×C4C2×#116112yes—
580C2×C4C2×#116112yes—
581C2×C4D7×#4112yes—
582C2×C4#655314yes—
583C7C4×#54011yescharacteristic, complemented, Sylow
584C22—142no—
585C22—148no—
586C22—148no—
587C22—144no—
588C22—148no—
589C22—281no—
590C22—284no—
591C22—284no—
592C22—281no—
593C22—284no—
594C22—282no—
595C22—284no—
596C22C23×C4×D711yescharacteristic
597C22C22×#116111yescharacteristic
598C22C2×D7×#4111yescharacteristic
599C22C2×#655312yes—
600C22#9061612yes—
601C4—22no—
602C4—28no—
603C4—24no—
604C4—44no—
605C4—42no—
606C4—142no—
607C4—144no—
608C4—144no—
609C4—281no—
610C4—281no—
611C4—284no—
612C4C4×#116114yes—
613C4#9038914yesdirect product factor
614C2—282no—
615C2—288no—
616C2C2×C4×#116111yescharacteristic
617C2C4×#655312yes—
618C2C2×#9038911yescharacteristic
619C2#1174321612yes—
620C2#1174334111yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC4×C7×#125C2
socle, cosocleC23×C7C25
prime radicalC2×#90389C2
hypercenterC4×#125D7
hypocenterC7C4×#540
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
2. C4×C7×#125C2semidirect
3. #11740468C2semidirect
4. #11733643C2semidirect
5. #11733414C2semidirect
6. #11732401C2semidirect
7. #11732397C2semidirect
8. #11731669C2semidirect
9. #11731598C2semidirect
10. C4×#6457C2semidirect
11. C4×#6458C2semidirect
12. C4×#6458C2semidirect
13. C4×#6456C2semidirect
14. C4×#6437C2semidirect
15. C4×#6435C2semidirect
17. #90389C4direct (N × H)
82. C7×#125C2×C4semidirect
118. #6458C2×C4semidirect
119. #6458C2×C4semidirect
120. #6457C2×C4semidirect
122. #6456C2×C4semidirect
123. #6437C2×C4semidirect
128. #6435C2×C4semidirect
151. C4×#125D7semidirect
355. #125C4×D7semidirect
437. C4×C7#540semidirect
583. C7C4×#540semidirect
613. C4#90389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903892
C4×C7×#1252
#117404682
#117336432
#117334142
#117324012
#117323972
#117316692
#117315982
C4×#64572
C4×#64582
C4×#64562
C4×#64372
C4×#64352
C4×#5407