Finite Group Databasebeta

← C2×#11726031 #13320893

Subgroups — C2×#11726031 #13320893

Order 1792.

1474 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90287C211yesmaximal, characteristic
2C2×#89490C211yesmaximal, characteristic, complemented
3C2×#89421C211yesmaximal, characteristic, complemented
4C2×C7×#327C211yesmaximal, characteristic, complemented
5C2×#89332C211yesmaximal, characteristic, complemented
6C2×#89265C211yesmaximal, characteristic, complemented
7C2×#89246C211yesmaximal, characteristic, complemented
8#11726031C218yesmaximal, direct product factor
9C22×#1159—21no—
10C2×C7×#121C2211yescharacteristic
11C2×#6503C411yescharacteristic, complemented
12C2×#6502—21no—
13C2×D4×Dic7C411yescharacteristic, complemented
14C2×#6493C2211yescharacteristic
15C22×Dic7⋊C4—21no—
16C22×C4×Dic7—21no—
17C22×C4×Dic7C2211yescharacteristic
18#90287—22no—
19#90287—22no—
20#90287C414yescomplemented
21#90287C2214yes—
22C2×#6456C411yescharacteristic, complemented
23C2×#6451C411yescharacteristic, complemented
24C2×#6448—21no—
25C2×(C22⋊D7)⋊C4—21no—
26C2×C7×C22⋊C8C2211yescharacteristic
27C2×C7×#95C2211yescharacteristic
28C2×C7⋊#95C2211yescharacteristic
29C2×C22⋊(C7⋊C8)C2211yescharacteristic
30C2×Dic7⋊C8—21no—
31C2×C8×Dic7—21no—
32#89490—22no—
33#89490C2214yescomplemented
34#89421—22no—
35#89421C2214yescomplemented
36C7×#327C2214yescomplemented
37#89332C2214yescomplemented
38#89265C2214yescomplemented
39#89246C2214yescomplemented
40C2×#1502—71nomaximal, Sylow
41C22×C7×D4—21no—
42C22×C7×D4C2×C411yescharacteristic
43C23×C4×C7—21no—
44C23×C4×C7C2311yescharacteristic
45C22×C22⋊D7—21no—
46C22×C22⋊D7—21no—
47C22×C22⋊D7—21no—
48C23×Dic7—21no—
49C23×Dic7—21no—
50C23×Dic7D411yescharacteristic
51C23×Dic7D411yescharacteristic
52C2×#1159—24no—
53C2×#1159—24no—
54C2×#1159—44no—
55C2×#1159—44no—
56C22×D28C2×C411yescharacteristic
57C22×C4×D7—21no—
58C22×Dic14—21no—
59C22×C7×C8—21no—
60C7×#121—21no—
61C7×#121—21no—
62C7×#121C2×C412yes—
63C7×#121C2312yes—
64C2×C7×C4⋊C4C2×C411yescharacteristic
65C2×C7×C22⋊C4—21no—
66C2×C22⋊Dic7—21no—
67#6503—22no—
68#6503C2×C414yescomplemented
69#6502—24no—
70#6502—24no—
71D4×Dic7—22no—
72D4×Dic7C2×C414yescomplemented
73#6493—21no—
74#6493—21no—
75#6493C2×C412yes—
76#6493C2312yes—
77C2×(C2×D7)⋊C4—21no—
78C2×(C2×D7)⋊C4—21no—
79C2×C4⋊Dic7C2×C411yescharacteristic
80C2×Dic7⋊C4—28no—
81C2×Dic7⋊C4—21no—
82C2×Dic7⋊C4—24no—
83C2×C4×Dic7—24no—
84C2×C4×Dic7—44no—
85C2×C4×Dic7C2×C411yescharacteristic
86C2×C4×Dic7C2×C411yescharacteristic
87C2×C4×Dic7C2×C412yes—
88C2×C4×Dic7D412yes—
89C2×C4×Dic7D411yescharacteristic
90C2×C4×Dic7D411yescharacteristic
91C2×C4×Dic7D412yes—
92C2×C4×Dic7C2312yes—
93C22×C7⋊C8—21no—
94#6456—22no—
95#6456C2×C414yescomplemented
96#6451—22no—
97#6451C2×C414yescomplemented
98#6448—24no—
99#6448—24no—
100(C22⋊D7)⋊C4—24no—
101(C22⋊D7)⋊C4—24no—
102C7×C22⋊C8—21no—
103C7×C22⋊C8C2312yes—
104C7×#95—21no—
105C7×#95C2312yes—
106C7⋊#95—21no—
107C7⋊#95C2312yes—
108C22⋊(C7⋊C8)—21no—
109C22⋊(C7⋊C8)C2312yes—
110Dic7⋊C8—24no—
111C8×Dic7—24no—
112C2×#532—71no—
113C2×#431—71no—
114C2×C4×C4⋊C4—71no—
115#1502—78no—
116C2×#327—71no—
117C2×#327—71no—
118C2×#327—71no—
119C2×#327D711yescharacteristic, complemented
120C24×C7—21no—
121C24×C7C2×D411yescharacteristic
122C23×D7—21no—
123C2×C7×D4—22no—
124C2×C7×D4—22no—
125C2×C7×D4—21no—
126C2×C7×D4—42no—
127C2×C7×D4—42no—
128C2×C7×D4—42no—
129C2×C7×D4C22×C412yes—
130C22×C4×C7—24no—
131C22×C4×C7—21no—
132C22×C4×C7—22no—
133C22×C4×C7—42no—
134C22×C4×C7—42no—
135C22×C4×C7—42no—
136C22×C4×C7C22×C411yescharacteristic
137C22×C4×C7C22×C411yescharacteristic
138C22×C4×C7C2×D411yescharacteristic
139C22×C4×C7C2×D411yescharacteristic
140C22×C4×C7C2×D411yescharacteristic
141C22×C4×C7C2411yescharacteristic
142C2×C22⋊D7—22no—
143C2×C22⋊D7—22no—
144C2×C22⋊D7—24no—
145C2×C22⋊D7—24no—
146C2×C22⋊D7—42no—
147C2×C22⋊D7—42no—
148C2×C22⋊D7—44no—
149C2×C22⋊D7—44no—
150C22×Dic7—24no—
151C22×Dic7—24no—
152C22×Dic7—21no—
153C22×Dic7—22no—
154C22×Dic7—24no—
155C22×Dic7—42no—
156C22×Dic7—42no—
157C22×Dic7—44no—
158C22×Dic7C22⋊C411yescharacteristic
159C22×Dic7C22⋊C412yes—
160C22×Dic7C22⋊C411yescharacteristic
161C22×Dic7C22⋊C411yescharacteristic
162C22×Dic7C22⋊C412yes—
163C22×Dic7C22⋊C411yescharacteristic
164C22×Dic7D814yes—
165C22×Dic7SD1614yes—
166C22×Dic7C2×D412yes—
167C22×Dic7C2×D412yes—
168#1159—416no—
169#1159—48no—
170#1159—48no—
171C2×D28—21no—
172C2×D28—42no—
173C2×D28C22×C412yes—
174C2×C4×D7—24no—
175C2×C4×D7—44no—
176C2×Dic14—24no—
177C2×Dic14—44no—
178C2×C7×C8—22no—
179C2×C7×C8—42no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4C22×C412yes—
182C7×C22⋊C4—22no—
183C7×C22⋊C4—22no—
184C22⋊Dic7—24no—
185(C2×D7)⋊C4—22no—
186(C2×D7)⋊C4—22no—
187(C2×D7)⋊C4—24no—
188C4⋊Dic7—21no—
189C4⋊Dic7C22×C412yes—
190Dic7⋊C4—216no—
191Dic7⋊C4—24no—
192C4×Dic7—48no—
193C4×Dic7C22⋊C412yes—
194C4×Dic7C22⋊C412yes—
195C4×Dic7C22⋊C412yes—
196C4×Dic7C22⋊C412yes—
197C4×Dic7C22×C412yes—
198C4×Dic7C22×C412yes—
199C4×Dic7C2×D412yes—
200C4×Dic7C2×D412yes—
201C2×C7⋊C8—22no—
202C2×C7⋊C8—42no—
203C22×#41—141no—
204#532—74no—
205#532—74no—
206#532—142no—
207#532—142no—
208C2×C4⋊Q8—71no—
209C2×#127—71no—
210C2×#124—141no—
211C2×#121—71no—
212C2×#121—141no—
213C2×#121C2×D711yescharacteristic
214C2×C4×D4—71no—
215C2×C4×D4—71no—
216C2×C4×D4—141no—
217C22×C4⋊C4—141no—
218C22×C42—71no—
219C22×C42—141no—
220#431—74no—
221#431—142no—
222C2×C4⋊C8—141no—
223C2×C22⋊C8—71no—
224C2×C22⋊C8C2×D711yescharacteristic
225C2×C4×C8—141no—
226C4×C4⋊C4—74no—
227C4×C4⋊C4—142no—
228C2×#95—71no—
229C2×#95C2×D711yescharacteristic
230#327—74no—
231#327—74no—
232#327—74no—
233#327C2×D714yescomplemented
234C23×C7—22no—
235C23×C7—22no—
236C23×C7—22no—
237C23×C7—42no—
238C23×C7—42no—
239C23×C7—42no—
240C23×C7C2×C22⋊C411yescharacteristic
241C23×C7C2×C22⋊C411yescharacteristic
242C23×C7C2×D812yes—
243C23×C7C2×SD1612yes—
244C23×C7C22×D411yescharacteristic
245C22×D7—22no—
246C22×D7—42no—
247C22×D7—42no—
248C22×D7—42no—
249C7×D4—42no—
250C7×D4—42no—
251C7×D4—42no—
252C7×D4—42no—
253C7×D4—44no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—24no—
257C2×C4×C7—22no—
258C2×C4×C7—41no—
259C2×C4×C7—41no—
260C2×C4×C7—41no—
261C2×C4×C7—41no—
262C2×C4×C7—42no—
263C2×C4×C7—48no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7C2×C22⋊C411yescharacteristic
267C2×C4×C7C2×C22⋊C411yescharacteristic
268C2×C4×C7C23×C411yescharacteristic
269C2×C4×C7C22×D411yescharacteristic
270C22⋊D7—42no—
271C22⋊D7—42no—
272C22⋊D7—44no—
273C22⋊D7—48no—
274C22⋊D7—48no—
275C2×Dic7—22no—
276C2×Dic7—24no—
277C2×Dic7—24no—
278C2×Dic7—24no—
279C2×Dic7—22no—
280C2×Dic7—42no—
281C2×Dic7—48no—
282C2×Dic7—42no—
283C2×Dic7—42no—
284C2×Dic7—48no—
285C2×Dic7#10214yes—
286C2×Dic7#10214yes—
287C2×Dic7#10218yes—
288C2×Dic7#10414yes—
289C2×Dic7C2×C22⋊C412yes—
290C2×Dic7C2×C22⋊C412yes—
291C2×Dic7C2×C22⋊C412yes—
292C2×Dic7C2×C22⋊C412yes—
293C2×Dic7C2×D814yes—
294C2×Dic7C2×SD1614yes—
295D28—42no—
296D28—42no—
297C4×D7—48no—
298Dic14—48no—
299C7×C8—42no—
300C7⋊C8—42no—
301C2×#41—144no—
302C2×#41—144no—
303C2×#41—284no—
304C2×#41—284no—
305C22×Q8—141no—
306C22×D4—21no—
307C22×D4—71no—
308C22×D4—141no—
309C22×D4—141no—
310C22×D4—141no—
311C22×D4C4×D711yescharacteristic
312C23×C4—21no—
313C23×C4—71no—
314C23×C4—71no—
315C23×C4—141no—
316C23×C4—141no—
317C23×C4—141no—
318C23×C4C22×D711yescharacteristic
319C22×C8—21no—
320C22×C8—141no—
321C4⋊Q8—74no—
322C4⋊Q8—142no—
323#127—74no—
324#127—142no—
325#124—144no—
326#124—144no—
327#121—21no—
328#121—21no—
329#121—72no—
330#121—72no—
331#121—144no—
332#121—144no—
333#121—141no—
334#121—141no—
335#121C4×D712yes—
336#121C22×D712yes—
337C4×D4—74no—
338C4×D4—74no—
339C4×D4—144no—
340C4×D4—144no—
341C4×D4—142no—
342C4×D4—142no—
343C2×C4⋊C4—71no—
344C2×C4⋊C4—144no—
345C2×C4⋊C4—141no—
346C2×C4⋊C4—148no—
347C2×C4⋊C4C4×D711yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—141no—
350C2×C22⋊C4—141no—
351C2×C22⋊C4—141no—
352C2×C42—71no—
353C2×C42—71no—
354C2×C42—72no—
355C2×C42—71no—
356C2×C42—71no—
357C2×C42—72no—
358C2×C42—72no—
359C2×C42—72no—
360C2×C42—144no—
361C2×C42—284no—
362C4⋊C8—144no—
363C22⋊C8—21no—
364C22⋊C8—72no—
365C22⋊C8—141no—
366C22⋊C8C22×D712yes—
367C4×C8—144no—
368#95—21no—
369#95—72no—
370#95—141no—
371#95C22×D712yes—
372C22×C7—21no—
373C22×C7—21no—
374C22×C7—21no—
375C22×C7—21no—
376C22×C7—24no—
377C22×C7—24no—
378C22×C7—42no—
379C22×C7—42no—
380C22×C7—42no—
381C22×C7—84no—
382C22×C7#41012yes—
383C22×C7C2×#10212yes—
384C22×C7C2×#10212yes—
385C22×C7C2×#10412yes—
386C22×C7C22×C22⋊C411yescharacteristic
387C22×C7C22×D811yescharacteristic
388C22×C7C22×SD1611yescharacteristic
389C2×D7—42no—
390C2×D7—42no—
391C2×D7—42no—
392C2×D7—84no—
393C4×C7—21no—
394C4×C7—21no—
395C4×C7—21no—
396C4×C7—21no—
397C4×C7—44no—
398C4×C7—42no—
399Dic7—22no—
400Dic7—44no—
401Dic7—42no—
402Dic7C2×#10214yes—
403Dic7C2×#10214yes—
404Dic7C2×#10414yes—
405C24—21no—
406C24—141no—
407C24D4×D711yescharacteristic
408#41—288no—
409#41—288no—
410#41—2816no—
411C2×Q8—144no—
412C2×Q8—284no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—72no—
420C2×D4—144no—
421C2×D4—144no—
422C2×D4—142no—
423C2×D4—142no—
424C2×D4—141no—
425C2×D4—282no—
426C2×D4—284no—
427C2×D4—284no—
428C2×D4—282no—
429C2×D4—282no—
430C2×D4C2×C4×D712yes—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—72no—
438C22×C4—71no—
439C22×C4—71no—
440C22×C4—71no—
441C22×C4—74no—
442C22×C4—74no—
443C22×C4—72no—
444C22×C4—72no—
445C22×C4—71no—
446C22×C4—72no—
447C22×C4—144no—
448C22×C4—144no—
449C22×C4—144no—
450C22×C4—144no—
451C22×C4—141no—
452C22×C4—142no—
453C22×C4—284no—
454C22×C4—284no—
455C22×C4—282no—
456C22×C4—282no—
457C22×C4C2×C4×D711yescharacteristic
458C22×C4C2×C4×D711yescharacteristic
459C22×C4D4×D711yescharacteristic
460C22×C4D4×D711yescharacteristic
461C22×C4D4×D711yescharacteristic
462C22×C4C23×D711yescharacteristic
463C2×C8—22no—
464C2×C8—42no—
465C2×C8—142no—
466C2×C8—282no—
467C4⋊C4—21no—
468C4⋊C4—72no—
469C4⋊C4—144no—
470C4⋊C4—1416no—
471C4⋊C4—141no—
472C4⋊C4C2×C4×D712yes—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—144no—
476C22⋊C4—144no—
477C22⋊C4—142no—
478C22⋊C4—142no—
479C42—72no—
480C42—72no—
481C42—72no—
482C42—72no—
483C42—72no—
484C42—72no—
485C42—72no—
486C42—72no—
487C42—288no—
488C2×C7—21no—
489C2×C7—21no—
490C2×C7—22no—
491C2×C7—82no—
492C2×C7#150214yescomplemented
493C2×C7C2×#41011yescharacteristic
494C2×C7C22×#10211yescharacteristic
495C2×C7C22×#10411yescharacteristic
496D7—82no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—142no—
504C23—282no—
505C23—282no—
506C23—282no—
507C23D7×C22⋊C411yescharacteristic
508C23D7×C22⋊C411yescharacteristic
509C23D7×D812yes—
510C23D7×SD1612yes—
511C23C2×D4×D711yescharacteristic
512Q8—288no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—44no—
518D4—282no—
519D4—282no—
520D4—288no—
521D4—288no—
522D4—282no—
523D4—282no—
524D4—284no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—48no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—72no—
538C2×C4—72no—
539C2×C4—72no—
540C2×C4—74no—
541C2×C4—74no—
542C2×C4—74no—
543C2×C4—74no—
544C2×C4—78no—
545C2×C4—74no—
546C2×C4—72no—
547C2×C4—144no—
548C2×C4—144no—
549C2×C4—142no—
550C2×C4—144no—
551C2×C4—142no—
552C2×C4—288no—
553C2×C4—288no—
554C2×C4—282no—
555C2×C4—288no—
556C2×C4—282no—
557C2×C4—282no—
558C2×C4D7×C22⋊C411yescharacteristic
559C2×C4D7×C22⋊C411yescharacteristic
560C2×C4C22×C4×D711yescharacteristic
561C2×C4C2×D4×D711yescharacteristic
562C8—42no—
563C8—282no—
564C7C2×#150211yescharacteristic, complemented, Sylow
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—24no—
570C22—24no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—84no—
575C22—282no—
576C22—282no—
577C22—282no—
578C22—564no—
579C22#8951212yes—
580C22D7×#10212yes—
581C22D7×#10212yes—
582C22D7×#10412yes—
583C22C2×D7×C22⋊C411yescharacteristic
584C22C2×D7×D811yescharacteristic
585C22C2×D7×SD1611yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—44no—
591C4—42no—
592C4—74no—
593C4—74no—
594C4—74no—
595C4—142no—
596C4—284no—
597C4—282no—
598C2—21no—
599C2—21no—
600C2—22no—
601C2—82no—
602C2—562no—
603C2#1172603114yesdirect product factor
604C2C2×#8951211yescharacteristic
605C2C2×D7×#10211yescharacteristic
606C2C2×D7×#10411yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#327C2
socleC23×C7C2×C22⋊C4
prime radicalC2×#90287C2
cosocleC22×C4×C7C24
hypercenterC2×#327D7
hypocenterC7C2×#1502
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#89490C2semidirect
3. C2×#89421C2semidirect
4. C2×C7×#327C2semidirect
5. C2×#89332C2semidirect
6. C2×#89265C2semidirect
7. C2×#89246C2semidirect
8. #11726031C2direct (N × H)
11. C2×#6503C4semidirect
13. C2×D4×Dic7C4semidirect
20. #90287C4semidirect
22. C2×#6456C4semidirect
23. C2×#6451C4semidirect
33. #89490C22semidirect
35. #89421C22semidirect
36. C7×#327C22semidirect
37. #89332C22semidirect
38. #89265C22semidirect
39. #89246C22semidirect
68. #6503C2×C4semidirect
72. D4×Dic7C2×C4semidirect
95. #6456C2×C4semidirect
97. #6451C2×C4semidirect
119. C2×#327D7semidirect
233. #327C2×D7semidirect
492. C2×C7#1502semidirect
564. C7C2×#1502semidirect
603. C2#11726031direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902872
C2×#894902
C2×#894212
C2×C7×#3272
C2×#893322
C2×#892652
C2×#892462
#117260312
C2×#15027