Finite Group Databasebeta

← C2×#11738447 #14226577

Subgroups — C2×#11738447 #14226577

Order 1792.

2178 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×#90416C211yesmaximal, characteristic
2C2×#90269C211yesmaximal, characteristic, complemented
3C2×C7×#475C211yesmaximal, characteristic, complemented
4C2×#89866C211yesmaximal, characteristic, complemented
5C2×#89799C211yesmaximal, characteristic, complemented
6#11738447C2116yesmaximal, direct product factor
7C2×#89642C212yesmaximal, complemented
8C2×#89636C212yesmaximal, complemented
9C2×#89620C211yesmaximal, characteristic, complemented
10C2×D7×C4⋊C8C211yesmaximal, characteristic, complemented
11C2×#89590C212yesmaximal, complemented
12C2×#89579C212yesmaximal, complemented
13C22×#1161—21no—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C4×C7×Q8C2211yescharacteristic
16C2×#6510—21no—
17C2×#6509C2211yescharacteristic
18C2×#6507C2211yescharacteristic
19C22×#1143C2212yes—
20C22×#1132C2212yes—
21C22×C8×D7C2212yes—
22#90416—24no—
23#90416C2218yes—
24#90269—24no—
25#90269C2218yescomplemented
26C2×#6460C2211yescharacteristic
27C2×#6459—21no—
28C2×#6458—21no—
29C2×#6458C2212yes—
30C2×#6456—21no—
31C2×#6456C2212yes—
32C2×#6452—21no—
33C2×#6451C2211yescharacteristic
34C2×#6437C2211yescharacteristic
35C2×#6435—21no—
36C2×C42×D7C2211yescharacteristic
37C2×C4×Dic14—21no—
38C2×C4×Dic14C2211yescharacteristic
39C7×#475C2218yescomplemented
40C2×C7×#106C2212yes—
41C2×C7×C4⋊C8C2211yescharacteristic
42C2×C7×#103C2212yes—
43C2×#6395C2212yes—
44C2×Dic7⋊C8C2212yes—
45#89866C2218yescomplemented
46#89799C2218yescomplemented
47C2×#6384C2212yes—
48C2×#6383C2212yes—
49C2×#6382C2212yes—
50C2×C4⋊(C7⋊C8)C2211yescharacteristic
51#89642C22116yescomplemented
52#89636C22116yescomplemented
53#89620C2218yescomplemented
54D7×C4⋊C8C2218yescomplemented
55#89590C22116yescomplemented
56#89579C22116yescomplemented
57C2×#3246—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C22×C7×Q8C2311yescharacteristic
60C2×#1161—28no—
61C2×#1161—48no—
62C22×D28—22no—
63C22×D28—21no—
64C22×D28—21no—
65C22×D28C2312yes—
66C22×C4×D7—22no—
67C22×C4×D7D411yescharacteristic
68C22×C4×D7D411yescharacteristic
69C22×C4×D7C2311yescharacteristic
70C22×Dic14—21no—
71C22×Dic14C2311yescharacteristic
72C22×C7×C8C2312yes—
73C7×C4⋊Q8—22no—
74C7×C4⋊Q8C2314yes—
75C4×C7×Q8—22no—
76C4×C7×Q8C2314yes—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2312yes—
81C2×C42×C7—21no—
82C2×C42×C7C2311yescharacteristic
83#6510—28no—
84#6509—22no—
85#6509C2314yes—
86#6507—22no—
87#6507C2314yes—
88C2×#1143—44no—
89C2×#1143C2318yes—
90C2×(C2×D7)⋊C4—21no—
91C2×(C2×D7)⋊C4—21no—
92C2×(C2×D7)⋊C4—22no—
93C2×(C2×D7)⋊C4—22no—
94C2×C4⋊Dic7—21no—
95C2×C4⋊Dic7C2311yescharacteristic
96C2×Dic7⋊C4—21no—
97C2×Dic7⋊C4—21no—
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—21no—
101C2×C4×Dic7—21no—
102C2×C4×Dic7D411yescharacteristic
103C2×C4×Dic7D411yescharacteristic
104C2×C4×Dic7C2311yescharacteristic
105C22×C7⋊C8C2312yes—
106C2×#1132—44no—
107C2×#1132C2318yes—
108C2×C8×D7—44no—
109C2×C8×D7C2318yes—
110#6460—22no—
111#6460C2314yes—
112#6459—28no—
113#6458—24no—
114#6458—28no—
115#6458C2318yes—
116#6456—24no—
117#6456—28no—
118#6456C2318yes—
119#6452—28no—
120#6451—22no—
121#6451C2314yes—
122#6437—22no—
123#6437C2314yes—
124#6435—28no—
125C42×D7D414yes—
126C42×D7C2314yes—
127C4×Dic14—22no—
128C4×Dic14—28no—
129C4×Dic14C2314yes—
130C7×#106C2318yes—
131C7×C4⋊C8C2314yes—
132C7×#103C2318yes—
133#6395C2318yes—
134Dic7⋊C8C2318yes—
135#6384C2318yes—
136#6383C2318yes—
137#6382C2318yes—
138C4⋊(C7⋊C8)C2314yes—
139C2×#533—71no—
140C2×#532—71no—
141#3246—716no—
142C2×#475—71no—
143C2×#475D711yescharacteristic, complemented
144C2×#476—72no—
145C2×#465—72no—
146C2×#465—72no—
147C2×#460—71no—
148C2×#460—71no—
149C2×#461—72no—
150C22×C4⋊C8—71no—
151C23×D7—22no—
152C23×D7C2×D411yescharacteristic
153C2×C7×Q8—21no—
154C2×C7×Q8—24no—
155C2×C7×Q8—22no—
156C2×C7×Q8—22no—
157C2×C7×Q8—44no—
158C2×C7×Q8C2412yes—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—22no—
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2411yescharacteristic
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7C2×D411yescharacteristic
168C22×Dic7C2×D411yescharacteristic
169C22×Dic7C2×D411yescharacteristic
170#1161—432no—
171C2×D28—24no—
172C2×D28—24no—
173C2×D28—28no—
174C2×D28—22no—
175C2×D28—24no—
176C2×D28—24no—
177C2×D28—44no—
178C2×D28—48no—
179C2×D28—44no—
180C2×D28C2414yes—
181C2×C4×D7—22no—
182C2×C4×D7—22no—
183C2×C4×D7—28no—
184C2×C4×D7—42no—
185C2×C4×D7—48no—
186C2×C4×D7SD1618yescomplemented
187C2×C4×D7C2×D412yes—
188C2×C4×D7C2×D414yes—
189C2×C4×D7C2×D414yes—
190C2×C4×D7C2412yes—
191C2×Dic14—22no—
192C2×Dic14—22no—
193C2×Dic14—21no—
194C2×Dic14—24no—
195C2×Dic14—44no—
196C2×Dic14C2412yes—
197C2×C7×C8—24no—
198C2×C7×C8C2414yes—
199C7×C4⋊C4—21no—
200C7×C4⋊C4—24no—
201C7×C4⋊C4—24no—
202C7×C4⋊C4—22no—
203C7×C4⋊C4C2414yes—
204C7×C4⋊C4C2412yes—
205C42×C7—24no—
206C42×C7C2×D412yes—
207C42×C7C2412yes—
208#1143—48no—
209(C2×D7)⋊C4—24no—
210(C2×D7)⋊C4—24no—
211(C2×D7)⋊C4—28no—
212(C2×D7)⋊C4—28no—
213C4⋊Dic7—21no—
214C4⋊Dic7—24no—
215C4⋊Dic7C2412yes—
216Dic7⋊C4—24no—
217Dic7⋊C4—24no—
218Dic7⋊C4—24no—
219Dic7⋊C4—24no—
220Dic7⋊C4—24no—
221C4×Dic7—24no—
222C4×Dic7C2×D414yes—
223C4×Dic7C2×D412yes—
224C4×Dic7C2×D414yes—
225C4×Dic7C2412yes—
226C2×C7⋊C8—24no—
227C2×C7⋊C8C2414yes—
228#1132—48no—
229C8×D7—48no—
230C22×#41—141no—
231C22×SD16—72no—
232C22×SD16—72no—
233C23×C8—72no—
234#533—78no—
235#533—144no—
236#532—78no—
237#532—144no—
238C2×C4⋊Q8—71no—
239C2×C4⋊Q8—71no—
240C2×C4⋊Q8C2×D711yescharacteristic
241C2×#127—71no—
242C2×#125—141no—
243C2×#124—141no—
244C2×C22⋊Q8—71no—
245C2×C22⋊Q8—71no—
246C2×C22⋊Q8—141no—
247C2×#121—72no—
248C2×#121—141no—
249C2×C4×Q8—71no—
250C2×C4×Q8—141no—
251C2×C4×Q8C2×D711yescharacteristic
252C2×C4×D4—72no—
253C2×C4×D4—141no—
254C2×#117—141no—
255C22×C42—71no—
256#476—716no—
257#475—78no—
258#475C2×D718yescomplemented
259#465—716no—
260#465—716no—
261#461—716no—
262#460—78no—
263#460—78no—
264C2×#106—72no—
265C2×#106C2×D712yes—
266C2×C4⋊C8—72no—
267C2×C4⋊C8—71no—
268C2×C4⋊C8—78no—
269C2×C4⋊C8C2×D711yescharacteristic
270C2×#103—72no—
271C2×#103C2×D712yes—
272C2×#102—72no—
273C2×#102—72no—
274C23×C7C22×D411yescharacteristic
275C22×D7—22no—
276C22×D7—22no—
277C22×D7—24no—
278C22×D7—44no—
279C22×D7—44no—
280C22×D7—44no—
281C22×D7C2×SD1614yes—
282C22×D7C22×D412yes—
283C7×Q8—22no—
284C7×Q8—22no—
285C7×Q8—42no—
286C7×Q8—48no—
287C2×C4×C7—22no—
288C2×C4×C7—22no—
289C2×C4×C7—22no—
290C2×C4×C7—24no—
291C2×C4×C7—42no—
292C2×C4×C7—44no—
293C2×C4×C7—42no—
294C2×C4×C7C2×SD1614yes—
295C2×C4×C7C22×D412yes—
296C2×C4×C7C22×D411yescharacteristic
297C2×C4×C7C22×D412yes—
298C2×C4×C7H(5,𝔽2)12yes—
299C2×C4×C72−1+412yes—
300C2×C4×C7C2511yescharacteristic
301C2×Dic7—22no—
302C2×Dic7—22no—
303C2×Dic7—22no—
304C2×Dic7—22no—
305C2×Dic7—42no—
306C2×Dic7—42no—
307C2×Dic7C2×SD1614yes—
308C2×Dic7C22×D412yes—
309C2×Dic7C22×D412yes—
310C2×Dic7C22×D412yes—
311D28—24no—
312D28—24no—
313D28—48no—
314D28—416no—
315D28—44no—
316D28—48no—
317C4×D7—24no—
318C4×D7—22no—
319C4×D7—22no—
320C4×D7—44no—
321C4×D7—416no—
322C4×D7C2×SD16116yescomplemented
323Dic14—22no—
324Dic14—22no—
325Dic14—48no—
326Dic14—42no—
327C7×C8—24no—
328C7⋊C8—24no—
329C2×#41—148no—
330C2×#41—288no—
331C22×Q8—21no—
332C22×Q8—71no—
333C22×Q8—141no—
334C22×Q8C22×D711yescharacteristic
335C22×D4—72no—
336C22×D4—142no—
337C22×D4—141no—
338C22×D4—141no—
339C23×C4—71no—
340C23×C4—71no—
341C23×C4—71no—
342C23×C4—142no—
343C2×SD16—78no—
344C2×SD16—78no—
345C2×SD16—284no—
346C2×SD16—284no—
347C22×C8—72no—
348C22×C8—78no—
349C22×C8—284no—
350C22×C8C22×D712yes—
351C4⋊Q8—22no—
352C4⋊Q8—74no—
353C4⋊Q8—74no—
354C4⋊Q8—142no—
355C4⋊Q8—142no—
356C4⋊Q8C22×D714yes—
357#127—74no—
358#127—142no—
359#125—148no—
360#124—148no—
361C22⋊Q8—74no—
362C22⋊Q8—74no—
363C22⋊Q8—142no—
364C22⋊Q8—148no—
365C22⋊Q8—142no—
366#121—78no—
367#121—144no—
368#121—148no—
369C4×Q8—22no—
370C4×Q8—74no—
371C4×Q8—148no—
372C4×Q8—142no—
373C4×Q8C22×D714yes—
374C4×D4—78no—
375C4×D4—144no—
376C4×D4—148no—
377#117—148no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—71no—
381C2×C4⋊C4—141no—
382C2×C4⋊C4—141no—
383C2×C4⋊C4—141no—
384C2×C4⋊C4—141no—
385C2×C4⋊C4—141no—
386C2×C4⋊C4—141no—
387C2×C4⋊C4C22×D712yes—
388C2×C4⋊C4C22×D711yescharacteristic
389C2×C22⋊C4—142no—
390C2×C22⋊C4—142no—
391C2×C22⋊C4—141no—
392C2×C22⋊C4—141no—
393C2×C42—21no—
394C2×C42—71no—
395C2×C42—71no—
396C2×C42—71no—
397C2×C42—74no—
398C2×C42—74no—
399C2×C42—141no—
400C2×C42C22×D711yescharacteristic
401#106—78no—
402#106C22×D718yes—
403C4⋊C8—78no—
404C4⋊C8—74no—
405C4⋊C8C22×D714yes—
406#103—78no—
407#103C22×D718yes—
408#102—78no—
409#102—78no—
410C22×C7#53712yes—
411C22×C7C22×SD1612yes—
412C22×C7#57512yes—
413C22×C7C23×D411yescharacteristic
414C2×D7—22no—
415C2×D7—28no—
416C2×D7—22no—
417C2×D7—44no—
418C2×D7—44no—
419C2×D7—44no—
420C2×D7—88no—
421C2×D7C22×SD1614yes—
422C4×C7—22no—
423C4×C7—42no—
424C4×C7—44no—
425C4×C7—42no—
426C4×C7#53712yes—
427C4×C7C22×SD1614yes—
428C4×C7C2×H(5,𝔽2)11yescharacteristic
429C4×C7C2×2−1+411yescharacteristic
430Dic7—22no—
431Dic7—22no—
432Dic7—42no—
433Dic7—42no—
434Dic7C22×SD1614yes—
435C24—71no—
436C24—142no—
437#41—2832no—
438C2×Q8—21no—
439C2×Q8—24no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—44no—
443C2×Q8—72no—
444C2×Q8—144no—
445C2×Q8—141no—
446C2×Q8—142no—
447C2×Q8—142no—
448C2×Q8—284no—
449C2×Q8C23×D712yes—
450C2×D4—74no—
451C2×D4—148no—
452C2×D4—144no—
453C2×D4—142no—
454C2×D4—144no—
455C2×D4—144no—
456C2×D4—144no—
457C2×D4—284no—
458C2×D4—288no—
459C2×D4—284no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—71no—
464C22×C4—78no—
465C22×C4—74no—
466C22×C4—71no—
467C22×C4—71no—
468C22×C4—72no—
469C22×C4—72no—
470C22×C4—74no—
471C22×C4—148no—
472C22×C4—142no—
473C22×C4—142no—
474C22×C4—141no—
475C22×C4—141no—
476C22×C4—282no—
477C22×C4—288no—
478C22×C4D4×D711yescharacteristic
479C22×C4D4×D711yescharacteristic
480C22×C4C23×D711yescharacteristic
481SD16—288no—
482SD16—288no—
483C2×C8—24no—
484C2×C8—74no—
485C2×C8—144no—
486C2×C8—288no—
487C2×C8C23×D714yes—
488C4⋊C4—24no—
489C4⋊C4—24no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—72no—
493C4⋊C4—144no—
494C4⋊C4—144no—
495C4⋊C4—144no—
496C4⋊C4—144no—
497C4⋊C4—144no—
498C4⋊C4—144no—
499C4⋊C4—141no—
500C4⋊C4C23×D712yes—
501C4⋊C4C23×D714yes—
502C22⋊C4—148no—
503C22⋊C4—148no—
504C22⋊C4—144no—
505C22⋊C4—144no—
506C42—24no—
507C42—74no—
508C42—72no—
509C42—74no—
510C42—72no—
511C42—144no—
512C42D4×D712yes—
513C42C23×D712yes—
514C2×C7#324614yescomplemented
515C2×C7C2×#53711yescharacteristic
516C2×C7C23×SD1611yescharacteristic
517C2×C7C2×#57511yescharacteristic
518D7—24no—
519D7—84no—
520C23—74no—
521C23—72no—
522C23—142no—
523C23—142no—
524C23—144no—
525C23—284no—
526C23—284no—
527C23—284no—
528C23C2×D4×D711yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—48no—
532Q8—42no—
533Q8—142no—
534Q8—142no—
535Q8—288no—
536Q8—282no—
537D4—144no—
538D4—144no—
539D4—288no—
540D4—2816no—
541D4—288no—
542D4—284no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—74no—
551C2×C4—72no—
552C2×C4—716no—
553C2×C4—72no—
554C2×C4—72no—
555C2×C4—142no—
556C2×C4—142no—
557C2×C4—144no—
558C2×C4—142no—
559C2×C4—142no—
560C2×C4—142no—
561C2×C4—142no—
562C2×C4—284no—
563C2×C4—2816no—
564C2×C4—282no—
565C2×C4—282no—
566C2×C4D7×SD1614yes—
567C2×C4C2×D4×D712yes—
568C2×C4C2×D4×D712yes—
569C2×C4C2×D4×D711yescharacteristic
570C2×C4#655112yes—
571C2×C4#655312yes—
572C2×C4C24×D711yescharacteristic
573C8—24no—
574C8—144no—
575C7C2×#324611yescharacteristic, complemented, Sylow
576C22—74no—
577C22—142no—
578C22—142no—
579C22—148no—
580C22—284no—
581C22—284no—
582C22—284no—
583C22—568no—
584C22#9032012yes—
585C22C2×D7×SD1612yes—
586C22#9046812yes—
587C22C22×D4×D711yescharacteristic
588C4—22no—
589C4—42no—
590C4—42no—
591C4—44no—
592C4—74no—
593C4—142no—
594C4—142no—
595C4—282no—
596C4—282no—
597C4#9032012yes—
598C4C2×D7×SD1614yes—
599C4C2×#655111yescharacteristic
600C4C2×#655311yescharacteristic
601C2—144no—
602C2—564no—
603C2#1173844714yesdirect product factor
604C2C2×#9032011yescharacteristic
605C2C22×D7×SD1611yescharacteristic
606C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#475C2
socleC23×C7C22×D4
prime radicalC2×#90416C2
hypercenterC2×#475D7
hypocenterC7C2×#3246
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#90269C2semidirect
3. C2×C7×#475C2semidirect
4. C2×#89866C2semidirect
5. C2×#89799C2semidirect
6. #11738447C2direct (N × H)
7. C2×#89642C2semidirect
8. C2×#89636C2semidirect
9. C2×#89620C2semidirect
10. C2×D7×C4⋊C8C2semidirect
11. C2×#89590C2semidirect
12. C2×#89579C2semidirect
25. #90269C22semidirect
39. C7×#475C22semidirect
45. #89866C22semidirect
46. #89799C22semidirect
51. #89642C22semidirect
52. #89636C22semidirect
53. #89620C22semidirect
54. D7×C4⋊C8C22semidirect
55. #89590C22semidirect
56. #89579C22semidirect
143. C2×#475D7semidirect
186. C2×C4×D7SD16semidirect
258. #475C2×D7semidirect
322. C4×D7C2×SD16semidirect
514. C2×C7#3246semidirect
575. C7C2×#3246semidirect
603. C2#11738447direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904162
C2×#902692
C2×C7×#4752
C2×#898662
C2×#897992
#117384472
C2×#896422
C2×#896362
C2×#896202
C2×D7×C4⋊C82
C2×#895902
C2×#895792
C2×#32467