Finite Group Databasebeta

← C2×#11737880 #14225069

Subgroups — C2×#11737880 #14225069

Order 1792.

2146 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
1C2×D7×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#90248C211yesmaximal, characteristic
3C2×C7×#461C211yesmaximal, characteristic, complemented
4C2×#89942C212yesmaximal
5C2×#89939C212yesmaximal, complemented
6C2×#89862C211yesmaximal, characteristic, complemented
7C2×#89791C211yesmaximal, characteristic, complemented
8#11737880C2116yesmaximal, direct product factor
9C2×#89621C211yesmaximal, characteristic, complemented
10C2×#89607C211yesmaximal, characteristic, complemented
11C2×#89580C212yesmaximal, complemented
12C2×#89569C212yesmaximal, complemented
13C22×Q8×D7C2212yes—
14C22×C7×SD16C2212yes—
15C2×C7×C4⋊Q8C2211yescharacteristic
16C2×C4×C7×D4C2211yescharacteristic
17C2×#6507C2212yes—
18C22×#1144C2212yes—
19C2×#6501C2211yescharacteristic
20C2×#6499C2211yescharacteristic
21C22×#1142C2212yes—
22C2×C4×C22⋊D7—21no—
23C2×#6489—21no—
24C22×Dic28C2212yes—
25D7×C4⋊Q8—24no—
26D7×C4⋊Q8C2218yescomplemented
27#90248—24no—
28#90248C2218yes—
29C2×#6460C2211yescharacteristic
30C2×D7×C4⋊C4—21no—
31C2×D7×C4⋊C4—21no—
32C2×#6453C2211yescharacteristic
33C2×#6451—21no—
34C2×#6451—21no—
35C2×#6446—21no—
36C2×#6442—21no—
37C2×C42×D7C2211yescharacteristic
38C2×#6432C2211yescharacteristic
39C2×C4×Dic14C2211yescharacteristic
40C7×#461C2218yescomplemented
41C2×C7×C4⋊C8C2211yescharacteristic
42C2×C7×#103C2212yes—
43C2×#6409C2212yes—
44#89942C22116yes—
45#89939C22116yescomplemented
46C2×(C2×D7)⋊C8C2212yes—
47C2×#6390C2212yes—
48C2×#6389C2212yes—
49#89862C2218yescomplemented
50#89791C2218yescomplemented
51C2×#6384C2212yes—
52C2×C4⋊(C7⋊C8)C2211yescharacteristic
53#89621C2218yescomplemented
54#89607C2218yescomplemented
55#89580C22116yescomplemented
56#89569C22116yescomplemented
57C2×#3218—71nomaximal, Sylow
58C22×C7×Q8C2312yes—
59C22×C7×D4C2311yescharacteristic
60C23×C4×C7—21no—
61C22×C22⋊D7—21no—
62C2×Q8×D7—24no—
63C2×Q8×D7—44no—
64C2×Q8×D7—44no—
65C2×Q8×D7C2318yes—
66C22×C4×D7—22no—
67C22×C4×D7D411yescharacteristic
68C22×C4×D7D411yescharacteristic
69C22×C4×D7C2311yescharacteristic
70C22×Dic14—22no—
71C22×Dic14C2312yes—
72C22×Dic14C2311yescharacteristic
73C2×C7×SD16—44no—
74C2×C7×SD16C2318yes—
75C22×C7×C8C2312yes—
76C7×C4⋊Q8—22no—
77C7×C4⋊Q8C2314yes—
78C4×C7×D4—22no—
79C4×C7×D4C2314yes—
80C2×C7×C4⋊C4—21no—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C22⋊C4—21no—
84C2×C42×C7C2311yescharacteristic
85C2×C22⋊Dic7—21no—
86C2×C22⋊Dic7—21no—
87C2×C22⋊Dic7—21no—
88#6507—24no—
89#6507C2318yes—
90C2×#1144—44no—
91C2×#1144C2318yes—
92#6501—22no—
93#6501C2314yes—
94#6499—22no—
95#6499C2314yes—
96C2×#1142—44no—
97C2×#1142C2318yes—
98C4×C22⋊D7—28no—
99C2×(C2×D7)⋊C4—21no—
100#6489—28no—
101C2×C4⋊Dic7—21no—
102C2×C4⋊Dic7—21no—
103C2×C4⋊Dic7—21no—
104C2×C4⋊Dic7—21no—
105C2×C4⋊Dic7C2311yescharacteristic
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—22no—
110C2×C4×Dic7—21no—
111C2×C4×Dic7D411yescharacteristic
112C2×C4×Dic7D411yescharacteristic
113C2×C4×Dic7C2311yescharacteristic
114C22×C7⋊C8C2312yes—
115C2×Dic28—44no—
116C2×Dic28C2318yes—
117#6460—22no—
118#6460C2314yes—
119D7×C4⋊C4—28no—
120D7×C4⋊C4—28no—
121#6453—22no—
122#6453C2314yes—
123#6451—28no—
124#6451—28no—
125#6446—28no—
126#6442—28no—
127C42×D7D414yes—
128C42×D7C2314yes—
129#6432—22no—
130#6432C2314yes—
131C4×Dic14—22no—
132C4×Dic14C2314yes—
133C7×C4⋊C8C2314yes—
134C7×#103C2318yes—
135#6409C2318yes—
136(C2×D7)⋊C8C2318yes—
137#6390C2318yes—
138#6389C2318yes—
139#6384C2318yes—
140C4⋊(C7⋊C8)C2314yes—
141C22×C4⋊Q8—71no—
142C2×#529—71no—
143#3218—716no—
144C2×#497—72no—
145C2×#491—72no—
146C2×#462—71no—
147C2×#462—71no—
148C2×#461—71no—
149C2×#461D711yescharacteristic, complemented
150C2×#451—72no—
151C2×#448—72no—
152C2×#432—71no—
153C24×C7—21no—
154C23×D7C2×D411yescharacteristic
155C2×C7×Q8—22no—
156C2×C7×Q8—24no—
157C2×C7×Q8—24no—
158C2×C7×Q8C2414yes—
159C2×C7×D4—21no—
160C2×C7×D4—22no—
161C2×C7×D4—22no—
162C2×C7×D4C2412yes—
163C22×C4×C7—22no—
164C22×C4×C7—21no—
165C22×C4×C7—24no—
166C22×C4×C7—44no—
167C22×C4×C7C2×D411yescharacteristic
168C22×C4×C7C2×D411yescharacteristic
169C22×C4×C7C2411yescharacteristic
170C2×C22⋊D7—24no—
171C2×C22⋊D7—44no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—22no—
175C22×Dic7C2×D411yescharacteristic
176C22×Dic7C2×D411yescharacteristic
177C22×Dic7C2×D411yescharacteristic
178Q8×D7—48no—
179Q8×D7—48no—
180Q8×D7—416no—
181C2×C4×D7—24no—
182C2×C4×D7—24no—
183C2×C4×D7—22no—
184C2×C4×D7—22no—
185C2×C4×D7—28no—
186C2×C4×D7—48no—
187C2×C4×D7C2×D412yes—
188C2×C4×D7C2×D414yes—
189C2×C4×D7C2×D414yes—
190C2×C4×D7C2412yes—
191C2×Dic14—22no—
192C2×Dic14—24no—
193C2×Dic14—24no—
194C2×Dic14—22no—
195C2×Dic14—21no—
196C2×Dic14—22no—
197C2×Dic14—28no—
198C2×Dic14—48no—
199C2×Dic14C2412yes—
200C2×Dic14C2414yes—
201C7×SD16—48no—
202C2×C7×C8—24no—
203C2×C7×C8C2414yes—
204C7×C4⋊C4—24no—
205C7×C4⋊C4—24no—
206C7×C4⋊C4—21no—
207C7×C4⋊C4C2412yes—
208C7×C22⋊C4—24no—
209C42×C7C2×D412yes—
210C42×C7C2412yes—
211C22⋊Dic7—24no—
212C22⋊Dic7—24no—
213C22⋊Dic7—24no—
214#1144—48no—
215#1142—48no—
216(C2×D7)⋊C4—24no—
217C4⋊Dic7—21no—
218C4⋊Dic7—24no—
219C4⋊Dic7—24no—
220C4⋊Dic7—24no—
221C4⋊Dic7—24no—
222C4⋊Dic7C2412yes—
223Dic7⋊C4—24no—
224Dic7⋊C4—24no—
225Dic7⋊C4—28no—
226Dic7⋊C4—28no—
227C4×Dic7—24no—
228C4×Dic7C2×D412yes—
229C4×Dic7C2×D414yes—
230C4×Dic7C2×D414yes—
231C4×Dic7C2412yes—
232C2×C7⋊C8—24no—
233C2×C7⋊C8C2414yes—
234Dic28—48no—
235C23×Q8—72no—
236C22×Q16—72no—
237C22×Q16—72no—
238C22×SD16—72no—
239C22×SD16C2×D712yes—
240C2×C4⋊Q8—72no—
241C2×C4⋊Q8—78no—
242C2×C4⋊Q8—71no—
243C2×C4⋊Q8—141no—
244C2×C4⋊Q8—141no—
245C2×C4⋊Q8—144no—
246C2×C4⋊Q8C2×D711yescharacteristic
247#529—78no—
248#529—144no—
249C2×#126—141no—
250C2×#125—71no—
251C2×#124—71no—
252C2×#123—141no—
253C2×C22⋊Q8—71no—
254C2×#121—71no—
255C2×C4×Q8—71no—
256C2×C4×D4—141no—
257C2×C4×D4C2×D711yescharacteristic
258C2×#117—141no—
259C22×C4⋊C4—141no—
260C22×C4⋊C4—141no—
261C22×C42—71no—
262#497—716no—
263#491—716no—
264#462—78no—
265#462—78no—
266#461—78no—
267#461C2×D718yescomplemented
268#451—716no—
269#448—716no—
270#432—78no—
271C2×C4⋊C8—71no—
272C2×C4⋊C8C2×D711yescharacteristic
273C2×#103—72no—
274C2×#103—72no—
275C2×#103—72no—
276C2×#103C2×D712yes—
277C2×C22⋊C8—72no—
278C2×#97—72no—
279C23×C7—22no—
280C23×C7—42no—
281C23×C7—42no—
282C23×C7—42no—
283C23×C7C22×D411yescharacteristic
284C22×D7—22no—
285C22×D7—22no—
286C22×D7#13714yes—
287C22×D7C22×D412yes—
288C7×Q8—24no—
289C7×Q8—24no—
290C7×Q8—44no—
291C7×D4—22no—
292C7×D4—22no—
293C7×D4—42no—
294C2×C4×C7—22no—
295C2×C4×C7—24no—
296C2×C4×C7—22no—
297C2×C4×C7—44no—
298C2×C4×C7—42no—
299C2×C4×C7—48no—
300C2×C4×C7#13714yes—
301C2×C4×C7C22×D412yes—
302C2×C4×C7C22×D411yescharacteristic
303C2×C4×C7C22×D412yes—
304C2×C4×C7H(5,𝔽2)12yes—
305C2×C4×C7H(5,𝔽2)12yes—
306C2×C4×C7C2511yescharacteristic
307C22⋊D7—48no—
308C2×Dic7—22no—
309C2×Dic7—22no—
310C2×Dic7—22no—
311C2×Dic7—22no—
312C2×Dic7—22no—
313C2×Dic7—24no—
314C2×Dic7—44no—
315C2×Dic7—42no—
316C2×Dic7—42no—
317C2×Dic7C22×D412yes—
318C2×Dic7C22×D412yes—
319C2×Dic7C22×D412yes—
320C4×D7—28no—
321C4×D7—24no—
322C4×D7—28no—
323C4×D7—22no—
324C4×D7—22no—
325C4×D7—416no—
326Dic14—22no—
327Dic14—24no—
328Dic14—24no—
329Dic14—22no—
330Dic14—416no—
331Dic14—42no—
332Dic14—44no—
333C7×C8—24no—
334C7⋊C8—24no—
335C22×Q8—78no—
336C22×Q8—71no—
337C22×Q8—72no—
338C22×Q8—142no—
339C22×Q8—144no—
340C22×Q8—284no—
341C22×Q8—284no—
342C22×Q8C22×D712yes—
343C22×D4—141no—
344C22×D4C22×D711yescharacteristic
345C23×C4—21no—
346C23×C4—71no—
347C23×C4—71no—
348C23×C4—71no—
349C23×C4—142no—
350C2×Q16—78no—
351C2×Q16—78no—
352C2×Q16—284no—
353C2×Q16—284no—
354C2×SD16—44no—
355C2×SD16—78no—
356C2×SD16—284no—
357C2×SD16C22×D718yes—
358C22×C8—72no—
359C22×C8C22×D712yes—
360C4⋊Q8—22no—
361C4⋊Q8—78no—
362C4⋊Q8—74no—
363C4⋊Q8—148no—
364C4⋊Q8—148no—
365C4⋊Q8—144no—
366C4⋊Q8—142no—
367C4⋊Q8C22×D714yes—
368#126—148no—
369#125—74no—
370#125—142no—
371#124—74no—
372#124—142no—
373#123—148no—
374C22⋊Q8—74no—
375C22⋊Q8—142no—
376#121—74no—
377#121—142no—
378C4×Q8—74no—
379C4×Q8—142no—
380C4×D4—22no—
381C4×D4—148no—
382C4×D4C22×D714yes—
383#117—148no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—71no—
387C2×C4⋊C4—148no—
388C2×C4⋊C4—148no—
389C2×C4⋊C4—142no—
390C2×C4⋊C4—142no—
391C2×C4⋊C4—141no—
392C2×C4⋊C4—141no—
393C2×C4⋊C4—141no—
394C2×C4⋊C4—141no—
395C2×C4⋊C4—141no—
396C2×C4⋊C4—141no—
397C2×C4⋊C4C22×D711yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—141no—
400C2×C22⋊C4—141no—
401C2×C22⋊C4—141no—
402C2×C22⋊C4—141no—
403C2×C42—71no—
404C2×C42—71no—
405C2×C42—71no—
406C2×C42—74no—
407C2×C42—74no—
408C2×C42—141no—
409C2×C42C22×D711yescharacteristic
410C4⋊C8—74no—
411C4⋊C8C22×D714yes—
412#103—78no—
413#103—78no—
414#103—78no—
415#103C22×D718yes—
416C22⋊C8—78no—
417#97—78no—
418C22×C7—42no—
419C22×C7—42no—
420C22×C7—42no—
421C22×C7—84no—
422C22×C7#53512yes—
423C22×C7C2×#13712yes—
424C22×C7C2×#13712yes—
425C22×C7C23×D411yescharacteristic
426C2×D7—22no—
427C2×D7—28no—
428C2×D7—22no—
429C2×D7C2×#13714yes—
430C4×C7—22no—
431C4×C7—44no—
432C4×C7—42no—
433C4×C7#53512yes—
434C4×C7C2×#13714yes—
435C4×C7C2×H(5,𝔽2)11yescharacteristic
436C4×C7C2×H(5,𝔽2)11yescharacteristic
437Dic7—22no—
438Dic7—22no—
439Dic7—22no—
440Dic7—44no—
441Dic7—42no—
442Dic7—42no—
443C24—21no—
444C24—71no—
445C2×Q8—22no—
446C2×Q8—24no—
447C2×Q8—24no—
448C2×Q8—74no—
449C2×Q8—72no—
450C2×Q8—148no—
451C2×Q8—141no—
452C2×Q8—142no—
453C2×Q8—142no—
454C2×Q8—144no—
455C2×Q8—144no—
456C2×Q8—142no—
457C2×Q8—288no—
458C2×Q8—288no—
459C2×Q8—288no—
460C2×Q8—2816no—
461C2×Q8C23×D714yes—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—144no—
466C2×D4—284no—
467C2×D4C23×D712yes—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—44no—
472C22×C4—71no—
473C22×C4—71no—
474C22×C4—71no—
475C22×C4—74no—
476C22×C4—74no—
477C22×C4—72no—
478C22×C4—72no—
479C22×C4—144no—
480C22×C4—148no—
481C22×C4—144no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—141no—
485C22×C4—141no—
486C22×C4—142no—
487C22×C4—288no—
488C22×C4D4×D711yescharacteristic
489C22×C4D4×D711yescharacteristic
490C22×C4C23×D711yescharacteristic
491Q16—288no—
492Q16—288no—
493SD16—48no—
494SD16—288no—
495C2×C8—24no—
496C2×C8—74no—
497C2×C8—144no—
498C2×C8C23×D714yes—
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—21no—
502C4⋊C4—72no—
503C4⋊C4—148no—
504C4⋊C4—148no—
505C4⋊C4—144no—
506C4⋊C4—144no—
507C4⋊C4—144no—
508C4⋊C4—144no—
509C4⋊C4—141no—
510C4⋊C4—144no—
511C4⋊C4—144no—
512C4⋊C4C23×D712yes—
513C22⋊C4—24no—
514C22⋊C4—144no—
515C22⋊C4—144no—
516C22⋊C4—144no—
517C22⋊C4—144no—
518C42—74no—
519C42—72no—
520C42—74no—
521C42—72no—
522C42—144no—
523C42D4×D712yes—
524C42C23×D712yes—
525C2×C7—82no—
526C2×C7#321814yescomplemented
527C2×C7C2×#53511yescharacteristic
528C2×C7C22×#13711yescharacteristic
529C2×C7C22×#13711yescharacteristic
530D7—24no—
531C23—22no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—74no—
536C23—72no—
537C23—142no—
538C23—142no—
539C23C2×D4×D711yescharacteristic
540Q8—24no—
541Q8—24no—
542Q8—44no—
543Q8—142no—
544Q8—144no—
545Q8—144no—
546Q8—142no—
547Q8—2816no—
548Q8—282no—
549Q8—284no—
550D4—22no—
551D4—22no—
552D4—42no—
553D4—288no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—48no—
560C2×C4—72no—
561C2×C4—72no—
562C2×C4—72no—
563C2×C4—148no—
564C2×C4—142no—
565C2×C4—142no—
566C2×C4—142no—
567C2×C4—148no—
568C2×C4—144no—
569C2×C4—142no—
570C2×C4—142no—
571C2×C4—142no—
572C2×C4—142no—
573C2×C4—144no—
574C2×C4—2816no—
575C2×C4—282no—
576C2×C4—284no—
577C2×C4—282no—
578C2×C4#647814yes—
579C2×C4C2×D4×D712yes—
580C2×C4C2×D4×D712yes—
581C2×C4C2×D4×D711yescharacteristic
582C2×C4#654812yes—
583C2×C4#655312yes—
584C2×C4C24×D711yescharacteristic
585C8—24no—
586C8—144no—
587C7C2×#321811yescharacteristic, complemented, Sylow
588C22—42no—
589C22—42no—
590C22—42no—
591C22—74no—
592C22—84no—
593C22—148no—
594C22—142no—
595C22—142no—
596C22#9029812yes—
597C22C2×#647812yes—
598C22D7×#13712yes—
599C22C22×D4×D711yescharacteristic
600C4—22no—
601C4—44no—
602C4—42no—
603C4—142no—
604C4—142no—
605C4—142no—
606C4—282no—
607C4—284no—
608C4—282no—
609C4#9029812yes—
610C4C2×#647814yes—
611C4C2×#654811yescharacteristic
612C4C2×#655311yescharacteristic
613C2—82no—
614C2—144no—
615C2#1173788014yesdirect product factor
616C2C2×#9029811yescharacteristic
617C2C22×#647811yescharacteristic
618C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#461C2
socleC23×C7C22×D4
prime radicalC2×#6501C22
hypercenterC2×#461D7
hypocenterC7C2×#3218
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×D7×C4⋊Q8C2semidirect
3. C2×C7×#461C2semidirect
5. C2×#89939C2semidirect
6. C2×#89862C2semidirect
7. C2×#89791C2semidirect
8. #11737880C2direct (N × H)
9. C2×#89621C2semidirect
10. C2×#89607C2semidirect
11. C2×#89580C2semidirect
12. C2×#89569C2semidirect
26. D7×C4⋊Q8C22semidirect
40. C7×#461C22semidirect
45. #89939C22semidirect
49. #89862C22semidirect
50. #89791C22semidirect
53. #89621C22semidirect
54. #89607C22semidirect
55. #89580C22semidirect
56. #89569C22semidirect
149. C2×#461D7semidirect
267. #461C2×D7semidirect
526. C2×C7#3218semidirect
587. C7C2×#3218semidirect
615. C2#11737880direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D7×C4⋊Q82
C2×#902482
C2×C7×#4612
C2×#899422
C2×#899392
C2×#898622
C2×#897912
#117378802
C2×#896212
C2×#896072
C2×#895802
C2×#895692
C2×#32187