Finite Group Databasebeta

← C2×#11737925 #14224986

Subgroups — C2×#11737925 #14224986

Order 1792.

2134 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C4⋊Q8C211yesmaximal, characteristic
2C2×#90269C211yesmaximal, characteristic
3C2×C7×#462C211yesmaximal, characteristic, complemented
4C2×#89958C212yesmaximal
5C2×#89953C212yesmaximal, complemented
6C2×#89862C211yesmaximal, characteristic, complemented
7C2×#89803C211yesmaximal, characteristic, complemented
8#11737925C2116yesmaximal, direct product factor
9C2×#89621C211yesmaximal, characteristic, complemented
10C2×#89605C211yesmaximal, characteristic
11C2×#89580C212yesmaximal
12C2×#89564C212yesmaximal, complemented
13C22×Q8×D7C2212yes—
14C22×C7×Q16C2212yes—
15C2×C7×C4⋊Q8C2211yescharacteristic
16C2×C4×C7×Q8C2211yescharacteristic
17C2×#6509C2211yescharacteristic
18C2×#6507C2212yes—
19C2×#6507C2211yescharacteristic
20C22×#1144C2212yes—
21C22×#1144C2212yes—
22C22×Dic28C2212yes—
23D7×C4⋊Q8—24no—
24D7×C4⋊Q8C2218yes—
25#90269—24no—
26#90269C2218yes—
27C2×#6460C2211yescharacteristic
28C2×#6459—21no—
29C2×D7×C4⋊C4—21no—
30C2×D7×C4⋊C4—21no—
31C2×#6452—21no—
32C2×#6451—21no—
33C2×#6451—21no—
34C2×#6451C2211yescharacteristic
35C2×#6435—21no—
36C2×C42×D7C2211yescharacteristic
37C2×#6432C2211yescharacteristic
38C2×C4×Dic14—21no—
39C2×C4×Dic14C2211yescharacteristic
40C7×#462C2218yescomplemented
41C2×C7×C4⋊C8C2211yescharacteristic
42C2×C7×#103C2212yes—
43C2×#6409C2212yes—
44#89958C22116yes—
45#89953C22116yescomplemented
46C2×(C2×D7)⋊C8C2212yes—
47C2×#6390C2212yes—
48C2×C8×Dic7C2212yes—
49#89862C2218yescomplemented
50#89803C2218yescomplemented
51C2×#6384C2212yes—
52C2×C4⋊(C7⋊C8)C2211yescharacteristic
53#89621C2218yescomplemented
54#89605C2218yes—
55#89580C22116yes—
56#89564C22116yescomplemented
57C2×#3209—71nomaximal, Sylow
58C22×C7×Q8C2311yescharacteristic
59C22×C7×Q8C2312yes—
60C2×Q8×D7—24no—
61C2×Q8×D7—44no—
62C2×Q8×D7—44no—
63C2×Q8×D7C2318yes—
64C22×C4×D7—22no—
65C22×C4×D7D411yescharacteristic
66C22×C4×D7D411yescharacteristic
67C22×C4×D7C2311yescharacteristic
68C22×Dic14—21no—
69C22×Dic14—22no—
70C22×Dic14C2312yes—
71C22×Dic14C2311yescharacteristic
72C2×C7×Q16—44no—
73C2×C7×Q16C2318yes—
74C22×C7×C8C2312yes—
75C7×C4⋊Q8—22no—
76C7×C4⋊Q8C2314yes—
77C4×C7×Q8—22no—
78C4×C7×Q8C2314yes—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4—21no—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C42×C7—21no—
84C2×C42×C7C2311yescharacteristic
85#6509—22no—
86#6509C2314yes—
87#6507—24no—
88#6507—22no—
89#6507C2318yes—
90#6507C2314yes—
91C2×#1144—44no—
92C2×#1144—44no—
93C2×#1144C2318yes—
94C2×#1144C2318yes—
95C2×(C2×D7)⋊C4—21no—
96C2×(C2×D7)⋊C4—21no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7—21no—
99C2×C4⋊Dic7—21no—
100C2×C4⋊Dic7C2311yescharacteristic
101C2×Dic7⋊C4—21no—
102C2×Dic7⋊C4—21no—
103C2×Dic7⋊C4—21no—
104C2×Dic7⋊C4—21no—
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—22no—
107C2×Dic7⋊C4—22no—
108C2×C4×Dic7—21no—
109C2×C4×Dic7D411yescharacteristic
110C2×C4×Dic7D411yescharacteristic
111C2×C4×Dic7C2311yescharacteristic
112C22×C7⋊C8C2312yes—
113C2×Dic28—44no—
114C2×Dic28C2318yes—
115#6460—22no—
116#6460C2314yes—
117#6459—28no—
118D7×C4⋊C4—28no—
119D7×C4⋊C4—28no—
120#6452—28no—
121#6451—28no—
122#6451—28no—
123#6451—22no—
124#6451C2314yes—
125#6435—28no—
126C42×D7D414yes—
127C42×D7C2314yes—
128#6432—22no—
129#6432C2314yes—
130C4×Dic14—22no—
131C4×Dic14—28no—
132C4×Dic14C2314yes—
133C7×C4⋊C8C2314yes—
134C7×#103C2318yes—
135#6409C2318yes—
136(C2×D7)⋊C8C2318yes—
137#6390C2318yes—
138C8×Dic7C2318yes—
139#6384C2318yes—
140C4⋊(C7⋊C8)C2314yes—
141C2×#533—71no—
142C22×C4⋊Q8—71no—
143#3209—716no—
144C2×#494—72no—
145C2×#487—72no—
146C2×#462—71no—
147C2×#462—71no—
148C2×#462—71no—
149C2×#462D711yescharacteristic, complemented
150C2×#451—72no—
151C2×#451—72no—
152C2×#431—71no—
153C23×D7C2×D411yescharacteristic
154C2×C7×Q8—21no—
155C2×C7×Q8—22no—
156C2×C7×Q8—22no—
157C2×C7×Q8—24no—
158C2×C7×Q8—22no—
159C2×C7×Q8—24no—
160C2×C7×Q8C2414yes—
161C2×C7×Q8C2412yes—
162C22×C4×C7—21no—
163C22×C4×C7—22no—
164C22×C4×C7—21no—
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2411yescharacteristic
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—22no—
171C22×Dic7C2×D411yescharacteristic
172C22×Dic7C2×D411yescharacteristic
173C22×Dic7C2×D411yescharacteristic
174Q8×D7—48no—
175Q8×D7—48no—
176Q8×D7—416no—
177C2×C4×D7—22no—
178C2×C4×D7—22no—
179C2×C4×D7—24no—
180C2×C4×D7—28no—
181C2×C4×D7—48no—
182C2×C4×D7Q1618yescomplemented
183C2×C4×D7C2×D412yes—
184C2×C4×D7C2×D414yes—
185C2×C4×D7C2×D414yes—
186C2×C4×D7C2412yes—
187C2×Dic14—22no—
188C2×Dic14—24no—
189C2×Dic14—22no—
190C2×Dic14—24no—
191C2×Dic14—21no—
192C2×Dic14—22no—
193C2×Dic14—24no—
194C2×Dic14—28no—
195C2×Dic14—48no—
196C2×Dic14—44no—
197C2×Dic14C2412yes—
198C2×Dic14C2414yes—
199C7×Q16—48no—
200C2×C7×C8—24no—
201C2×C7×C8C2414yes—
202C7×C4⋊C4—24no—
203C7×C4⋊C4—24no—
204C7×C4⋊C4—21no—
205C7×C4⋊C4—24no—
206C7×C4⋊C4C2412yes—
207C42×C7—24no—
208C42×C7C2×D412yes—
209C42×C7C2412yes—
210#1144—48no—
211#1144—48no—
212(C2×D7)⋊C4—24no—
213(C2×D7)⋊C4—24no—
214C4⋊Dic7—21no—
215C4⋊Dic7—24no—
216C4⋊Dic7—24no—
217C4⋊Dic7—24no—
218C4⋊Dic7C2412yes—
219Dic7⋊C4—24no—
220Dic7⋊C4—24no—
221Dic7⋊C4—24no—
222Dic7⋊C4—24no—
223Dic7⋊C4—24no—
224Dic7⋊C4—28no—
225Dic7⋊C4—28no—
226C4×Dic7—24no—
227C4×Dic7C2×D414yes—
228C4×Dic7C2×D412yes—
229C4×Dic7C2×D414yes—
230C4×Dic7C2412yes—
231C2×C7⋊C8—24no—
232C2×C7⋊C8C2414yes—
233Dic28—48no—
234C23×Q8—72no—
235C22×Q16—72no—
236C22×Q16—72no—
237C22×Q16—72no—
238C22×Q16C2×D712yes—
239#533—78no—
240#533—144no—
241C2×C4⋊Q8—71no—
242C2×C4⋊Q8—72no—
243C2×C4⋊Q8—71no—
244C2×C4⋊Q8—78no—
245C2×C4⋊Q8—71no—
246C2×C4⋊Q8—141no—
247C2×C4⋊Q8—141no—
248C2×C4⋊Q8—144no—
249C2×C4⋊Q8C2×D711yescharacteristic
250C2×#125—141no—
251C2×C22⋊Q8—71no—
252C2×C22⋊Q8—71no—
253C2×C22⋊Q8—141no—
254C2×C4×Q8—71no—
255C2×C4×Q8—141no—
256C2×C4×Q8C2×D711yescharacteristic
257C2×#117—141no—
258C22×C4⋊C4—141no—
259C22×C4⋊C4—141no—
260C22×C42—71no—
261#494—716no—
262#487—716no—
263#462—78no—
264#462—78no—
265#462—78no—
266#462C2×D718yescomplemented
267#451—716no—
268#451—716no—
269#431—78no—
270C2×C4⋊C8—71no—
271C2×C4⋊C8C2×D711yescharacteristic
272C2×#103—72no—
273C2×#103—72no—
274C2×#103—72no—
275C2×#103C2×D712yes—
276C2×C22⋊C8—72no—
277C2×C4×C8—72no—
278C23×C7C22×D411yescharacteristic
279C22×D7—22no—
280C22×D7—22no—
281C22×D7C2×Q1614yes—
282C22×D7C22×D412yes—
283C7×Q8—22no—
284C7×Q8—24no—
285C7×Q8—22no—
286C7×Q8—24no—
287C7×Q8—44no—
288C7×Q8—42no—
289C2×C4×C7—22no—
290C2×C4×C7—22no—
291C2×C4×C7—24no—
292C2×C4×C7—22no—
293C2×C4×C7—44no—
294C2×C4×C7—42no—
295C2×C4×C7—42no—
296C2×C4×C7C2×Q1614yes—
297C2×C4×C7C22×D412yes—
298C2×C4×C7C22×D411yescharacteristic
299C2×C4×C7C22×D412yes—
300C2×C4×C7H(5,𝔽2)12yes—
301C2×C4×C7H(5,𝔽2)12yes—
302C2×C4×C7C2511yescharacteristic
303C2×Dic7—22no—
304C2×Dic7—22no—
305C2×Dic7—22no—
306C2×Dic7—24no—
307C2×Dic7—44no—
308C2×Dic7—42no—
309C2×Dic7—42no—
310C2×Dic7C2×Q1614yes—
311C2×Dic7#13714yes—
312C2×Dic7C22×D412yes—
313C2×Dic7C22×D412yes—
314C2×Dic7C22×D412yes—
315C4×D7—24no—
316C4×D7—22no—
317C4×D7—22no—
318C4×D7—28no—
319C4×D7—416no—
320C4×D7C2×Q16116yescomplemented
321Dic14—22no—
322Dic14—24no—
323Dic14—22no—
324Dic14—24no—
325Dic14—416no—
326Dic14—42no—
327Dic14—44no—
328Dic14—48no—
329C7×C8—24no—
330C7⋊C8—24no—
331C22×Q8—78no—
332C22×Q8—71no—
333C22×Q8—72no—
334C22×Q8—141no—
335C22×Q8—142no—
336C22×Q8—144no—
337C22×Q8—284no—
338C22×Q8—284no—
339C22×Q8C22×D711yescharacteristic
340C22×Q8C22×D712yes—
341C23×C4—71no—
342C23×C4—71no—
343C23×C4—71no—
344C23×C4—142no—
345C2×Q16—44no—
346C2×Q16—78no—
347C2×Q16—78no—
348C2×Q16—78no—
349C2×Q16—284no—
350C2×Q16—284no—
351C2×Q16—284no—
352C2×Q16C22×D718yes—
353C22×C8—72no—
354C22×C8C22×D712yes—
355C4⋊Q8—22no—
356C4⋊Q8—74no—
357C4⋊Q8—78no—
358C4⋊Q8—74no—
359C4⋊Q8—74no—
360C4⋊Q8—148no—
361C4⋊Q8—148no—
362C4⋊Q8—142no—
363C4⋊Q8—144no—
364C4⋊Q8—142no—
365C4⋊Q8—142no—
366C4⋊Q8C22×D714yes—
367#125—148no—
368C22⋊Q8—74no—
369C22⋊Q8—74no—
370C22⋊Q8—142no—
371C22⋊Q8—148no—
372C22⋊Q8—142no—
373C4×Q8—22no—
374C4×Q8—74no—
375C4×Q8—148no—
376C4×Q8—142no—
377C4×Q8C22×D714yes—
378#117—148no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—71no—
383C2×C4⋊C4—148no—
384C2×C4⋊C4—148no—
385C2×C4⋊C4—142no—
386C2×C4⋊C4—142no—
387C2×C4⋊C4—141no—
388C2×C4⋊C4—141no—
389C2×C4⋊C4—141no—
390C2×C4⋊C4—141no—
391C2×C4⋊C4—141no—
392C2×C4⋊C4—141no—
393C2×C4⋊C4—141no—
394C2×C4⋊C4—141no—
395C2×C4⋊C4C22×D711yescharacteristic
396C2×C22⋊C4—141no—
397C2×C22⋊C4—141no—
398C2×C42—21no—
399C2×C42—71no—
400C2×C42—71no—
401C2×C42—71no—
402C2×C42—74no—
403C2×C42—74no—
404C2×C42—141no—
405C2×C42C22×D711yescharacteristic
406C4⋊C8—74no—
407C4⋊C8C22×D714yes—
408#103—78no—
409#103—78no—
410#103—78no—
411#103C22×D718yes—
412C22⋊C8—78no—
413C4×C8—78no—
414C22×C7#53512yes—
415C22×C7C22×Q1612yes—
416C22×C7C2×#13712yes—
417C22×C7C23×D411yescharacteristic
418C2×D7—22no—
419C2×D7—28no—
420C2×D7—22no—
421C2×D7C22×Q1614yes—
422C4×C7—22no—
423C4×C7—44no—
424C4×C7—42no—
425C4×C7—42no—
426C4×C7#53512yes—
427C4×C7C22×Q1614yes—
428C4×C7C2×H(5,𝔽2)11yescharacteristic
429C4×C7C2×H(5,𝔽2)11yescharacteristic
430Dic7—22no—
431Dic7—44no—
432Dic7—42no—
433Dic7—42no—
434Dic7C22×Q1614yes—
435Dic7C2×#13714yes—
436C24—71no—
437C2×Q8—21no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—24no—
441C2×Q8—22no—
442C2×Q8—24no—
443C2×Q8—74no—
444C2×Q8—72no—
445C2×Q8—144no—
446C2×Q8—148no—
447C2×Q8—141no—
448C2×Q8—142no—
449C2×Q8—142no—
450C2×Q8—144no—
451C2×Q8—142no—
452C2×Q8—144no—
453C2×Q8—284no—
454C2×Q8—288no—
455C2×Q8—288no—
456C2×Q8—288no—
457C2×Q8—2816no—
458C2×Q8C23×D714yes—
459C2×Q8C23×D712yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—71no—
464C22×C4—71no—
465C22×C4—78no—
466C22×C4—74no—
467C22×C4—71no—
468C22×C4—74no—
469C22×C4—72no—
470C22×C4—72no—
471C22×C4—144no—
472C22×C4—148no—
473C22×C4—142no—
474C22×C4—142no—
475C22×C4—141no—
476C22×C4—141no—
477C22×C4—142no—
478C22×C4—288no—
479C22×C4D4×D711yescharacteristic
480C22×C4D4×D711yescharacteristic
481C22×C4C23×D711yescharacteristic
482Q16—48no—
483Q16—288no—
484Q16—288no—
485Q16—288no—
486C2×C8—24no—
487C2×C8—74no—
488C2×C8—144no—
489C2×C8C23×D714yes—
490C4⋊C4—24no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—21no—
494C4⋊C4—72no—
495C4⋊C4—148no—
496C4⋊C4—148no—
497C4⋊C4—144no—
498C4⋊C4—144no—
499C4⋊C4—144no—
500C4⋊C4—144no—
501C4⋊C4—144no—
502C4⋊C4—144no—
503C4⋊C4—141no—
504C4⋊C4—144no—
505C4⋊C4—144no—
506C4⋊C4C23×D712yes—
507C22⋊C4—144no—
508C22⋊C4—144no—
509C42—24no—
510C42—74no—
511C42—74no—
512C42—72no—
513C42—72no—
514C42—144no—
515C42D4×D712yes—
516C42C23×D712yes—
517C2×C7#320914yescomplemented
518C2×C7C2×#53511yescharacteristic
519C2×C7C23×Q1611yescharacteristic
520C2×C7C22×#13711yescharacteristic
521D7—24no—
522C23—74no—
523C23—72no—
524C23—142no—
525C23—142no—
526C23C2×D4×D711yescharacteristic
527Q8—22no—
528Q8—24no—
529Q8—22no—
530Q8—24no—
531Q8—42no—
532Q8—44no—
533Q8—142no—
534Q8—144no—
535Q8—142no—
536Q8—144no—
537Q8—288no—
538Q8—2816no—
539Q8—282no—
540Q8—284no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—44no—
547C2×C4—42no—
548C2×C4—74no—
549C2×C4—74no—
550C2×C4—72no—
551C2×C4—72no—
552C2×C4—716no—
553C2×C4—72no—
554C2×C4—148no—
555C2×C4—142no—
556C2×C4—144no—
557C2×C4—142no—
558C2×C4—142no—
559C2×C4—142no—
560C2×C4—142no—
561C2×C4—144no—
562C2×C4—2816no—
563C2×C4—282no—
564C2×C4—284no—
565C2×C4—282no—
566C2×C4D7×Q1614yes—
567C2×C4C2×D4×D712yes—
568C2×C4C2×D4×D712yes—
569C2×C4C2×D4×D711yescharacteristic
570C2×C4#654812yes—
571C2×C4#655312yes—
572C2×C4C24×D711yescharacteristic
573C8—24no—
574C8—144no—
575C7C2×#320911yescharacteristic, complemented, Sylow
576C22—74no—
577C22—142no—
578C22—142no—
579C22—148no—
580C22#9029812yes—
581C22C2×D7×Q1612yes—
582C22D7×#13712yes—
583C22C22×D4×D711yescharacteristic
584C4—22no—
585C4—42no—
586C4—44no—
587C4—42no—
588C4—74no—
589C4—74no—
590C4—142no—
591C4—282no—
592C4—284no—
593C4—282no—
594C4#9029812yes—
595C4C2×D7×Q1614yes—
596C4C2×#654811yescharacteristic
597C4C2×#655311yescharacteristic
598C2—144no—
599C2#1173792514yesdirect product factor
600C2C2×#9029811yescharacteristic
601C2C22×D7×Q1611yescharacteristic
602C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#462C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenterC2×#462D7
hypocenterC7C2×#3209
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. C2×C7×#462C2semidirect
5. C2×#89953C2semidirect
6. C2×#89862C2semidirect
7. C2×#89803C2semidirect
8. #11737925C2direct (N × H)
9. C2×#89621C2semidirect
12. C2×#89564C2semidirect
40. C7×#462C22semidirect
45. #89953C22semidirect
49. #89862C22semidirect
50. #89803C22semidirect
53. #89621C22semidirect
56. #89564C22semidirect
149. C2×#462D7semidirect
182. C2×C4×D7Q16semidirect
266. #462C2×D7semidirect
320. C4×D7C2×Q16semidirect
517. C2×C7#3209semidirect
575. C7C2×#3209semidirect
599. C2#11737925direct (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×#902692
C2×C7×#4622
C2×#899582
C2×#899532
C2×#898622
C2×#898032
#117379252
C2×#896212
C2×#896052
C2×#895802
C2×#895642
C2×#32097