Finite Group Databasebeta

← C2×#11728075 #13382730

Subgroups — C2×#11728075 #13382730

Order 1792.

1006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#418C211yesmaximal, characteristic
2C22×#6407C211yesmaximal, characteristic
3C2×#89987C211yesmaximal, characteristic
4C2×#89897C211yesmaximal, characteristic, complemented
5C2×#89351C211yesmaximal, characteristic, complemented
6C2×#89328C211yesmaximal, characteristic, complemented
7C2×#89326C211yesmaximal, characteristic, complemented
8#11728075C218yesmaximal, direct product factor
9C23×C7×D4C2211yescharacteristic
10C22×C7×M16C2211yescharacteristic
11C2×C7×#117C2211yescharacteristic
12C2×#6489C2211yescharacteristic
13C22×#1136C2211yescharacteristic
14C22×#1136C2211yescharacteristic
15C22×#1136C2211yescharacteristic
16C7×#418—22no—
17C7×#418C2214yes—
18C2×C7×#102—22no—
19C2×#6407—22no—
20C2×#6407—22no—
21C2×#6407C2214yes—
22#89987—22no—
23#89987C2214yes—
24C2×#6406—22no—
25#89897—22no—
26#89897C2214yescomplemented
27C2×#6393—22no—
28#89351C2214yescomplemented
29#89328C2214yescomplemented
30#89326C2214yescomplemented
31C2×#2081—71nomaximal, Sylow
32C25×C7—21no—
33C22×C7×D4—21no—
34C22×C7×D4—21no—
35C22×C7×D4—21no—
36C22×C7×D4—21no—
37C22×C7×D4—21no—
38C22×C7×D4—21no—
39C22×C7×D4—21no—
40C22×C7×D4—21no—
41C22×C7×D4—21no—
42C22×C7×D4—21no—
43C22×C7×D4—21no—
44C22×C7×D4D412yes—
45C22×C7×D4D412yes—
46C22×C7×D4C2312yes—
47C23×C4×C7C2311yescharacteristic
48C2×C7×M16—21no—
49C2×C7×M16—21no—
50C2×C7×M16—21no—
51C2×C7×M16—21no—
52C2×C7×M16D412yes—
53C2×C7×M16C2312yes—
54C22×C7×C8D412yes—
55C7×#117—21no—
56C7×#117—21no—
57C7×#117—21no—
58C7×#117C2312yes—
59C2×C7×C4⋊C4—21no—
60C2×C7×C22⋊C4—21no—
61C2×C42×C7—21no—
62C2×C22⋊Dic7—21no—
63#6489—21no—
64#6489—21no—
65#6489—21no—
66#6489C2312yes—
67C2×C4⋊Dic7—21no—
68C2×C4×Dic7—21no—
69C2×#1136—21no—
70C2×#1136—21no—
71C2×#1136—21no—
72C2×#1136—21no—
73C2×#1136—21no—
74C2×#1136—21no—
75C2×#1136—21no—
76C2×#1136—21no—
77C2×#1136—21no—
78C2×#1136—21no—
79C2×#1136—21no—
80C2×#1136—21no—
81C2×#1136—21no—
82C2×#1136—21no—
83C2×#1136—21no—
84C2×#1136C2312yes—
85C2×#1136C2312yes—
86C2×#1136C2312yes—
87C22×C7⋊C8—21no—
88C22×C7⋊C8—21no—
89C22×C7⋊C8—21no—
90C7×#102—28no—
91#6407—28no—
92#6406—28no—
93#6393—28no—
94C2×#430—71no—
95C2×#418—71no—
96C2×#418D711yescharacteristic
97C22×#100—71no—
98#2081—78no—
99C2×#344—71no—
100C2×#344—71no—
101C2×H(3,ℤ/4)—71no—
102C24×C7—22no—
103C24×C7—22no—
104C24×C7—22no—
105C24×C7—41no—
106C24×C7—41no—
107C24×C7—41no—
108C24×C7—41no—
109C24×C7—84no—
110C24×C7#4111yescharacteristic
111C2×C7×D4—22no—
112C2×C7×D4—22no—
113C2×C7×D4—22no—
114C2×C7×D4—22no—
115C2×C7×D4—22no—
116C2×C7×D4—22no—
117C2×C7×D4—22no—
118C2×C7×D4—22no—
119C2×C7×D4—22no—
120C2×C7×D4—22no—
121C2×C7×D4—22no—
122C2×C7×D4—22no—
123C2×C7×D4—22no—
124C2×C7×D4—22no—
125C2×C7×D4—22no—
126C2×C7×D4—41no—
127C2×C7×D4—41no—
128C2×C7×D4—41no—
129C2×C7×D4—41no—
130C2×C7×D4—41no—
131C2×C7×D4—41no—
132C2×C7×D4—41no—
133C2×C7×D4—41no—
134C2×C7×D4—41no—
135C2×C7×D4—41no—
136C2×C7×D4—41no—
137C2×C7×D4—41no—
138C2×C7×D4C2×D414yes—
139C22×C4×C7—41no—
140C22×C4×C7C2×D411yescharacteristic
141C22×C4×C7C2×D411yescharacteristic
142C22×C4×C7C2×D411yescharacteristic
143C22×C4×C7C2×D411yescharacteristic
144C22×C4×C7#4111yescharacteristic
145C22×C4×C7#4111yescharacteristic
146C22×C4×C7#4111yescharacteristic
147C22×C4×C7#4111yescharacteristic
148C22×C4×C7#4111yescharacteristic
149C22×C4×C7#4111yescharacteristic
150C22×C4×C7#4111yescharacteristic
151C22×C4×C7#4111yescharacteristic
152C22×C4×C7#4111yescharacteristic
153C22×C4×C7C2411yescharacteristic
154C22×Dic7—41no—
155C7×M16—22no—
156C7×M16—22no—
157C7×M16—22no—
158C7×M16—22no—
159C2×C7×C8—22no—
160C2×C7×C8—22no—
161C2×C7×C8C2×D414yes—
162C7×C4⋊C4—22no—
163C7×C4⋊C4—41no—
164C7×C22⋊C4—22no—
165C7×C22⋊C4—41no—
166C42×C7—22no—
167C42×C7—41no—
168C22⋊Dic7—22no—
169C22⋊Dic7—41no—
170C4⋊Dic7—22no—
171C4⋊Dic7—41no—
172C4×Dic7—22no—
173C4×Dic7—41no—
174#1136—22no—
175#1136—22no—
176#1136—22no—
177#1136—22no—
178#1136—22no—
179#1136—22no—
180#1136—41no—
181#1136—41no—
182#1136—41no—
183#1136—41no—
184#1136—41no—
185#1136—41no—
186C2×C7⋊C8—22no—
187C2×C7⋊C8—22no—
188C2×C7⋊C8—22no—
189C2×C7⋊C8—41no—
190C2×C7⋊C8—41no—
191C2×C7⋊C8—41no—
192C2×C7⋊C8—41no—
193C2×C7⋊C8—41no—
194C2×C7⋊C8—41no—
195C23×D4C2×D711yescharacteristic
196C22×M16—71no—
197C22×M16—71no—
198C22×M16—71no—
199C22×M16C2×D711yescharacteristic
200C2×#117—71no—
201C2×#117C2×D711yescharacteristic
202#430—74no—
203#430—142no—
204C2×#108—142no—
205#418—22no—
206#418—74no—
207#418—142no—
208#418C2×D714yes—
209C2×#102—22no—
210C2×#102—142no—
211C2×#100—74no—
212C2×#100—142no—
213C2×#100—142no—
214#344—74no—
215#344—74no—
216H(3,ℤ/4)—74no—
217C23×C7—24no—
218C23×C7—42no—
219C23×C7—42no—
220C23×C7—42no—
221C23×C7—42no—
222C23×C7—42no—
223C23×C7—42no—
224C23×C7—42no—
225C23×C7—84no—
226C23×C7—84no—
227C23×C7—84no—
228C23×C7—84no—
229C23×C7—84no—
230C23×C7—84no—
231C23×C7—84no—
232C23×C7#12311yescharacteristic
233C23×C7#12311yescharacteristic
234C23×C7#12411yescharacteristic
235C23×C7#12411yescharacteristic
236C23×C7#12611yescharacteristic
237C23×C7#12611yescharacteristic
238C23×C7C2×#4111yescharacteristic
239C7×D4—24no—
240C7×D4—24no—
241C7×D4—42no—
242C7×D4—42no—
243C7×D4—42no—
244C7×D4—42no—
245C7×D4—42no—
246C7×D4—42no—
247C2×C4×C7—42no—
248C2×C4×C7—82no—
249C2×C4×C7#12111yescharacteristic
250C2×C4×C7#12111yescharacteristic
251C2×C4×C7#12111yescharacteristic
252C2×C4×C7#12111yescharacteristic
253C2×C4×C7#12311yescharacteristic
254C2×C4×C7#12311yescharacteristic
255C2×C4×C7#12311yescharacteristic
256C2×C4×C7#12311yescharacteristic
257C2×C4×C7#12311yescharacteristic
258C2×C4×C7#12311yescharacteristic
259C2×C4×C7#12311yescharacteristic
260C2×C4×C7#12311yescharacteristic
261C2×C4×C7#12311yescharacteristic
262C2×C4×C7#12311yescharacteristic
263C2×C4×C7#12411yescharacteristic
264C2×C4×C7#12411yescharacteristic
265C2×C4×C7#12611yescharacteristic
266C2×C4×C7#12611yescharacteristic
267C2×C4×C7#12611yescharacteristic
268C2×C4×C7#12611yescharacteristic
269C2×C4×C7#12611yescharacteristic
270C2×C4×C7#12611yescharacteristic
271C2×C4×C7C22×D411yescharacteristic
272C2×C4×C7C22×D411yescharacteristic
273C2×C4×C7C2×#4111yescharacteristic
274C2×C4×C7C2×#4111yescharacteristic
275C2×C4×C7C2×#4111yescharacteristic
276C2×C4×C7C2×#4111yescharacteristic
277C2×Dic7—42no—
278C2×Dic7—82no—
279C7×C8—24no—
280C7⋊C8—42no—
281C7⋊C8—42no—
282C7⋊C8—42no—
283C25—21no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4D2812yes—
296C22×D4D2812yes—
297C22×D4C22×D712yes—
298C23×C4C22×D711yescharacteristic
299C2×M16—21no—
300C2×M16—21no—
301C2×M16—21no—
302C2×M16—21no—
303C2×M16—72no—
304C2×M16—72no—
305C2×M16—72no—
306C2×M16—141no—
307C2×M16—141no—
308C2×M16—141no—
309C2×M16—141no—
310C2×M16—141no—
311C2×M16—141no—
312C2×M16—141no—
313C2×M16—141no—
314C2×M16—141no—
315C2×M16—141no—
316C2×M16—141no—
317C2×M16—141no—
318C2×M16—141no—
319C2×M16—141no—
320C2×M16—141no—
321C2×M16C22⋊D712yes—
322C2×M16C22×D712yes—
323C22×C8—141no—
324C22×C8—141no—
325C22×C8—141no—
326C22×C8C22⋊D712yes—
327#117—21no—
328#117—21no—
329#117—21no—
330#117—72no—
331#117—141no—
332#117—141no—
333#117—141no—
334#117C22×D712yes—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—141no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—141no—
339C2×C42—21no—
340C2×C42—141no—
341#108—148no—
342#102—28no—
343#102—148no—
344#100—148no—
345C22×C7—22no—
346C22×C7—22no—
347C22×C7—22no—
348C22×C7—41no—
349C22×C7—41no—
350C22×C7—41no—
351C22×C7—41no—
352C22×C7—44no—
353C22×C7—84no—
354C22×C7—84no—
355C22×C7—84no—
356C22×C7—84no—
357C22×C7—84no—
358C22×C7—84no—
359C22×C7—84no—
360C22×C7#39711yescharacteristic
361C22×C7#39711yescharacteristic
362C22×C7#39711yescharacteristic
363C22×C7#39711yescharacteristic
364C22×C7C2×#12311yescharacteristic
365C22×C7C2×#12411yescharacteristic
366C22×C7C2×#12611yescharacteristic
367C4×C7—82no—
368C4×C7#39711yescharacteristic
369C4×C7#39711yescharacteristic
370C4×C7#39711yescharacteristic
371C4×C7#39711yescharacteristic
372C4×C7C2×#12111yescharacteristic
373C4×C7C2×#12311yescharacteristic
374C4×C7C2×#12311yescharacteristic
375C4×C7C2×#12611yescharacteristic
376Dic7—82no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—41no—
381C24—41no—
382C24—41no—
383C24—41no—
384C24—84no—
385C24#115911yescharacteristic
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4C2×D2814yes—
414C22×C4—41no—
415C22×C4—281no—
416C22×C4C2×D2811yescharacteristic
417C22×C4C2×D2811yescharacteristic
418C22×C4#115711yescharacteristic
419C22×C4#115711yescharacteristic
420C22×C4#115911yescharacteristic
421C22×C4#115911yescharacteristic
422C22×C4#115911yescharacteristic
423C22×C4#115911yescharacteristic
424C22×C4#115911yescharacteristic
425C22×C4#115911yescharacteristic
426C22×C4#115911yescharacteristic
427C22×C4C2×C22⋊D711yescharacteristic
428C22×C4C2×C22⋊D711yescharacteristic
429C22×C4C23×D711yescharacteristic
430M16—22no—
431M16—22no—
432M16—22no—
433M16—22no—
434M16—142no—
435M16—142no—
436M16—142no—
437M16—142no—
438M16—142no—
439M16—142no—
440M16—281no—
441M16—281no—
442M16—281no—
443M16—281no—
444M16—281no—
445M16—281no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—142no—
449C2×C8—142no—
450C2×C8—142no—
451C2×C8—281no—
452C2×C8—281no—
453C2×C8—281no—
454C2×C8—281no—
455C2×C8—281no—
456C2×C8—281no—
457C2×C8C2×C22⋊D714yes—
458C4⋊C4—22no—
459C4⋊C4—41no—
460C4⋊C4—142no—
461C4⋊C4—281no—
462C22⋊C4—22no—
463C22⋊C4—41no—
464C22⋊C4—142no—
465C22⋊C4—281no—
466C42—22no—
467C42—41no—
468C42—142no—
469C42—281no—
470C2×C7—21no—
471C2×C7—21no—
472C2×C7—21no—
473C2×C7—21no—
474C2×C7—21no—
475C2×C7—21no—
476C2×C7—84no—
477C2×C7#208112yescomplemented
478C2×C7C2×#39711yescharacteristic
479C23—24no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—84no—
488C23—84no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23—84no—
493C23—84no—
494C23#644211yescharacteristic
495C23#644211yescharacteristic
496C23#644911yescharacteristic
497C23#644911yescharacteristic
498C23#649911yescharacteristic
499C23#649911yescharacteristic
500C23C2×#115911yescharacteristic
501D4—24no—
502D4—24no—
503D4—42no—
504D4—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—42no—
509C2×C4—42no—
510C2×C4—82no—
511C2×C4—282no—
512C2×C4—562no—
513C2×C4#644211yescharacteristic
514C2×C4#644211yescharacteristic
515C2×C4#644211yescharacteristic
516C2×C4#644211yescharacteristic
517C2×C4#644211yescharacteristic
518C2×C4#644211yescharacteristic
519C2×C4#644911yescharacteristic
520C2×C4#644911yescharacteristic
521C2×C4#644911yescharacteristic
522C2×C4#644911yescharacteristic
523C2×C4#644911yescharacteristic
524C2×C4#644911yescharacteristic
525C2×C4#649311yescharacteristic
526C2×C4#649311yescharacteristic
527C2×C4#649311yescharacteristic
528C2×C4#649311yescharacteristic
529C2×C4#649811yescharacteristic
530C2×C4#649811yescharacteristic
531C2×C4#649811yescharacteristic
532C2×C4#649811yescharacteristic
533C2×C4#649911yescharacteristic
534C2×C4#649911yescharacteristic
535C2×C4C22×D2811yescharacteristic
536C2×C4C2×#115711yescharacteristic
537C2×C4C2×#115911yescharacteristic
538C2×C4C2×#115911yescharacteristic
539C2×C4C2×#115911yescharacteristic
540C2×C4C22×C22⋊D711yescharacteristic
541C8—24no—
542C8—282no—
543C8—282no—
544C8—282no—
545C7C2×#208111yescharacteristic, complemented, Sylow
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—44no—
554C22—84no—
555C22—84no—
556C22—84no—
557C22—84no—
558C22—84no—
559C22—84no—
560C22—84no—
561C22#8972511yescharacteristic
562C22#8972511yescharacteristic
563C22#8972511yescharacteristic
564C22#8972511yescharacteristic
565C22C2×#644211yescharacteristic
566C22C2×#644911yescharacteristic
567C22C2×#649911yescharacteristic
568C4—82no—
569C4—562no—
570C4#8972511yescharacteristic
571C4#8972511yescharacteristic
572C4#8972511yescharacteristic
573C4#8972511yescharacteristic
574C4C2×#644211yescharacteristic
575C4C2×#644911yescharacteristic
576C4C2×#649311yescharacteristic
577C4C2×#649811yescharacteristic
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—21no—
583C2—21no—
584C2—84no—
585C2#1172807512yesdirect product factor
586C2C2×#8972511yescharacteristic
subgroupG/H
centerC22#89725
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#418C2
socleC22×C7#397
prime radicalC23×C7×D4C22
hypercenterC2×#418D7
hypocenterC7C2×#2081
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
4. C2×#89897C2semidirect
5. C2×#89351C2semidirect
6. C2×#89328C2semidirect
7. C2×#89326C2semidirect
8. #11728075C2direct (N × H)
26. #89897C22semidirect
28. #89351C22semidirect
29. #89328C22semidirect
30. #89326C22semidirect
477. C2×C7#2081semidirect
545. C7C2×#2081semidirect
585. C2#11728075direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4182
C22×#64072
C2×#899872
C2×#898972
C2×#893512
C2×#893282
C2×#893262
#117280752
C2×#20817