Finite Group Databasebeta

← C7×#14002 #13191218

Subgroups — C7×#14002 #13191218

Order 1792.

1838 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#390C211yesmaximal, characteristic
2C2×C7×#390C211yesmaximal, characteristic
3C2×C7×#390C211yesmaximal, characteristic
4C2×C7×#382C211yesmaximal, characteristic, complemented
5C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
6C7×#1440C214yesmaximal, complemented
7C7×#1437C214yesmaximal, complemented
8C7×C4⋊#95C211yesmaximal, characteristic, complemented
9C4×C7×#95C211yesmaximal, characteristic, complemented
10C23×C7×D4C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C22⋊C4C2212yes—
15C22×C7×C22⋊C4C2214yes—
16C22×C7×C22⋊C4C2212yes—
17C22×C7×C22⋊C4C2214yes—
18C22×C42×C7C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C42×C7C2212yes—
22C7×#390—24no—
23C7×#390—24no—
24C7×#390C418yescomplemented
25C7×#382—24no—
26C4×C7×C4⋊C4—24no—
27C2×C7×#95C2212yes—
28C2×C7×#95C2214yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2214yes—
32#14002C711yesmaximal, characteristic, direct product factor, Sylow
33C25×C7C2312yes—
34C22×C7×D4—22no—
35C22×C7×D4—22no—
36C22×C7×D4—22no—
37C22×C7×D4—22no—
38C22×C7×D4—22no—
39C22×C7×D4—22no—
40C22×C7×D4C2×C414yes—
41C23×C4×C7C2312yes—
42C23×C4×C7C2312yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2312yes—
46C23×C4×C7C2312yes—
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C2×C7×C4⋊C4—22no—
50C2×C7×C4⋊C4—22no—
51C2×C7×C4⋊C4—22no—
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4C2×C414yes—
57C2×C7×C4⋊C4D414yes—
58C2×C7×C22⋊C4—28no—
59C2×C7×C22⋊C4—24no—
60C2×C7×C22⋊C4—24no—
61C2×C7×C22⋊C4—28no—
62C2×C7×C22⋊C4—28no—
63C2×C7×C22⋊C4—44no—
64C2×C7×C22⋊C4—44no—
65C2×C7×C22⋊C4—44no—
66C2×C7×C22⋊C4—44no—
67C2×C7×C22⋊C4C2×C4116yes—
68C2×C42×C7—22no—
69C2×C42×C7—22no—
70C2×C42×C7—22no—
71C2×C42×C7—22no—
72C2×C42×C7—24no—
73C2×C42×C7—22no—
74C2×C42×C7—22no—
75C2×C42×C7—22no—
76C2×C42×C7—44no—
77C2×C42×C7C2×C414yes—
78C2×C42×C7D414yes—
79C7×#95—24no—
80C7×#95—28no—
81C7×#95—24no—
82C7×#95—24no—
83C7×#95—44no—
84C2×#390C2×C711yescharacteristic
85C2×#390C2×C711yescharacteristic
86C2×#390C2×C711yescharacteristic
87C2×#382C2×C711yescharacteristic, complemented
88C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
89#1440C2×C714yescomplemented
90#1437C2×C714yescomplemented
91C4⋊#95C2×C711yescharacteristic, complemented
92C4×#95C2×C711yescharacteristic, complemented
93C24×C7—22no—
94C24×C7—22no—
95C24×C7—24no—
96C24×C7—24no—
97C24×C7—22no—
98C24×C7—22no—
99C24×C7—22no—
100C24×C7—22no—
101C24×C7—24no—
102C24×C7—24no—
103C24×C7C22×C414yes—
104C24×C7C2411yescharacteristic
105C2×C7×D4—28no—
106C2×C7×D4—28no—
107C2×C7×D4—28no—
108C2×C7×D4—44no—
109C2×C7×D4—44no—
110C2×C7×D4—44no—
111C2×C7×D4—44no—
112C22×C4×C7—21no—
113C22×C4×C7—21no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—24no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—24no—
133C22×C4×C7—24no—
134C22×C4×C7—24no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—24no—
142C22×C4×C7—22no—
143C22×C4×C7—24no—
144C22×C4×C7C22×C414yes—
145C22×C4×C7C22×C414yes—
146C22×C4×C7C22×C412yes—
147C22×C4×C7C2×D412yes—
148C22×C4×C7C2×D414yes—
149C22×C4×C7C2×D412yes—
150C22×C4×C7C2×D412yes—
151C22×C4×C7C2×D412yes—
152C22×C4×C7#4114yes—
153C22×C4×C7#4114yes—
154C22×C4×C7#4112yes—
155C22×C4×C7#4112yes—
156C22×C4×C7#4112yes—
157C22×C4×C7#4112yes—
158C7×C4⋊C4—28no—
159C7×C4⋊C4—28no—
160C7×C4⋊C4—44no—
161C7×C22⋊C4—416no—
162C7×C22⋊C4—416no—
163C7×C22⋊C4—48no—
164C7×C22⋊C4—48no—
165C42×C7—28no—
166C42×C7—28no—
167C42×C7—48no—
168C42×C7—44no—
169C23×D4C22×C711yescharacteristic
170C22×C4⋊C4C22×C711yescharacteristic
171C22×C4⋊C4C22×C711yescharacteristic
172C22×C4⋊C4C22×C711yescharacteristic
173C22×C22⋊C4C22×C712yes—
174C22×C22⋊C4C22×C714yes—
175C22×C22⋊C4C22×C712yes—
176C22×C22⋊C4C22×C714yes—
177C22×C42C22×C711yescharacteristic
178C22×C42C22×C711yescharacteristic
179C22×C42C22×C711yescharacteristic
180C22×C42C22×C712yes—
181#390—24no—
182#390—24no—
183#390C4×C718yescomplemented
184#382—24no—
185C4×C4⋊C4—24no—
186C2×#95C22×C712yes—
187C2×#95C22×C712yes—
188C2×#95C22×C714yes—
189C2×#95C22×C712yes—
190C2×#95C22×C714yes—
191C23×C7—24no—
192C23×C7—24no—
193C23×C7—24no—
194C23×C7—28no—
195C23×C7—28no—
196C23×C7—42no—
197C23×C7—42no—
198C23×C7—42no—
199C23×C7—42no—
200C23×C7—42no—
201C23×C7—44no—
202C23×C7—42no—
203C23×C7—42no—
204C23×C7—42no—
205C23×C7—44no—
206C23×C7—44no—
207C23×C7—44no—
208C23×C7—44no—
209C23×C7—44no—
210C23×C7—44no—
211C23×C7—44no—
212C23×C7—44no—
213C23×C7—44no—
214C23×C7C23×C411yescharacteristic
215C23×C7C22×D411yescharacteristic
216C23×C7C22×D411yescharacteristic
217C23×C7C2×#4111yescharacteristic
218C23×C7C2×#4111yescharacteristic
219C23×C7C2×#4111yescharacteristic
220C23×C7C2×#4111yescharacteristic
221C23×C7C2×#4112yes—
222C23×C7C2×#4112yes—
223C23×C7H(5,𝔽2)12yes—
224C23×C7H(5,𝔽2)12yes—
225C7×D4—416no—
226C2×C4×C7—22no—
227C2×C4×C7—22no—
228C2×C4×C7—24no—
229C2×C4×C7—24no—
230C2×C4×C7—24no—
231C2×C4×C7—24no—
232C2×C4×C7—24no—
233C2×C4×C7—24no—
234C2×C4×C7—28no—
235C2×C4×C7—24no—
236C2×C4×C7—22no—
237C2×C4×C7—24no—
238C2×C4×C7—22no—
239C2×C4×C7—22no—
240C2×C4×C7—24no—
241C2×C4×C7—28no—
242C2×C4×C7—24no—
243C2×C4×C7—42no—
244C2×C4×C7—42no—
245C2×C4×C7—42no—
246C2×C4×C7—42no—
247C2×C4×C7—42no—
248C2×C4×C7—44no—
249C2×C4×C7—42no—
250C2×C4×C7—42no—
251C2×C4×C7—42no—
252C2×C4×C7—42no—
253C2×C4×C7—42no—
254C2×C4×C7—42no—
255C2×C4×C7—42no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—44no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—44no—
263C2×C4×C7—44no—
264C2×C4×C7#11714yes—
265C2×C4×C7C4×D414yes—
266C2×C4×C7C4×D414yes—
267C2×C4×C7#12114yes—
268C2×C4×C7#12314yes—
269C2×C4×C7#12414yes—
270C2×C4×C7#12414yes—
271C2×C4×C7#12614yes—
272C25C23×C712yes—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4C2×C4×C714yes—
280C23×C4C23×C712yes—
281C23×C4C23×C712yes—
282C23×C4C23×C712yes—
283C23×C4C23×C712yes—
284C23×C4C23×C711yescharacteristic
285C23×C4C23×C712yes—
286C23×C4C23×C711yescharacteristic
287C23×C4C23×C711yescharacteristic
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4C2×C4×C714yes—
296C2×C4⋊C4C7×D414yes—
297C2×C22⋊C4—28no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—28no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—44no—
303C2×C22⋊C4—44no—
304C2×C22⋊C4—44no—
305C2×C22⋊C4—44no—
306C2×C22⋊C4C2×C4×C7116yes—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—24no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—44no—
316C2×C42C2×C4×C714yes—
317C2×C42C7×D414yes—
318#95—24no—
319#95—28no—
320#95—24no—
321#95—24no—
322#95—44no—
323C22×C7—44no—
324C22×C7—48no—
325C22×C7—48no—
326C22×C7—44no—
327C22×C7—44no—
328C22×C7—84no—
329C22×C7—82no—
330C22×C7—82no—
331C22×C7—84no—
332C22×C7—82no—
333C22×C7—82no—
334C22×C7C2×#11711yescharacteristic
335C22×C7C2×C4×D411yescharacteristic
336C22×C7C2×C4×D411yescharacteristic
337C22×C7C4×#4112yes—
338C22×C7#51812yes—
339C22×C7C2×#12111yescharacteristic
340C22×C7C2×#12311yescharacteristic
341C22×C7C2×#12411yescharacteristic
342C22×C7C2×#12411yescharacteristic
343C22×C7C2×#12611yescharacteristic
344C22×C7#52912yes—
345C22×C7#53211yescharacteristic
346C22×C7#53511yescharacteristic
347C22×C7#53511yescharacteristic
348C22×C7#54012yes—
349C22×C7#54612yes—
350C22×C7#55012yes—
351C22×C7#55312yes—
352C22×C7#55312yes—
353C22×C7#55312yes—
354C22×C7#55512yes—
355C22×C7#55912yes—
356C22×C7#55912yes—
357C4×C7—24no—
358C4×C7—44no—
359C4×C7—44no—
360C4×C7—44no—
361C4×C7—42no—
362C4×C7—44no—
363C4×C7—82no—
364C4×C7#38818yes—
365C24—22no—
366C24—22no—
367C24—24no—
368C24—24no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—24no—
374C24—24no—
375C24C22×C4×C714yes—
376C24C24×C711yescharacteristic
377C2×D4—28no—
378C2×D4—28no—
379C2×D4—28no—
380C2×D4—44no—
381C2×D4—44no—
382C2×D4—44no—
383C2×D4—44no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4C22×C4×C714yes—
417C22×C4C22×C4×C714yes—
418C22×C4C22×C4×C712yes—
419C22×C4C2×C7×D412yes—
420C22×C4C2×C7×D414yes—
421C22×C4C2×C7×D412yes—
422C22×C4C2×C7×D412yes—
423C22×C4C2×C7×D412yes—
424C22×C4C7×#4114yes—
425C22×C4C7×#4114yes—
426C22×C4C7×#4112yes—
427C22×C4C7×#4112yes—
428C22×C4C7×#4112yes—
429C22×C4C7×#4112yes—
430C4⋊C4—28no—
431C4⋊C4—28no—
432C4⋊C4—44no—
433C22⋊C4—416no—
434C22⋊C4—416no—
435C22⋊C4—48no—
436C22⋊C4—48no—
437C42—28no—
438C42—28no—
439C42—48no—
440C42—44no—
441C2×C7—84no—
442C2×C7C2×#38811yescharacteristic
443C2×C7C4×#12411yescharacteristic
444C2×C7#232811yescharacteristic
445C2×C7#235712yes—
446C2×C7#236312yes—
447C2×C7#249012yes—
448C2×C7#250011yescharacteristic
449C2×C7#250411yescharacteristic
450C2×C7#251312yes—
451C2×C7#254411yescharacteristic
452C2×C7#254811yescharacteristic
453C23—24no—
454C23—24no—
455C23—24no—
456C23—28no—
457C23—28no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—44no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23—44no—
473C23—44no—
474C23—44no—
475C23—44no—
476C23C23×C4×C711yescharacteristic
477C23C22×C7×D411yescharacteristic
478C23C22×C7×D411yescharacteristic
479C23C2×C7×#4111yescharacteristic
480C23C2×C7×#4111yescharacteristic
481C23C2×C7×#4111yescharacteristic
482C23C2×C7×#4111yescharacteristic
483C23C2×C7×#4112yes—
484C23C2×C7×#4112yes—
485C23C7×H(5,𝔽2)12yes—
486C23C7×H(5,𝔽2)12yes—
487D4—416no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—28no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—28no—
504C2×C4—24no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4C7×#11714yes—
527C2×C4C4×C7×D414yes—
528C2×C4C4×C7×D414yes—
529C2×C4C7×#12114yes—
530C2×C4C7×#12314yes—
531C2×C4C7×#12414yes—
532C2×C4C7×#12414yes—
533C2×C4C7×#12614yes—
534C7#1400211yescharacteristic, direct product factor, Sylow
535C22—44no—
536C22—44no—
537C22—44no—
538C22—48no—
539C22—48no—
540C22—84no—
541C22—82no—
542C22—82no—
543C22—84no—
544C22—82no—
545C22—82no—
546C22C2×C7×#11711yescharacteristic
547C22C2×C4×C7×D411yescharacteristic
548C22C2×C4×C7×D411yescharacteristic
549C22C4×C7×#4112yes—
550C22C7×#51812yes—
551C22C2×C7×#12111yescharacteristic
552C22C2×C7×#12311yescharacteristic
553C22C2×C7×#12411yescharacteristic
554C22C2×C7×#12411yescharacteristic
555C22C2×C7×#12611yescharacteristic
556C22C7×#52912yes—
557C22C7×#53211yescharacteristic
558C22C7×#53511yescharacteristic
559C22C7×#53511yescharacteristic
560C22C7×#54012yes—
561C22C7×#54612yes—
562C22C7×#55012yes—
563C22C7×#55312yes—
564C22C7×#55312yes—
565C22C7×#55312yes—
566C22C7×#55512yes—
567C22C7×#55912yes—
568C22C7×#55912yes—
569C4—24no—
570C4—44no—
571C4—42no—
572C4—44no—
573C4—44no—
574C4—44no—
575C4—82no—
576C4C7×#38818yes—
577C2—84no—
578C2C2×C7×#38811yescharacteristic
579C2C4×C7×#12411yescharacteristic
580C2C7×#232811yescharacteristic
581C2C7×#235712yes—
582C2C7×#236312yes—
583C2C7×#249012yes—
584C2C7×#250011yescharacteristic
585C2C7×#250411yescharacteristic
586C2C7×#251312yes—
587C2C7×#254411yescharacteristic
588C2C7×#254811yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C7×#382C2semidirect
5. C2×C4×C7×C4⋊C4C2semidirect
6. C7×#1440C2semidirect
7. C7×#1437C2semidirect
8. C7×C4⋊#95C2semidirect
9. C4×C7×#95C2semidirect
24. C7×#390C4semidirect
32. #14002C7direct (N × H)
87. C2×#382C2×C7semidirect
88. C2×C4×C4⋊C4C2×C7semidirect
89. #1440C2×C7semidirect
90. #1437C2×C7semidirect
91. C4⋊#95C2×C7semidirect
92. C4×#95C2×C7semidirect
183. #390C4×C7semidirect
534. C7#14002direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3902
C2×C7×#3822
C2×C4×C7×C4⋊C42
C7×#14402
C7×#14372
C7×C4⋊#952
C4×C7×#952
#140027