Finite Group Databasebeta

← C7×#13423 #13190639

Subgroups — C7×#13423 #13190639

Order 1792.

558 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2709C211yesmaximal, characteristic
2C2×C7×#353C211yesmaximal, characteristic
3C2×C7×#352C211yesmaximal, characteristic, complemented
4C7×#1890C211yesmaximal, characteristic, complemented
5C7×#1887C211yesmaximal, characteristic
6C7×#1867C211yesmaximal, characteristic, complemented
7C7×#1390C211yesmaximal, characteristic, complemented
8C2×C7×#127C2211yescharacteristic
9C2×C7×#123C2211yescharacteristic
10C7×#518C2211yescharacteristic
11C7×#418—21no—
12C2×C7×#100C2211yescharacteristic
13C2×C7×#99C2211yescharacteristic
14C2×C7×#99C2211yescharacteristic
15C7×#394—21no—
16C7×#394—21no—
17C7×#394—21no—
18C7×#387—21no—
19C7×#386—21no—
20C7×#386—21no—
21C7×#386C2211yescharacteristic
22C7×#385—21no—
23C7×#381—21no—
24C7×#353—22no—
25C7×#352—22no—
26C7×#342—21no—
27C7×#342—21no—
28C7×#339—21no—
29#13423C711yesmaximal, characteristic, direct product factor, Sylow
30C22×C7×D4—21no—
31C22×C7×D4—21no—
32C22×C7×D4D411yescharacteristic
33C22×C7×D4C2311yescharacteristic
34C23×C4×C7D411yescharacteristic
35C23×C4×C7D411yescharacteristic
36C2×C7×M16—21no—
37C7×#127—21no—
38C7×#127—21no—
39C7×#127—21no—
40C7×#127—21no—
41C7×#123—21no—
42C7×#123—21no—
43C7×#123—21no—
44C7×#123—21no—
45C4×C7×D4—41no—
46C4×C7×D4—41no—
47C7×#117—21no—
48C2×C7×C4⋊C4—21no—
49C2×C7×C4⋊C4—21no—
50C2×C7×C4⋊C4—41no—
51C2×C7×C22⋊C4—21no—
52C2×C7×C22⋊C4—21no—
53C2×C7×C22⋊C4—21no—
54C2×C7×C22⋊C4—21no—
55C2×C7×C22⋊C4—21no—
56C2×C7×C22⋊C4—21no—
57C2×C7×C22⋊C4—21no—
58C2×C7×C22⋊C4—21no—
59C2×C7×C22⋊C4—21no—
60C2×C7×C22⋊C4—21no—
61C2×C7×C22⋊C4D411yescharacteristic
62C2×C7×C22⋊C4D411yescharacteristic
63C2×C42×C7D411yescharacteristic
64C7×#102—41no—
65C7×#102—41no—
66C7×#100—21no—
67C7×#100—21no—
68C7×#99—21no—
69C7×#99—21no—
70C7×#99—21no—
71C7×#99D412yes—
72C7×#95—21no—
73C7×#95—21no—
74C7×#95—21no—
75C7×#95—21no—
76C7×#95—41no—
77C7×#95—41no—
78C7×#95—41no—
79#2709C2×C711yescharacteristic
80C2×#353C2×C711yescharacteristic
81C2×#352C2×C711yescharacteristic, complemented
82#1890C2×C711yescharacteristic, complemented
83#1887C2×C711yescharacteristic
84#1867C2×C711yescharacteristic, complemented
85#1390C2×C711yescharacteristic, complemented
86C24×C7—21no—
87C24×C7C2×D411yescharacteristic
88C24×C7C2×D411yescharacteristic
89C2×C7×D4—21no—
90C2×C7×D4—21no—
91C2×C7×D4—41no—
92C2×C7×D4—41no—
93C2×C7×D4—41no—
94C2×C7×D4—41no—
95C2×C7×D4—42no—
96C2×C7×D4—42no—
97C2×C7×D4—41no—
98C2×C7×D4—41no—
99C2×C7×D4—41no—
100C2×C7×D4—41no—
101C2×C7×D4—81no—
102C2×C7×D4—81no—
103C2×C7×D4C2×D411yescharacteristic
104C2×C7×D4#4111yescharacteristic
105C2×C7×D4#4111yescharacteristic
106C2×C7×D4#4111yescharacteristic
107C22×C4×C7—21no—
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—21no—
111C22×C4×C7—21no—
112C22×C4×C7—21no—
113C22×C4×C7—21no—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—41no—
119C22×C4×C7—41no—
120C22×C4×C7—41no—
121C22×C4×C7—41no—
122C22×C4×C7—41no—
123C22×C4×C7—81no—
124C22×C4×C7C2×D411yescharacteristic
125C7×M16—41no—
126C7×M16—41no—
127C2×C7×C8—41no—
128C7×C4⋊C4—21no—
129C7×C4⋊C4—21no—
130C7×C4⋊C4—42no—
131C7×C4⋊C4—41no—
132C7×C4⋊C4—41no—
133C7×C4⋊C4—82no—
134C7×C22⋊C4—22no—
135C7×C22⋊C4—21no—
136C7×C22⋊C4—21no—
137C7×C22⋊C4—41no—
138C7×C22⋊C4—41no—
139C7×C22⋊C4—41no—
140C7×C22⋊C4—41no—
141C7×C22⋊C4—41no—
142C7×C22⋊C4—41no—
143C7×C22⋊C4—41no—
144C7×C22⋊C4—41no—
145C7×C22⋊C4—41no—
146C7×C22⋊C4—81no—
147C7×C22⋊C4—81no—
148C7×C22⋊C4—81no—
149C7×C22⋊C4—81no—
150C7×C22⋊C4—81no—
151C42×C7—21no—
152C42×C7—21no—
153C42×C7—41no—
154C2×#127C22×C711yescharacteristic
155C2×#123C22×C711yescharacteristic
156#518C22×C711yescharacteristic
157#418—21no—
158C2×#100C22×C711yescharacteristic
159C2×#99C22×C711yescharacteristic
160C2×#99C22×C711yescharacteristic
161#394—21no—
162#394—21no—
163#394—21no—
164#387—21no—
165#386—21no—
166#386—21no—
167#386C22×C711yescharacteristic
168#385—21no—
169#381—21no—
170#353—22no—
171#352—22no—
172#342—21no—
173#342—21no—
174#339—21no—
175C23×C7—21no—
176C23×C7—21no—
177C23×C7—21no—
178C23×C7—21no—
179C23×C7—41no—
180C23×C7—41no—
181C23×C7—41no—
182C23×C7—41no—
183C23×C7—41no—
184C23×C7—41no—
185C23×C7—41no—
186C23×C7—41no—
187C23×C7—41no—
188C23×C7—41no—
189C23×C7—41no—
190C23×C7#12011yescharacteristic
191C23×C7#12111yescharacteristic
192C23×C7#12111yescharacteristic
193C23×C7#12311yescharacteristic
194C23×C7#12411yescharacteristic
195C7×D4—41no—
196C7×D4—41no—
197C7×D4—41no—
198C7×D4—41no—
199C7×D4—42no—
200C7×D4—81no—
201C7×D4—82no—
202C7×D4—82no—
203C7×D4—82no—
204C7×D4—82no—
205C2×C4×C7—21no—
206C2×C4×C7—21no—
207C2×C4×C7—22no—
208C2×C4×C7—41no—
209C2×C4×C7—41no—
210C2×C4×C7—42no—
211C2×C4×C7—41no—
212C2×C4×C7—41no—
213C2×C4×C7—41no—
214C2×C4×C7—41no—
215C2×C4×C7—41no—
216C2×C4×C7—41no—
217C2×C4×C7—42no—
218C2×C4×C7—42no—
219C2×C4×C7—41no—
220C2×C4×C7—41no—
221C2×C4×C7—41no—
222C2×C4×C7—41no—
223C2×C4×C7—41no—
224C2×C4×C7—41no—
225C2×C4×C7—41no—
226C2×C4×C7—41no—
227C2×C4×C7—81no—
228C2×C4×C7—81no—
229C2×C4×C7—81no—
230C2×C4×C7—81no—
231C2×C4×C7—81no—
232C2×C4×C7—81no—
233C2×C4×C7—81no—
234C2×C4×C7—81no—
235C2×C4×C7—81no—
236C2×C4×C7—81no—
237C2×C4×C7—81no—
238C2×C4×C7#12111yescharacteristic
239C2×C4×C7#12311yescharacteristic
240C7×C8—81no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4C7×D411yescharacteristic
244C22×D4C23×C711yescharacteristic
245C23×C4C7×D411yescharacteristic
246C23×C4C7×D411yescharacteristic
247C2×M16—21no—
248#127—21no—
249#127—21no—
250#127—21no—
251#127—21no—
252#123—21no—
253#123—21no—
254#123—21no—
255#123—21no—
256C4×D4—41no—
257C4×D4—41no—
258#117—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—41no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4C7×D411yescharacteristic
273C2×C22⋊C4C7×D411yescharacteristic
274C2×C42C7×D411yescharacteristic
275#102—41no—
276#102—41no—
277#100—21no—
278#100—21no—
279#99—21no—
280#99—21no—
281#99—21no—
282#99C7×D412yes—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—21no—
287#95—41no—
288#95—41no—
289#95—41no—
290C22×C7—21no—
291C22×C7—21no—
292C22×C7—21no—
293C22×C7—21no—
294C22×C7—21no—
295C22×C7—21no—
296C22×C7—41no—
297C22×C7—41no—
298C22×C7—41no—
299C22×C7—41no—
300C22×C7—41no—
301C22×C7—41no—
302C22×C7—41no—
303C22×C7—41no—
304C22×C7—81no—
305C22×C7—81no—
306C22×C7—81no—
307C22×C7—81no—
308C22×C7—81no—
309C22×C7—81no—
310C22×C7—81no—
311C22×C7—81no—
312C22×C7—81no—
313C22×C7#39411yescharacteristic
314C22×C7B(4,𝔽2)11yescharacteristic
315C22×C7#45811yescharacteristic
316C4×C7—21no—
317C4×C7—21no—
318C4×C7—42no—
319C4×C7—81no—
320C4×C7—81no—
321C4×C7—82no—
322C4×C7—81no—
323C4×C7—81no—
324C4×C7—81no—
325C4×C7—81no—
326C4×C7—161no—
327C24—21no—
328C24C2×C7×D411yescharacteristic
329C24C2×C7×D411yescharacteristic
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—81no—
343C2×D4—81no—
344C2×D4C2×C7×D411yescharacteristic
345C2×D4C7×#4111yescharacteristic
346C2×D4C7×#4111yescharacteristic
347C2×D4C7×#4111yescharacteristic
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—81no—
365C22×C4C2×C7×D411yescharacteristic
366M16—41no—
367M16—41no—
368C2×C8—41no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—42no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—82no—
375C22⋊C4—22no—
376C22⋊C4—21no—
377C22⋊C4—21no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—81no—
388C22⋊C4—81no—
389C22⋊C4—81no—
390C22⋊C4—81no—
391C22⋊C4—81no—
392C42—21no—
393C42—21no—
394C42—41no—
395C2×C7—21no—
396C2×C7—21no—
397C2×C7—41no—
398C2×C7—41no—
399C2×C7—41no—
400C2×C7—41no—
401C2×C7—161no—
402C2×C7#204411yescharacteristic
403C2×C7#219811yescharacteristic
404C2×C7#220011yescharacteristic
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23C7×#12011yescharacteristic
421C23C7×#12111yescharacteristic
422C23C7×#12111yescharacteristic
423C23C7×#12311yescharacteristic
424C23C7×#12411yescharacteristic
425D4—41no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—42no—
430D4—81no—
431D4—82no—
432D4—82no—
433D4—82no—
434D4—82no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4C7×#12111yescharacteristic
469C2×C4C7×#12311yescharacteristic
470C8—81no—
471C7#1342311yescharacteristic, direct product factor, Sylow
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22C7×#39411yescharacteristic
496C22C7×B(4,𝔽2)11yescharacteristic
497C22C7×#45811yescharacteristic
498C4—21no—
499C4—21no—
500C4—42no—
501C4—81no—
502C4—81no—
503C4—82no—
504C4—81no—
505C4—81no—
506C4—81no—
507C4—81no—
508C4—161no—
509C2—21no—
510C2—21no—
511C2—41no—
512C2—41no—
513C2—41no—
514C2—41no—
515C2—161no—
516C2C7×#204411yescharacteristic
517C2C7×#219811yescharacteristic
518C2C7×#220011yescharacteristic
subgroupG/H
center, socleC22×C7B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C7
prime radicalC2×C7×#127C22
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C7 ◁ C22×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C7×#352C2semidirect
4. C7×#1890C2semidirect
6. C7×#1867C2semidirect
7. C7×#1390C2semidirect
29. #13423C7direct (N × H)
81. C2×#352C2×C7semidirect
82. #1890C2×C7semidirect
84. #1867C2×C7semidirect
85. #1390C2×C7semidirect
471. C7#13423direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#27092
C2×C7×#3532
C2×C7×#3522
C7×#18902
C7×#18872
C7×#18672
C7×#13902
#134237