Finite Group Databasebeta

← #13257592

Subgroups — #13257592

Order 1792.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89844C211yesmaximal, characteristic
2C7×#1957C211yesmaximal, characteristic, complemented
3C2×#89339C211yesmaximal, characteristic, complemented
4#11727541C211yesmaximal, characteristic, complemented
5C2×#89252C211yesmaximal, characteristic, complemented
6#11727338C211yesmaximal, characteristic, complemented
7#11725440C211yesmaximal, characteristic, complemented
8C2×C7×#127C2211yescharacteristic
9C22×#1141—21no—
10C2×C4×D28C2211yescharacteristic
11C2×C7×#102—21no—
12C2×C7×#102—21no—
13C2×C4×C7×C8C2211yescharacteristic
14C7×#384C2211yescharacteristic
15C2×#6406—21no—
16C2×(C2×D7)⋊C8—21no—
17C2×(C2×D7)⋊C8—21no—
18#89844—22no—
19#89844—22no—
20C2×#6383—21no—
21C2×C4⋊(C7⋊C8)C2211yescharacteristic
22C2×C4⋊(C7⋊C8)C2211yescharacteristic
23C2×C4⋊(C7⋊C8)C2211yescharacteristic
24#89339—22no—
25#89324—21no—
26#89252—22no—
27#10473—71nomaximal, Sylow
28C22×C7×D4—21no—
29C22×C7×D4—21no—
30C22×C7×D4—21no—
31C22×D28D411yescharacteristic
32C22×C4×D7—21no—
33C22×C7×C8D411yescharacteristic
34C22×C7×C8D411yescharacteristic
35C7×#127—21no—
36C7×#127—21no—
37C7×#127—21no—
38C7×#127D412yes—
39C2×C7×C4⋊C4—21no—
40C2×C7×C4⋊C4—21no—
41C2×C7×C4⋊C4—21no—
42C2×C42×C7C2311yescharacteristic
43C2×#1141—24no—
44C2×#1141—42no—
45C2×#1141—42no—
46C2×(C2×D7)⋊C4—21no—
47C2×C4⋊Dic7D411yescharacteristic
48C22×C7⋊C8—21no—
49C22×C7⋊C8—21no—
50C22×C7⋊C8—21no—
51C4×D28—21no—
52C4×D28—21no—
53C4×D28—21no—
54C4×D28—21no—
55C7×#102—42no—
56C7×#102—42no—
57C4×C7×C8—21no—
58C4×C7×C8—21no—
59#6406—24no—
60(C2×D7)⋊C8—42no—
61(C2×D7)⋊C8—42no—
62#6383—42no—
63C4⋊(C7⋊C8)—21no—
64C4⋊(C7⋊C8)—21no—
65C4⋊(C7⋊C8)—21no—
66C4⋊(C7⋊C8)—21no—
67C4⋊(C7⋊C8)—21no—
68C4⋊(C7⋊C8)D412yes—
69C2×#459—71no—
70#1957D711yescharacteristic, complemented
71#1954—71no—
72#1802—71no—
73C2×#334—71no—
74C2×#331—71no—
75#1296—71no—
76C24×C7—41no—
77C23×D7—21no—
78C2×C7×D4—22no—
79C2×C7×D4—22no—
80C2×C7×D4—22no—
81C2×C7×D4—41no—
82C2×C7×D4—41no—
83C2×C7×D4—41no—
84C2×C7×D4—41no—
85C2×C7×D4—41no—
86C2×C7×D4—41no—
87C2×C7×D4—41no—
88C2×C7×D4—41no—
89C2×C7×D4—41no—
90C2×C7×D4—41no—
91C2×C7×D4—41no—
92C2×C7×D4—81no—
93C2×C7×D4—81no—
94C22×C4×C7—41no—
95C22×C4×C7C2×D411yescharacteristic
96C22×C4×C7C2×D411yescharacteristic
97C22×C4×C7#4111yescharacteristic
98C22×Dic7—21no—
99C2×D28—21no—
100C2×D28—21no—
101C2×D28—21no—
102C2×D28—21no—
103C2×D28—21no—
104C2×D28SD1612yes—
105C2×C4×D7—41no—
106C2×C4×D7—41no—
107C2×C4×D7—41no—
108C2×C4×D7—41no—
109C2×C4×D7—41no—
110C2×C4×D7—41no—
111C2×C7×C8—21no—
112C2×C7×C8—21no—
113C2×C7×C8—21no—
114C2×C7×C8—21no—
115C2×C7×C8—21no—
116C2×C7×C8D812yescomplemented
117C7×C4⋊C4—41no—
118C7×C4⋊C4—41no—
119C7×C4⋊C4—41no—
120C7×C4⋊C4—41no—
121C7×C4⋊C4—81no—
122C42×C7C2×D411yescharacteristic
123C42×C7C2×D411yescharacteristic
124C42×C7#4111yescharacteristic
125C42×C7#4111yescharacteristic
126#1141—48no—
127(C2×D7)⋊C4—41no—
128(C2×D7)⋊C4—41no—
129C4⋊Dic7—21no—
130C4⋊Dic7—21no—
131C2×C7⋊C8—22no—
132C2×C7⋊C8—41no—
133C2×C7⋊C8—41no—
134C2×C7⋊C8—41no—
135C2×C7⋊C8—41no—
136C2×C7⋊C8—41no—
137C2×C7⋊C8—41no—
138C2×C7⋊C8—41no—
139C2×C7⋊C8—41no—
140C22×D8—141no—
141C2×#127C2×D711yescharacteristic
142C2×C4×D4—71no—
143#459—142no—
144#459—142no—
145C2×C4⋊C8—71no—
146C2×C4⋊C8—71no—
147C2×C4⋊C8—71no—
148C2×#102—21no—
149C2×#102—21no—
150C2×#102—141no—
151C2×#102—141no—
152C2×C22⋊C8—141no—
153C2×C22⋊C8—141no—
154C2×C4×C8C2×D711yescharacteristic
155#384C2×D711yescharacteristic
156#340—141no—
157#334—142no—
158#331—142no—
159C23×C7—42no—
160C23×C7—81no—
161C23×C7—81no—
162C23×C7—81no—
163C23×C7—81no—
164C23×C7—81no—
165C23×C7—81no—
166C23×C7#12111yescharacteristic
167C22×D7—22no—
168C22×D7—41no—
169C22×D7—41no—
170C22×D7—41no—
171C22×D7—41no—
172C22×D7—41no—
173C22×D7—41no—
174C7×D4—42no—
175C7×D4—42no—
176C7×D4—42no—
177C7×D4—42no—
178C7×D4—82no—
179C7×D4—82no—
180C7×D4—81no—
181C7×D4—81no—
182C7×D4—81no—
183C7×D4—81no—
184C2×C4×C7—21no—
185C2×C4×C7—21no—
186C2×C4×C7—81no—
187C2×C4×C7—81no—
188C2×C4×C7—81no—
189C2×C4×C7#12011yescharacteristic
190C2×C4×C7#12111yescharacteristic
191C2×C4×C7#12111yescharacteristic
192C2×C4×C7#12311yescharacteristic
193C2×C4×C7#12311yescharacteristic
194C2×C4×C7#12411yescharacteristic
195C2×C4×C7C2×D811yescharacteristic
196C2×C4×C7C2×SD1611yescharacteristic
197C2×C4×C7#13511yescharacteristic
198C2×C4×C7#13511yescharacteristic
199C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
200C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
202C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
203C2×Dic7—41no—
204C2×Dic7—41no—
205C2×Dic7—41no—
206D28—22no—
207D28—22no—
208D28—41no—
209D28—41no—
210C4×D7—81no—
211C4×D7—81no—
212C4×D7—81no—
213C4×D7—81no—
214C7×C8—22no—
215C7×C8—41no—
216C7⋊C8—42no—
217C7⋊C8—81no—
218C7⋊C8—81no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—71no—
223C23×C4—141no—
224C2×D8—144no—
225C2×D8—282no—
226C2×D8—282no—
227C22×C8—141no—
228C22×C8—141no—
229C22×C8—141no—
230C22×C8C22⋊D711yescharacteristic
231C22×C8C22⋊D711yescharacteristic
232#127—21no—
233#127—21no—
234#127—21no—
235#127D2812yes—
236C4×D4—141no—
237C4×D4—141no—
238C4×D4—141no—
239C4×D4—141no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—71no—
244C2×C22⋊C4—141no—
245C2×C42C22×D711yescharacteristic
246C4⋊C8—72no—
247C4⋊C8—141no—
248C4⋊C8—141no—
249C4⋊C8—141no—
250C4⋊C8—141no—
251C4⋊C8—141no—
252#102—42no—
253#102—42no—
254#102—144no—
255#102—282no—
256C22⋊C8—282no—
257C22⋊C8—282no—
258C4×C8—21no—
259C4×C8—21no—
260C22×C7—82no—
261C22×C7—82no—
262C22×C7—82no—
263C22×C7—161no—
264C22×C7—161no—
265C22×C7—161no—
266C22×C7—161no—
267C22×C7#39411yescharacteristic
268C22×C7#45911yescharacteristic
269C22×C7#46311yescharacteristic
270C22×C7#46511yescharacteristic
271C22×C7#46911yescharacteristic
272C22×C7#47111yescharacteristic
273C22×C7#47211yescharacteristic
274C2×D7—42no—
275C2×D7—42no—
276C2×D7—42no—
277C2×D7—81no—
278C2×D7—81no—
279C2×D7—81no—
280C2×D7—81no—
281C4×C7—21no—
282C4×C7—21no—
283C4×C7—161no—
284C4×C7#44911yescharacteristic
285C4×C7#45011yescharacteristic
286C4×C7#45911yescharacteristic
287C4×C7#46311yescharacteristic
288C4×C7#46611yescharacteristic
289C4×C7#46911yescharacteristic
290C4×C7#48111yescharacteristic
291C4×C7#48211yescharacteristic
292Dic7—81no—
293C24—41no—
294C24—141no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—72no—
310C2×D4—81no—
311C2×D4—81no—
312C2×D4—141no—
313C2×D4—141no—
314C2×D4—141no—
315C2×D4—141no—
316C2×D4—141no—
317C22×C4—41no—
318C22×C4—141no—
319C22×C4—281no—
320C22×C4—281no—
321C22×C4—281no—
322C22×C4—281no—
323C22×C4—281no—
324C22×C4—281no—
325C22×C4D4×D711yescharacteristic
326C22×C4#115911yescharacteristic
327C22×C4C2×C22⋊D711yescharacteristic
328D8—288no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—142no—
335C2×C8—281no—
336C2×C8—281no—
337C2×C8—281no—
338C2×C8—281no—
339C2×C8—281no—
340C2×C8—281no—
341C2×C8—281no—
342C2×C8—281no—
343C2×C8#114112yescomplemented
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—81no—
349C4⋊C4—141no—
350C4⋊C4—141no—
351C22⋊C4—281no—
352C22⋊C4—281no—
353C42C2×D2811yescharacteristic
354C42#115711yescharacteristic
355C42D4×D711yescharacteristic
356C42#115911yescharacteristic
357C2×C7—162no—
358C2×C7#166511yescharacteristic
359C2×C7#167711yescharacteristic
360C2×C7#168711yescharacteristic
361C2×C7#170111yescharacteristic
362C2×C7#203411yescharacteristic
363C2×C7#205111yescharacteristic
364C2×C7#205411yescharacteristic
365D7—82no—
366C23—42no—
367C23—81no—
368C23—81no—
369C23—81no—
370C23—81no—
371C23—81no—
372C23—81no—
373C23—142no—
374C23—281no—
375C23—281no—
376C23—281no—
377C23—281no—
378C23—281no—
379C23—281no—
380C23#650111yescharacteristic
381D4—42no—
382D4—42no—
383D4—42no—
384D4—42no—
385D4—82no—
386D4—82no—
387D4—81no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—142no—
392D4—142no—
393D4—281no—
394D4—281no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—281no—
401C2×C4—281no—
402C2×C4—281no—
403C2×C4—561no—
404C2×C4—561no—
405C2×C4—561no—
406C2×C4—561no—
407C2×C4#644511yescharacteristic
408C2×C4#644611yescharacteristic
409C2×C4#644811yescharacteristic
410C2×C4#644911yescharacteristic
411C2×C4#647411yescharacteristic
412C2×C4#647411yescharacteristic
413C2×C4D7×SD1611yescharacteristic
414C2×C4#647911yescharacteristic
415C2×C4#649311yescharacteristic
416C2×C4C2×#114111yescharacteristic
417C2×C4#649511yescharacteristic
418C2×C4#650211yescharacteristic
419C2×C4#651211yescharacteristic
420C2×C4#651311yescharacteristic
421C8—22no—
422C8—41no—
423C8—282no—
424C8—561no—
425C8—561no—
426C7#1047311yescharacteristic, complemented, Sylow
427C22—82no—
428C22—82no—
429C22—82no—
430C22—161no—
431C22—161no—
432C22—161no—
433C22—161no—
434C22—282no—
435C22—282no—
436C22—282no—
437C22—561no—
438C22—561no—
439C22—561no—
440C22—561no—
441C22#8973311yescharacteristic
442C22#8982911yescharacteristic
443C22#8984411yescharacteristic
444C22#8993111yescharacteristic
445C22#8993211yescharacteristic
446C22#8994311yescharacteristic
447C22#8994911yescharacteristic
448C4—21no—
449C4—21no—
450C4—161no—
451C4—561no—
452C4#8954811yescharacteristic
453C4#8954911yescharacteristic
454C4#8955111yescharacteristic
455C4#8955311yescharacteristic
456C4#8978711yescharacteristic
457C4#8978811yescharacteristic
458C4#8981011yescharacteristic
459C4#8981111yescharacteristic
460C2—162no—
461C2—562no—
462C2#1172740411yescharacteristic
463C2#1172793011yescharacteristic
464C2#1172795011yescharacteristic
465C2#1172895411yescharacteristic
466C2#1172895711yescharacteristic
467C2#1172902111yescharacteristic
468C2#1172903711yescharacteristic
subgroupG/H
centerC23#6501
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1957C2
socleC23×C7#121
prime radicalC2×#89844C2
hypercenter#1957D7
hypocenterC7#10473
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. C7×#1957C2semidirect
3. C2×#89339C2semidirect
4. #11727541C2semidirect
5. C2×#89252C2semidirect
6. #11727338C2semidirect
7. #11725440C2semidirect
70. #1957D7semidirect
116. C2×C7×C8D8semidirect
343. C2×C8#1141semidirect
426. C7#10473semidirect

Maximal subgroups

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

subgroupindex
C2×#898442
C7×#19572
C2×#893392
#117275412
C2×#892522
#117273382
#117254402
#104737