Finite Group Databasebeta

← #13257593

Subgroups — #13257593

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×#89787C211yesmaximal, characteristic
2C7×#1802C211yesmaximal, characteristic, complemented
3#11729368C211yesmaximal, characteristic, complemented
4C2×#89280C211yesmaximal, characteristic, complemented
5C2×#89275C211yesmaximal, characteristic, complemented
6#11727334C211yesmaximal, characteristic, complemented
7#11725440C211yesmaximal, characteristic, complemented
8C2×C4×C7×D4C2211yescharacteristic
9C22×#1141—21no—
10C2×#6437C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12C2×C7×#102—21no—
13C7×#384C2211yescharacteristic
14C2×C22⋊(C7⋊C8)—21no—
15C2×C22⋊(C7⋊C8)—21no—
16#89787—22no—
17#89787—22no—
18C2×#6383—21no—
19C2×#6383—21no—
20C2×#6383—21no—
21C2×C4⋊(C7⋊C8)C2211yescharacteristic
22C2×C4⋊(C7⋊C8)C2211yescharacteristic
23C2×C4×C7⋊C8C2211yescharacteristic
24C7×#340—21no—
25#89280—22no—
26#89275—22no—
27#10473—71nomaximal, Sylow
28C22×C7×D4D411yescharacteristic
29C23×C4×C7—21no—
30C22×D28—21no—
31C22×D28—21no—
32C22×D28—21no—
33C22×C7×C8—21no—
34C4×C7×D4—21no—
35C4×C7×D4—21no—
36C4×C7×D4—21no—
37C4×C7×D4—21no—
38C2×C7×C4⋊C4—21no—
39C2×C7×C4⋊C4—21no—
40C2×C7×C4⋊C4—21no—
41C2×C7×C4⋊C4D411yescharacteristic
42C2×C7×C22⋊C4—21no—
43C2×C42×C7C2311yescharacteristic
44C2×#1141—24no—
45C2×#1141—42no—
46C2×#1141—42no—
47C22×C7⋊C8—21no—
48C22×C7⋊C8—21no—
49C22×C7⋊C8D411yescharacteristic
50C22×C7⋊C8D411yescharacteristic
51#6437—21no—
52#6437—21no—
53#6437—21no—
54#6437D412yes—
55C7×C4⋊C8—21no—
56C7×C4⋊C8—21no—
57C7×#102—42no—
58C22⋊(C7⋊C8)—42no—
59C22⋊(C7⋊C8)—42no—
60#6383—24no—
61#6383—42no—
62#6383—42no—
63C4⋊(C7⋊C8)—21no—
64C4⋊(C7⋊C8)—21no—
65C4⋊(C7⋊C8)—21no—
66C4⋊(C7⋊C8)D412yes—
67C4×C7⋊C8—21no—
68C4×C7⋊C8—21no—
69C2×#459—71no—
70#1957—71no—
71#1954—71no—
72#1802D711yescharacteristic, complemented
73C2×#334—71no—
74C2×#331—71no—
75#1296—71no—
76C24×C7—21no—
77C23×D7—41no—
78C2×C7×D4—21no—
79C2×C7×D4—21no—
80C2×C7×D4—21no—
81C2×C7×D4—21no—
82C2×C7×D4—21no—
83C2×C7×D4SD1612yes—
84C22×C4×C7—21no—
85C22×C4×C7—41no—
86C22×C4×C7—41no—
87C22×C4×C7—41no—
88C22×C4×C7—41no—
89C22×C4×C7—41no—
90C22×C4×C7—41no—
91C22×C4×C7—41no—
92C22×C4×C7C2×D411yescharacteristic
93C22×C4×C7C2×D411yescharacteristic
94C22×C4×C7#4111yescharacteristic
95C2×D28—22no—
96C2×D28—22no—
97C2×D28—22no—
98C2×D28—41no—
99C2×D28—41no—
100C2×D28—41no—
101C2×D28—41no—
102C2×D28—41no—
103C2×D28—41no—
104C2×D28—41no—
105C2×D28—41no—
106C2×D28—41no—
107C2×D28—41no—
108C2×D28—41no—
109C2×D28—81no—
110C2×D28—81no—
111C2×C7×C8—41no—
112C2×C7×C8—41no—
113C2×C7×C8—41no—
114C7×C4⋊C4—21no—
115C7×C4⋊C4—21no—
116C7×C4⋊C4—41no—
117C7×C4⋊C4—41no—
118C7×C4⋊C4—41no—
119C7×C4⋊C4—41no—
120C7×C4⋊C4—81no—
121C7×C22⋊C4—41no—
122C7×C22⋊C4—41no—
123C42×C7C2×D411yescharacteristic
124C42×C7C2×D411yescharacteristic
125C42×C7#4111yescharacteristic
126C42×C7#4111yescharacteristic
127#1141—48no—
128C2×C7⋊C8—21no—
129C2×C7⋊C8—21no—
130C2×C7⋊C8—22no—
131C2×C7⋊C8—21no—
132C2×C7⋊C8—21no—
133C2×C7⋊C8—21no—
134C2×C7⋊C8—41no—
135C2×C7⋊C8—41no—
136C2×C7⋊C8—41no—
137C2×C7⋊C8—41no—
138C2×C7⋊C8—41no—
139C2×C7⋊C8D812yescomplemented
140C22×D8—141no—
141C2×#127—71no—
142C2×C4×D4C2×D711yescharacteristic
143#459—142no—
144#459—142no—
145C2×C4⋊C8—71no—
146C2×C4⋊C8—71no—
147C2×C4⋊C8C2×D711yescharacteristic
148C2×#102—21no—
149C2×#102—141no—
150C2×#102—141no—
151C2×#102—141no—
152C2×C22⋊C8—141no—
153C2×C22⋊C8—141no—
154C2×C4×C8—71no—
155#384C2×D711yescharacteristic
156#340—21no—
157#334—142no—
158#331—142no—
159C23×C7—22no—
160C23×C7—41no—
161C23×C7—41no—
162C23×C7—41no—
163C23×C7—41no—
164C23×C7—41no—
165C23×C7—41no—
166C23×C7#12111yescharacteristic
167C22×D7—42no—
168C22×D7—81no—
169C22×D7—81no—
170C22×D7—81no—
171C22×D7—81no—
172C22×D7—81no—
173C22×D7—81no—
174C7×D4—22no—
175C7×D4—22no—
176C7×D4—41no—
177C7×D4—41no—
178C2×C4×C7—21no—
179C2×C4×C7—21no—
180C2×C4×C7—41no—
181C2×C4×C7—41no—
182C2×C4×C7—41no—
183C2×C4×C7—81no—
184C2×C4×C7—81no—
185C2×C4×C7—81no—
186C2×C4×C7—81no—
187C2×C4×C7—81no—
188C2×C4×C7—81no—
189C2×C4×C7—81no—
190C2×C4×C7#12011yescharacteristic
191C2×C4×C7#12111yescharacteristic
192C2×C4×C7#12111yescharacteristic
193C2×C4×C7#12311yescharacteristic
194C2×C4×C7#12311yescharacteristic
195C2×C4×C7#12411yescharacteristic
196C2×C4×C7C2×D811yescharacteristic
197C2×C4×C7C2×SD1611yescharacteristic
198C2×C4×C7#13511yescharacteristic
199C2×C4×C7#13511yescharacteristic
200C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
202C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
203C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
204D28—42no—
205D28—42no—
206D28—42no—
207D28—42no—
208D28—82no—
209D28—82no—
210D28—81no—
211D28—81no—
212D28—81no—
213D28—81no—
214C7×C8—81no—
215C7⋊C8—22no—
216C7⋊C8—42no—
217C7⋊C8—41no—
218C7⋊C8—81no—
219C22×D4—141no—
220C22×D4—141no—
221C22×D4—141no—
222C22×D4C22⋊D711yescharacteristic
223C23×C4—21no—
224C2×D8—144no—
225C2×D8—282no—
226C2×D8—282no—
227C22×C8—21no—
228C22×C8—71no—
229C22×C8—71no—
230C22×C8—141no—
231C22×C8—141no—
232#127—72no—
233#127—141no—
234#127—141no—
235#127—141no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C22⋊D711yescharacteristic
244C2×C22⋊C4—21no—
245C2×C42C22×D711yescharacteristic
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—72no—
249C4⋊C8—141no—
250C4⋊C8—141no—
251C4⋊C8—141no—
252#102—42no—
253#102—144no—
254#102—282no—
255#102—282no—
256C22⋊C8—282no—
257C22⋊C8—282no—
258C4×C8—141no—
259C4×C8—141no—
260C22×C7—42no—
261C22×C7—42no—
262C22×C7—42no—
263C22×C7—81no—
264C22×C7—81no—
265C22×C7—81no—
266C22×C7—81no—
267C22×C7#39411yescharacteristic
268C22×C7#45911yescharacteristic
269C22×C7#46311yescharacteristic
270C22×C7#46511yescharacteristic
271C22×C7#46911yescharacteristic
272C22×C7#47111yescharacteristic
273C22×C7#47211yescharacteristic
274C2×D7—82no—
275C2×D7—82no—
276C2×D7—82no—
277C2×D7—161no—
278C2×D7—161no—
279C2×D7—161no—
280C2×D7—161no—
281C4×C7—21no—
282C4×C7—21no—
283C4×C7—81no—
284C4×C7—161no—
285C4×C7#44911yescharacteristic
286C4×C7#45011yescharacteristic
287C4×C7#45911yescharacteristic
288C4×C7#46311yescharacteristic
289C4×C7#46611yescharacteristic
290C4×C7#46911yescharacteristic
291C4×C7#48111yescharacteristic
292C4×C7#48211yescharacteristic
293C24—21no—
294C24—281no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—142no—
301C2×D4—142no—
302C2×D4—142no—
303C2×D4—281no—
304C2×D4—281no—
305C2×D4—281no—
306C2×D4—281no—
307C2×D4—281no—
308C2×D4—281no—
309C2×D4—281no—
310C2×D4—281no—
311C2×D4—281no—
312C2×D4—281no—
313C2×D4—281no—
314C2×D4—561no—
315C2×D4—561no—
316C2×D4#114312yes—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4D4×D711yescharacteristic
326C22×C4#115911yescharacteristic
327C22×C4C2×C22⋊D711yescharacteristic
328D8—288no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—72no—
333C2×C8—141no—
334C2×C8—141no—
335C2×C8—141no—
336C2×C8—141no—
337C2×C8—141no—
338C2×C8—142no—
339C2×C8—281no—
340C2×C8—281no—
341C2×C8—281no—
342C2×C8—281no—
343C2×C8—281no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—81no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C42#115711yescharacteristic
354C42#115711yescharacteristic
355C42D4×D711yescharacteristic
356C42D4×D711yescharacteristic
357C2×C7—82no—
358C2×C7#166511yescharacteristic
359C2×C7#167711yescharacteristic
360C2×C7#168711yescharacteristic
361C2×C7#170111yescharacteristic
362C2×C7#203411yescharacteristic
363C2×C7#205111yescharacteristic
364C2×C7#205411yescharacteristic
365D7—162no—
366C23—22no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—282no—
374C23—561no—
375C23—561no—
376C23—561no—
377C23—561no—
378C23—561no—
379C23—561no—
380C23#650211yescharacteristic
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385D4—282no—
386D4—282no—
387D4—282no—
388D4—282no—
389D4—562no—
390D4—562no—
391D4—561no—
392D4—561no—
393D4—561no—
394D4—561no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4#644611yescharacteristic
408C2×C4#644711yescharacteristic
409C2×C4#644711yescharacteristic
410C2×C4#644811yescharacteristic
411C2×C4D7×D811yescharacteristic
412C2×C4#647411yescharacteristic
413C2×C4#647711yescharacteristic
414C2×C4#647911yescharacteristic
415C2×C4#649211yescharacteristic
416C2×C4#649511yescharacteristic
417C2×C4#650011yescharacteristic
418C2×C4C2×#114311yescharacteristic
419C2×C4#651211yescharacteristic
420C2×C4#651311yescharacteristic
421C8—81no—
422C8—142no—
423C8—281no—
424C8—282no—
425C8—561no—
426C7#1047311yescharacteristic, complemented, Sylow
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—562no—
435C22—562no—
436C22—562no—
437C22—1121no—
438C22—1121no—
439C22—1121no—
440C22—1121no—
441C22#8973111yescharacteristic
442C22#8981111yescharacteristic
443C22#8982011yescharacteristic
444C22#8992211yescharacteristic
445C22#8993711yescharacteristic
446C22#8997111yescharacteristic
447C22#8997511yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—161no—
452C4#8954711yescharacteristic
453C4#8955411yescharacteristic
454C4#8955811yescharacteristic
455C4#8955911yescharacteristic
456C4#8974011yescharacteristic
457C4#8977511yescharacteristic
458C4#8980911yescharacteristic
459C4#8981811yescharacteristic
460C2—82no—
461C2—1122no—
462C2#1172727811yescharacteristic
463C2#1172796611yescharacteristic
464C2#1172806111yescharacteristic
465C2#1172876311yescharacteristic
466C2#1172879711yescharacteristic
467C2#1172885411yescharacteristic
468C2#1172888811yescharacteristic
subgroupG/H
centerC23#6502
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1802C2
socleC23×C7#121
prime radicalC2×#89787C2
hypercenter#1802D7
hypocenterC7#10473
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C7×#1802C2semidirect
3. #11729368C2semidirect
4. C2×#89280C2semidirect
5. C2×#89275C2semidirect
6. #11727334C2semidirect
7. #11725440C2semidirect
72. #1802D7semidirect
139. C2×C7⋊C8D8semidirect
426. C7#10473semidirect

Maximal subgroups

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

subgroupindex
C2×#897872
C7×#18022
#117293682
C2×#892802
C2×#892752
#117273342
#117254402
#104737