Finite Group Databasebeta

← #13248374

Subgroups — #13248374

Order 1792.

672 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1141C211yesmaximal, characteristic
2C2×C8×D28C211yesmaximal, characteristic, complemented
3C7×#1954C211yesmaximal, characteristic, complemented
4C2×D4⋊(C7⋊C8)C211yesmaximal, characteristic, complemented
5C2×#89278C211yesmaximal, characteristic, complemented
6#11725509C211yesmaximal, characteristic, complemented
7C7⋊#1273C211yesmaximal, characteristic, complemented
8C2×C4×C7×D4C2211yescharacteristic
9C22×#1141C411yescharacteristic
10C22×C8×D7—21no—
11C2×C4×D28C2211yescharacteristic
12C2×C7×C4⋊C8C2211yescharacteristic
13C2×C7×C22⋊C8—21no—
14C2×C7×C22⋊C8—21no—
15C2×C4×C7×C8C2211yescharacteristic
16C2×#6406C411yescharacteristic
17C2×(C2×D7)⋊C8—21no—
18C4×#1141—22no—
19C4×#1141—22no—
20C2×#6383C411yescharacteristic
21C2×#6381C411yescharacteristic
22C2×C4⋊(C7⋊C8)C2211yescharacteristic
23C2×C4×C7⋊C8C2211yescharacteristic
24C2×C4×C7⋊C8C2211yescharacteristic
25C8×D28—22no—
26C8×D28—22no—
27D4⋊(C7⋊C8)—22no—
28#89278—22no—
29#8947—71nomaximal, Sylow
30C22×C7×D4C2×C411yescharacteristic
31C23×C4×C7—21no—
32C22×D28C2×C411yescharacteristic
33C22×C4×D7—21no—
34C22×C7×C8—21no—
35C22×C7×C8D411yescharacteristic
36C22×C7×C8D411yescharacteristic
37C4×C7×D4—21no—
38C4×C7×D4—21no—
39C4×C7×D4—21no—
40C4×C7×D4—21no—
41C2×C7×C4⋊C4C2×C411yescharacteristic
42C2×C7×C22⋊C4—21no—
43C2×C42×C7C2311yescharacteristic
44C2×#1141—22no—
45C2×#1141—22no—
46C2×#1141C814yescomplemented
47C2×(C2×D7)⋊C4—21no—
48C2×C4⋊Dic7C2×C411yescharacteristic
49C22×C7⋊C8—21no—
50C22×C7⋊C8—21no—
51C22×C7⋊C8C2×C411yescharacteristic
52C22×C7⋊C8C2×C411yescharacteristic
53C2×C8×D7—24no—
54C2×C8×D7—42no—
55C2×C8×D7—42no—
56C4×D28—21no—
57C4×D28—21no—
58C4×D28D412yes—
59C4×D28D412yes—
60C7×C4⋊C8—21no—
61C7×C4⋊C8—21no—
62C7×C22⋊C8—42no—
63C7×C22⋊C8—42no—
64C4×C7×C8—21no—
65C4×C7×C8—21no—
66#6406—22no—
67(C2×D7)⋊C8—24no—
68#6383—22no—
69#6381—22no—
70C4⋊(C7⋊C8)—21no—
71C4⋊(C7⋊C8)D412yes—
72C4×C7⋊C8—21no—
73C4×C7⋊C8—21no—
74C4×C7⋊C8—21no—
75C4×C7⋊C8—21no—
76C2×C4×D8—71no—
77C2×C8×D4—71no—
78#1954D711yescharacteristic, complemented
79C2×D4⋊C8—71no—
80C2×D4⋊C8—71no—
81#1277—71no—
82#1273—71no—
83C24×C7—21no—
84C23×D7—21no—
85C2×C7×D4—21no—
86C2×C7×D4—21no—
87C2×C7×D4—21no—
88C2×C7×D4—21no—
89C2×C7×D4—21no—
90C2×C7×D4C2×C812yescomplemented
91C22×C4×C7—21no—
92C22×C4×C7—41no—
93C22×C4×C7—41no—
94C22×C4×C7—41no—
95C22×C4×C7—41no—
96C22×C4×C7—41no—
97C22×C4×C7—41no—
98C22×C4×C7C22×C411yescharacteristic
99C22×C4×C7C2×D411yescharacteristic
100C22×C4×C7#4111yescharacteristic
101C22×Dic7—21no—
102C2×D28—21no—
103C2×D28—21no—
104C2×D28—21no—
105C2×D28C22⋊C412yes—
106C2×D28C2×C812yes—
107C2×D28M1612yes—
108C2×C4×D7—22no—
109C2×C4×D7—22no—
110C2×C4×D7—41no—
111C2×C4×D7—41no—
112C2×C4×D7—41no—
113C2×C4×D7—41no—
114C2×C7×C8—21no—
115C2×C7×C8—21no—
116C2×C7×C8—21no—
117C2×C7×C8—21no—
118C2×C7×C8—21no—
119C2×C7×C8—41no—
120C2×C7×C8—41no—
121C2×C7×C8—41no—
122C2×C7×C8D812yescomplemented
123C7×C4⋊C4—21no—
124C7×C4⋊C4—21no—
125C7×C22⋊C4—41no—
126C7×C22⋊C4—41no—
127C42×C7C2×D411yescharacteristic
128C42×C7C2×D411yescharacteristic
129C42×C7C2×D411yescharacteristic
130C42×C7#4111yescharacteristic
131#1141—28no—
132(C2×D7)⋊C4—22no—
133(C2×D7)⋊C4—22no—
134C4⋊Dic7—21no—
135C4⋊Dic7C22⋊C412yes—
136C2×C7⋊C8—21no—
137C2×C7⋊C8—21no—
138C2×C7⋊C8—22no—
139C2×C7⋊C8—21no—
140C2×C7⋊C8—22no—
141C2×C7⋊C8—21no—
142C2×C7⋊C8—21no—
143C2×C7⋊C8—41no—
144C2×C7⋊C8—41no—
145C2×C7⋊C8—41no—
146C2×C7⋊C8—41no—
147C2×C7⋊C8C2×C812yescomplemented
148C8×D7—48no—
149C22×D8—71no—
150C23×C8—141no—
151C2×C4×D4—71no—
152C2×C4×D4C2×D711yescharacteristic
153C4×D8—142no—
154C4×D8—142no—
155C8×D4—142no—
156C8×D4—142no—
157C2×#107—71no—
158C2×C4⋊C8—71no—
159C2×C4⋊C8C2×D711yescharacteristic
160C2×#102—71no—
161C2×#102—71no—
162C2×C22⋊C8—21no—
163C2×C22⋊C8—21no—
164C2×C22⋊C8—141no—
165C2×C4×C8—71no—
166C2×C4×C8—71no—
167C2×C4×C8C2×D711yescharacteristic
168D4⋊C8—142no—
169D4⋊C8—142no—
170C23×C7—22no—
171C23×C7—41no—
172C23×C7—41no—
173C23×C7—41no—
174C23×C7—41no—
175C23×C7—41no—
176C23×C7—41no—
177C23×C7C4×D411yescharacteristic
178C22×D7—22no—
179C22×D7—22no—
180C22×D7—22no—
181C22×D7—41no—
182C22×D7—41no—
183C22×D7—41no—
184C22×D7—41no—
185C7×D4—22no—
186C7×D4—22no—
187C7×D4—41no—
188C7×D4—41no—
189C2×C4×C7—21no—
190C2×C4×C7—21no—
191C2×C4×C7—41no—
192C2×C4×C7—41no—
193C2×C4×C7—41no—
194C2×C4×C7—81no—
195C2×C4×C7—81no—
196C2×C4×C7—81no—
197C2×C4×C7—81no—
198C2×C4×C7C2×C22⋊C411yescharacteristic
199C2×C4×C7C4×D411yescharacteristic
200C2×C4×C7#12011yescharacteristic
201C2×C4×C7#12111yescharacteristic
202C2×C4×C7#12111yescharacteristic
203C2×C4×C7#12311yescharacteristic
204C2×C4×C7C22×C811yescharacteristic
205C2×C4×C7C2×M1611yescharacteristic
206C2×C4×C7#13111yescharacteristic
207C2×C4×C7#13111yescharacteristic
208C2×C4×C7C2×D811yescharacteristic
209C2×C4×C7#13511yescharacteristic
210C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
212C2×Dic7—22no—
213C2×Dic7—41no—
214C2×Dic7—41no—
215D28—22no—
216D28—22no—
217D28—22no—
218D28C22⋊C814yescomplemented
219C4×D7—42no—
220C4×D7—42no—
221C4×D7—42no—
222C4×D7—42no—
223C7×C8—22no—
224C7×C8—41no—
225C7×C8—81no—
226C7⋊C8—22no—
227C7⋊C8—42no—
228C7⋊C8—41no—
229C7⋊C8—42no—
230C22×D4—71no—
231C22×D4C4×D711yescharacteristic
232C23×C4—21no—
233C23×C4—141no—
234C2×D8—74no—
235C2×D8—142no—
236C2×D8—142no—
237C22×C8—21no—
238C22×C8—71no—
239C22×C8—71no—
240C22×C8—144no—
241C22×C8—141no—
242C22×C8—141no—
243C22×C8—282no—
244C22×C8—282no—
245C22×C8C22⋊D711yescharacteristic
246C22×C8C22⋊D711yescharacteristic
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—72no—
252C4×D4—72no—
253C4×D4—141no—
254C4×D4—141no—
255C2×C4⋊C4—71no—
256C2×C4⋊C4C4×D711yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—141no—
259C2×C42C22×D711yescharacteristic
260#107—142no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—72no—
264C4⋊C8—141no—
265#102—142no—
266#102—142no—
267C22⋊C8—42no—
268C22⋊C8—42no—
269C22⋊C8—144no—
270C4×C8—21no—
271C4×C8—21no—
272C4×C8—141no—
273C4×C8—141no—
274C4×C8—141no—
275C4×C8—141no—
276C22×C7—42no—
277C22×C7—42no—
278C22×C7—42no—
279C22×C7—81no—
280C22×C7—81no—
281C22×C7—81no—
282C22×C7—81no—
283C22×C7#38611yescharacteristic
284C22×C7C8×D411yescharacteristic
285C22×C7#43511yescharacteristic
286C22×C7C4×D811yescharacteristic
287C22×C7#44211yescharacteristic
288C22×C7#44311yescharacteristic
289C22×C7#44411yescharacteristic
290C2×D7—24no—
291C2×D7—42no—
292C2×D7—42no—
293C2×D7—42no—
294C2×D7—42no—
295C2×D7—42no—
296C2×D7—42no—
297C4×C7—21no—
298C4×C7—21no—
299C4×C7—81no—
300C4×C7C2×C22⋊C811yescharacteristic
301C4×C7#40811yescharacteristic
302C4×C7C8×D411yescharacteristic
303C4×C7#43511yescharacteristic
304C4×C7#44711yescharacteristic
305C4×C7#44911yescharacteristic
306C4×C7#45911yescharacteristic
307C4×C7#46311yescharacteristic
308Dic7—42no—
309C24—21no—
310C24—141no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—72no—
317C2×D4—72no—
318C2×D4—72no—
319C2×D4—141no—
320C2×D4—141no—
321C2×D4—141no—
322C2×D4C8×D712yescomplemented
323C22×C4—21no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—141no—
331C22×C4—142no—
332C22×C4—142no—
333C22×C4—281no—
334C22×C4—281no—
335C22×C4—281no—
336C22×C4—281no—
337C22×C4C2×C4×D711yescharacteristic
338C22×C4#115711yescharacteristic
339C22×C4C2×C22⋊D711yescharacteristic
340D8—148no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—72no—
350C2×C8—141no—
351C2×C8—141no—
352C2×C8—142no—
353C2×C8—141no—
354C2×C8—141no—
355C2×C8—141no—
356C2×C8—142no—
357C2×C8—288no—
358C2×C8—281no—
359C2×C8—281no—
360C2×C8—281no—
361C2×C8—281no—
362C2×C8#114112yescomplemented
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—72no—
366C4⋊C4—141no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—142no—
370C22⋊C4—142no—
371C42D4×D711yescharacteristic
372C42D4×D711yescharacteristic
373C42D4×D711yescharacteristic
374C42#115911yescharacteristic
375C2×C7—82no—
376C2×C7C8×D811yescharacteristic
377C2×C7#158011yescharacteristic
378C2×C7#158111yescharacteristic
379C2×C7#158611yescharacteristic
380C2×C7#186911yescharacteristic
381C2×C7#187611yescharacteristic
382C2×C7#187911yescharacteristic
383D7—44no—
384C23—22no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—142no—
392C23—142no—
393C23—142no—
394C23—281no—
395C23—281no—
396C23—281no—
397C23—281no—
398C23C4×C22⋊D711yescharacteristic
399D4—22no—
400D4—22no—
401D4—41no—
402D4—41no—
403D4—74no—
404D4—142no—
405D4—142no—
406D4—142no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—142no—
417C2×C4—281no—
418C2×C4—281no—
419C2×C4—282no—
420C2×C4—282no—
421C2×C4—282no—
422C2×C4—282no—
423C2×C4D7×C22⋊C411yescharacteristic
424C2×C4(C22⋊D7)⋊C411yescharacteristic
425C2×C4#644611yescharacteristic
426C2×C4#644711yescharacteristic
427C2×C4C2×C8×D711yescharacteristic
428C2×C4#646411yescharacteristic
429C2×C4D7×M1611yescharacteristic
430C2×C4#647011yescharacteristic
431C2×C4C2×#114111yescharacteristic
432C2×C4#649511yescharacteristic
433C2×C4#650011yescharacteristic
434C2×C4#650111yescharacteristic
435C2×C4#651211yescharacteristic
436C2×C4#651311yescharacteristic
437C8—22no—
438C8—41no—
439C8—81no—
440C8—142no—
441C8—282no—
442C8—281no—
443C8—282no—
444C7#894711yescharacteristic, complemented, Sylow
445C22—42no—
446C22—42no—
447C22—42no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—144no—
453C22—282no—
454C22—282no—
455C22—282no—
456C22—282no—
457C22—282no—
458C22—282no—
459C22#8972811yescharacteristic
460C22C4×#114111yescharacteristic
461C22#8978611yescharacteristic
462C22C8×C22⋊D711yescharacteristic
463C22#8989911yescharacteristic
464C22#8991611yescharacteristic
465C22#8991711yescharacteristic
466C4—21no—
467C4—21no—
468C4—81no—
469C4—282no—
470C4D7×C22⋊C811yescharacteristic
471C4(C22⋊D7)⋊C811yescharacteristic
472C4#8949911yescharacteristic
473C4#8950011yescharacteristic
474C4#8980811yescharacteristic
475C4#8980911yescharacteristic
476C4#8982911yescharacteristic
477C4#8984411yescharacteristic
478C2—82no—
479C2—284no—
480C2#1172741111yescharacteristic
481C2#1172771111yescharacteristic
482C2#1172776511yescharacteristic
483C2C8×#114111yescharacteristic
484C2#1172859411yescharacteristic
485C2#1172861611yescharacteristic
486C2#1172861711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D7
commutatorC2×C4×C7C22×C8
FrattiniC2×C42C22×D7
FittingC7×#1954C2
socleC23×C7C4×D4
prime radicalC22×#1141C4
cosocleC2×C42×C7C23
hypercenter#1954D7
hypocenterC7#8947
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×C8×D28C2semidirect
3. C7×#1954C2semidirect
4. C2×D4⋊(C7⋊C8)C2semidirect
5. C2×#89278C2semidirect
6. #11725509C2semidirect
7. C7⋊#1273C2semidirect
46. C2×#1141C8semidirect
78. #1954D7semidirect
90. C2×C7×D4C2×C8semidirect
122. C2×C7×C8D8semidirect
147. C2×C7⋊C8C2×C8semidirect
218. D28C22⋊C8semidirect
322. C2×D4C8×D7semidirect
362. C2×C8#1141semidirect
444. C7#8947semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#11412
C2×C8×D282
C7×#19542
C2×D4⋊(C7⋊C8)2
C2×#892782
#117255092
C7⋊#12732
#89477