Finite Group Databasebeta

← #13246453

Subgroups — #13246453

Order 1792.

898 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
2C2×#89320C212yesmaximal
3#11729284C212yesmaximal, complemented
4#11725419C212yesmaximal, complemented
5C24×C4×C7C411yescharacteristic
6C22×C7×C22⋊C4C411yescharacteristic
7C22×C7×C22⋊C4C2211yescharacteristic
8C22×C42×C7C411yescharacteristic
9C22×C42×C7C2211yescharacteristic
10C4×C7×C22⋊C4—22no—
11C4×C7×C22⋊C4—22no—
12C2×C7×#95C411yescharacteristic
13C2×C7×#95C2211yescharacteristic
14C2×C22⋊(C7⋊C8)C2214yes—
15C2×C4⋊(C7⋊C8)—22no—
16#89320—24no—
17#89319—22no—
18#8557—71nomaximal, Sylow
19C25×C7C2×C411yescharacteristic
20C23×C4×C7—21no—
21C23×C4×C7—21no—
22C23×C4×C7—22no—
23C23×C4×C7—42no—
24C23×C4×C7—42no—
25C23×C4×C7C814yescomplemented
26C23×C4×C7C2×C411yescharacteristic
27C23×C4×C7C2×C411yescharacteristic
28C23×C4×C7C2×C411yescharacteristic
29C23×C4×C7C2×C411yescharacteristic
30C23×C4×C7C2×C411yescharacteristic
31C23×C4×C7C2311yescharacteristic
32C2×C7×C22⋊C4—22no—
33C2×C7×C22⋊C4—22no—
34C2×C7×C22⋊C4—22no—
35C2×C7×C22⋊C4—22no—
36C2×C7×C22⋊C4—22no—
37C2×C7×C22⋊C4D412yes—
38C2×C7×C22⋊C4Q812yes—
39C2×C42×C7—21no—
40C2×C42×C7—21no—
41C2×C42×C7—42no—
42C2×C42×C7—42no—
43C2×C42×C7D412yes—
44C2×C42×C7D412yes—
45C22×C7⋊C8—24no—
46C7×#95—22no—
47C7×#95—22no—
48C22⋊(C7⋊C8)—24no—
49C22⋊(C7⋊C8)—24no—
50C4⋊(C7⋊C8)—44no—
51C2×C4×C22⋊C4D711yescharacteristic
52#1797—72no—
53C2×#323—72no—
54#1280—72no—
55C24×C7—21no—
56C24×C7—21no—
57C24×C7—21no—
58C24×C7—21no—
59C24×C7—41no—
60C24×C7—41no—
61C24×C7—41no—
62C24×C7—41no—
63C24×C7C4⋊C412yes—
64C24×C7C2×C812yes—
65C24×C7M1612yes—
66C24×C7C22×C411yescharacteristic
67C22×C4×C7—22no—
68C22×C4×C7—22no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—24no—
78C22×C4×C7—24no—
79C22×C4×C7—41no—
80C22×C4×C7—41no—
81C22×C4×C7—41no—
82C22×C4×C7—41no—
83C22×C4×C7—42no—
84C22×C4×C7—42no—
85C22×C4×C7—48no—
86C22×C4×C7—48no—
87C22×C4×C7—42no—
88C22×C4×C7—42no—
89C22×C4×C7—41no—
90C22×C4×C7—41no—
91C22×C4×C7—41no—
92C22×C4×C7—41no—
93C22×C4×C7—41no—
94C22×C4×C7—41no—
95C22×C4×C7C22⋊C412yes—
96C22×C4×C7C22⋊C411yescharacteristic
97C22×C4×C7C22⋊C411yescharacteristic
98C22×C4×C7C4⋊C412yes—
99C22×C4×C7C2×C812yes—
100C22×C4×C7C2×C812yes—
101C22×C4×C7M1612yes—
102C22×C4×C7M1612yes—
103C22×C4×C7C2×D412yes—
104C22×C4×C7C2×D411yescharacteristic
105C22×C4×C7C2×Q811yescharacteristic
106C22×C4×C7#4112yes—
107C7×C22⋊C4—28no—
108C7×C22⋊C4—24no—
109C7×C22⋊C4—24no—
110C42×C7—24no—
111C42×C7—42no—
112C42×C7—42no—
113C42×C7—42no—
114C2×C7⋊C8—44no—
115C2×C7⋊C8—44no—
116C2×C7⋊C8—44no—
117C24×C4Dic711yescharacteristic
118C22×C22⋊C4Dic711yescharacteristic
119C22×C22⋊C4C2×D711yescharacteristic
120C22×C42Dic711yescharacteristic
121C22×C42C2×D711yescharacteristic
122C2×C4⋊C8—142no—
123C2×C22⋊C8—74no—
124C4×C22⋊C4—22no—
125C4×C22⋊C4—22no—
126C2×#95Dic711yescharacteristic
127C2×#95C2×D711yescharacteristic
128#336—142no—
129#323—144no—
130C23×C7—21no—
131C23×C7—21no—
132C23×C7—21no—
133C23×C7—21no—
134C23×C7—22no—
135C23×C7—22no—
136C23×C7—22no—
137C23×C7—22no—
138C23×C7—22no—
139C23×C7—22no—
140C23×C7—42no—
141C23×C7—42no—
142C23×C7—42no—
143C23×C7—42no—
144C23×C7—42no—
145C23×C7—42no—
146C23×C7—42no—
147C23×C7—42no—
148C23×C7—42no—
149C23×C7—42no—
150C23×C7—42no—
151C23×C7—42no—
152C23×C7—41no—
153C23×C7—41no—
154C23×C7—41no—
155C23×C7—41no—
156C23×C7C4⋊C814yescomplemented
157C23×C7C2×C22⋊C411yescharacteristic
158C23×C7C2×C4⋊C411yescharacteristic
159C23×C7#11711yescharacteristic
160C23×C7C22×C811yescharacteristic
161C23×C7C2×M1611yescharacteristic
162C23×C7C2×M1611yescharacteristic
163C23×C7C2×M1611yescharacteristic
164C2×C4×C7—22no—
165C2×C4×C7—21no—
166C2×C4×C7—22no—
167C2×C4×C7—21no—
168C2×C4×C7—24no—
169C2×C4×C7—24no—
170C2×C4×C7—22no—
171C2×C4×C7—22no—
172C2×C4×C7—22no—
173C2×C4×C7—22no—
174C2×C4×C7—22no—
175C2×C4×C7—22no—
176C2×C4×C7—41no—
177C2×C4×C7—41no—
178C2×C4×C7—42no—
179C2×C4×C7—48no—
180C2×C4×C7—42no—
181C2×C4×C7—42no—
182C2×C4×C7—42no—
183C2×C4×C7—42no—
184C2×C4×C7—42no—
185C2×C4×C7—41no—
186C2×C4×C7—41no—
187C2×C4×C7—41no—
188C2×C4×C7—41no—
189C2×C4×C7—41no—
190C2×C4×C7—41no—
191C2×C4×C7—48no—
192C2×C4×C7—42no—
193C2×C4×C7—42no—
194C2×C4×C7—42no—
195C2×C4×C7C22⋊C812yes—
196C2×C4×C7C22⋊C812yes—
197C2×C4×C7#9912yes—
198C2×C4×C7#10012yes—
199C2×C4×C7#12112yes—
200C2×C4×C7C22⋊Q812yes—
201C7⋊C8—84no—
202C25C2×Dic711yescharacteristic
203C23×C4—22no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—42no—
207C23×C4—42no—
208C23×C4C7⋊C814yescomplemented
209C23×C4C2×Dic711yescharacteristic
210C23×C4C2×Dic711yescharacteristic
211C23×C4C2×Dic711yescharacteristic
212C23×C4C2×Dic711yescharacteristic
213C23×C4C2×Dic711yescharacteristic
214C23×C4C22×D711yescharacteristic
215C22×C8—144no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4Dic1412yes—
222C2×C22⋊C4D2812yes—
223C2×C42—21no—
224C2×C42—21no—
225C2×C42—42no—
226C2×C42—42no—
227C2×C42C22⋊D712yes—
228C2×C42C22⋊D712yes—
229C4⋊C8—284no—
230C22⋊C8—144no—
231C22⋊C8—144no—
232#95—22no—
233#95—22no—
234C22×C7—21no—
235C22×C7—21no—
236C22×C7—21no—
237C22×C7—21no—
238C22×C7—21no—
239C22×C7—21no—
240C22×C7—21no—
241C22×C7—21no—
242C22×C7—21no—
243C22×C7—21no—
244C22×C7—21no—
245C22×C7—21no—
246C22×C7—24no—
247C22×C7—44no—
248C22×C7—44no—
249C22×C7—44no—
250C22×C7—44no—
251C22×C7—42no—
252C22×C7—42no—
253C22×C7—42no—
254C22×C7—42no—
255C22×C7—42no—
256C22×C7—42no—
257C22×C7#38011yescharacteristic
258C22×C7C2×C22⋊C811yescharacteristic
259C22×C7#40711yescharacteristic
260C22×C7C2×#9911yescharacteristic
261C22×C7#41011yescharacteristic
262C22×C7C2×#10011yescharacteristic
263C22×C7#41311yescharacteristic
264C22×C7C2×C4⋊C811yescharacteristic
265C22×C7#42311yescharacteristic
266C22×C7#43111yescharacteristic
267C22×C7#43211yescharacteristic
268C4×C7—22no—
269C4×C7—22no—
270C4×C7—22no—
271C4×C7—42no—
272C4×C7—42no—
273C4×C7—42no—
274C4×C7—42no—
275C4×C7#32314yescomplemented
276C24—21no—
277C24—21no—
278C24—21no—
279C24—21no—
280C24—41no—
281C24—41no—
282C24—41no—
283C24—41no—
284C24C2×C7⋊C812yes—
285C24#113612yes—
286C24C4⋊Dic712yes—
287C24C22×Dic711yescharacteristic
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—48no—
307C22×C4—48no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4C2×C7⋊C812yes—
317C22×C4C2×C7⋊C812yes—
318C22×C4#113612yes—
319C22×C4#113612yes—
320C22×C4C4⋊Dic712yes—
321C22×C4C22⋊Dic712yes—
322C22×C4C22⋊Dic711yescharacteristic
323C22×C4C22⋊Dic711yescharacteristic
324C22×C4C2×Dic1411yescharacteristic
325C22×C4C2×D2811yescharacteristic
326C22×C4#115712yes—
327C22×C4C2×C22⋊D712yes—
328C2×C8—284no—
329C2×C8—284no—
330C2×C8—284no—
331C22⋊C4—28no—
332C22⋊C4—24no—
333C22⋊C4—24no—
334C42—24no—
335C42—42no—
336C42—42no—
337C42—42no—
338C2×C7—21no—
339C2×C7—21no—
340C2×C7—21no—
341C2×C7—21no—
342C2×C7—44no—
343C2×C7C2×#32311yescharacteristic
344C2×C7#145811yescharacteristic
345C2×C7#146511yescharacteristic
346C2×C7#146611yescharacteristic
347C2×C7#179711yescharacteristic
348C2×C7#179911yescharacteristic
349C2×C7#180011yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23C4⋊(C7⋊C8)14yescomplemented
377C23C22×C7⋊C811yescharacteristic
378C23C2×#113611yescharacteristic
379C23C2×#113611yescharacteristic
380C23C2×#113611yescharacteristic
381C23C2×C4⋊Dic711yescharacteristic
382C23#648911yescharacteristic
383C23C2×C22⋊Dic711yescharacteristic
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—48no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—48no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4C22⋊(C7⋊C8)12yes—
416C2×C4C22⋊(C7⋊C8)12yes—
417C2×C4#640712yes—
418C2×C4#640812yes—
419C2×C4#648712yes—
420C2×C4#649312yes—
421C8—564no—
422C7#855711yescharacteristic, complemented, Sylow
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—24no—
436C22—44no—
437C22—44no—
438C22—44no—
439C22—44no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22C2×C4⋊(C7⋊C8)11yescharacteristic
447C22#8969611yescharacteristic
448C22#8969711yescharacteristic
449C22#8969811yescharacteristic
450C22C2×C22⋊(C7⋊C8)11yescharacteristic
451C22#8997911yescharacteristic
452C22#8998411yescharacteristic
453C22C2×#640711yescharacteristic
454C22C2×#640811yescharacteristic
455C22#9000911yescharacteristic
456C22#9001211yescharacteristic
457C4—22no—
458C4—22no—
459C4—22no—
460C4—42no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4#8932014yescomplemented
465C2—21no—
466C2—21no—
467C2—21no—
468C2—21no—
469C2—44no—
470C2#1172928411yescharacteristic
471C2C2×#8932011yescharacteristic
472C2#1172932511yescharacteristic
473C2#1172935611yescharacteristic
474C2#1172935711yescharacteristic
475C2#1172937111yescharacteristic
476C2#1172937311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC23×C7C22×C8
FrattiniC23×C4C22×D7
FittingC2×C4×C7×C22⋊C4C2
socleC23×C7C2×C22⋊C4
prime radicalC25×C7C2×C4
cosocleC23×C4×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#8557
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #11729284C2semidirect
4. #11725419C2semidirect
25. C23×C4×C7C8semidirect
156. C23×C7C4⋊C8semidirect
208. C23×C4C7⋊C8semidirect
275. C4×C7#323semidirect
376. C23C4⋊(C7⋊C8)semidirect
422. C7#8557semidirect
464. C4#89320semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
C2×#893202
#117292842
#117254192
#85577