Finite Group Databasebeta

← #13245293

Subgroups — #13245293

Order 1792.

802 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90419C211yesmaximal, characteristic
2C2×C7×#333C211yesmaximal, characteristic, complemented
3C2×#89341C211yesmaximal, characteristic, complemented
4#11728229C211yesmaximal, characteristic
5#11728229C211yesmaximal, characteristic
6C2×#89277C211yesmaximal, characteristic, complemented
7C2×#89281C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×#6509C412yes—
10C2×Q8×Dic7C412yes—
11#90419—22no—
12#90419—22no—
13#90419—22no—
14#90419—22no—
15C2×#6460—21no—
16C2×#6455—21no—
17C2×#6453—21no—
18C2×#6450—21no—
19C2×C42×D7C2211yescharacteristic
20C2×#6432C2211yescharacteristic
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×C4⋊C8C2211yescharacteristic
23C2×(C2×D7)⋊C8—21no—
24C2×(C2×D7)⋊C8—21no—
25C2×C4⋊(C7⋊C8)C2211yescharacteristic
26C2×C4⋊(C7⋊C8)C2211yescharacteristic
27C7×#333—22no—
28#89345—21no—
29#89345—21no—
30#89341—22no—
31#89281—22no—
32#89277—22no—
33#8343—71nomaximal, Sylow
34C22×C7×Q8C2×C412yes—
35C22×C4×D7C2×C411yescharacteristic
36C22×C4×D7D411yescharacteristic
37C22×C4×D7D411yescharacteristic
38C22×Dic14—21no—
39C22×C7×C8—21no—
40C22×C7×C8—21no—
41C7×C4⋊Q8—21no—
42C7×C4⋊Q8—21no—
43C7×C4⋊Q8D412yes—
44C7×C4⋊Q8D412yes—
45C2×C7×C4⋊C4—21no—
46C2×C7×C4⋊C4—21no—
47C2×C42×C7C2311yescharacteristic
48#6509—24no—
49#6509—24no—
50Q8×Dic7—24no—
51Q8×Dic7—24no—
52C2×(C2×D7)⋊C4—22no—
53C2×C4⋊Dic7—21no—
54C2×C4⋊Dic7—22no—
55C2×C4⋊Dic7C2×C412yes—
56C2×Dic7⋊C4—22no—
57C2×C4×Dic7—22no—
58C2×C4×Dic7C2×C411yescharacteristic
59C2×C4×Dic7D411yescharacteristic
60C2×C4×Dic7D411yescharacteristic
61C22×C7⋊C8—21no—
62C22×C7⋊C8—21no—
63#6460—24no—
64#6460—24no—
65#6455—24no—
66#6455—24no—
67#6453—24no—
68#6453—24no—
69#6450—24no—
70#6450—24no—
71C42×D7—21no—
72C42×D7—21no—
73C42×D7—21no—
74C42×D7—21no—
75#6432—21no—
76#6432—21no—
77#6432D412yes—
78#6432D412yes—
79C7×C4⋊C8—21no—
80C7×C4⋊C8—21no—
81C7×C4⋊C8—21no—
82C7×C4⋊C8—21no—
83(C2×D7)⋊C8—42no—
84(C2×D7)⋊C8—42no—
85C4⋊(C7⋊C8)—21no—
86C4⋊(C7⋊C8)—21no—
87C4⋊(C7⋊C8)—21no—
88C4⋊(C7⋊C8)—21no—
89C2×#533—71no—
90#1797—71no—
91#1797—71no—
92C2×#333—71no—
93C2×#333D711yescharacteristic, complemented
94C2×#332—71no—
95C2×#332—71no—
96C23×D7C22⋊C411yescharacteristic
97C2×C7×Q8—22no—
98C2×C7×Q8—42no—
99C2×C7×Q8—42no—
100C2×C7×Q8C22⋊C414yes—
101C22×C4×C7—22no—
102C22×C4×C7C22×C411yescharacteristic
103C22×C4×C7C2×D411yescharacteristic
104C22×C4×C7C2×D411yescharacteristic
105C22×Dic7—22no—
106C22×Dic7C22⋊C411yescharacteristic
107C22×Dic7C22⋊C411yescharacteristic
108C22×Dic7C22⋊C411yescharacteristic
109C2×C4×D7—21no—
110C2×C4×D7—21no—
111C2×C4×D7—21no—
112C2×C4×D7—21no—
113C2×C4×D7—21no—
114C2×C4×D7—21no—
115C2×C4×D7—21no—
116C2×C4×D7—21no—
117C2×C4×D7—21no—
118C2×C4×D7—21no—
119C2×C4×D7—21no—
120C2×C4×D7—21no—
121C2×C4×D7—41no—
122C2×C4×D7—41no—
123C2×C4×D7SD1612yes—
124C2×C4×D7Q1612yes—
125C2×Dic14—22no—
126C2×Dic14—22no—
127C2×Dic14—41no—
128C2×Dic14—41no—
129C2×Dic14—41no—
130C2×Dic14—41no—
131C2×C7×C8—41no—
132C2×C7×C8—41no—
133C2×C7×C8—41no—
134C2×C7×C8—41no—
135C2×C7×C8—41no—
136C2×C7×C8—41no—
137C7×C4⋊C4—22no—
138C7×C4⋊C4—22no—
139C7×C4⋊C4—22no—
140C7×C4⋊C4—22no—
141C42×C7C2×D411yescharacteristic
142C42×C7C2×D411yescharacteristic
143C42×C7C2×D411yescharacteristic
144C42×C7C2×D411yescharacteristic
145(C2×D7)⋊C4—28no—
146C4⋊Dic7—28no—
147C4⋊Dic7—22no—
148C4⋊Dic7—22no—
149C4⋊Dic7—22no—
150C4⋊Dic7C22⋊C414yes—
151Dic7⋊C4—28no—
152C4×Dic7—28no—
153C4×Dic7—21no—
154C4×Dic7—21no—
155C4×Dic7—21no—
156C4×Dic7—21no—
157C4×Dic7—21no—
158C4×Dic7—21no—
159C2×C7⋊C8—41no—
160C2×C7⋊C8—41no—
161C2×C7⋊C8—41no—
162C2×C7⋊C8—41no—
163C2×C7⋊C8—41no—
164C2×C7⋊C8—41no—
165#533—142no—
166#533—142no—
167#533—142no—
168#533—142no—
169C2×C4⋊Q8—71no—
170C2×C4⋊Q8C2×D711yescharacteristic
171C2×#125—141no—
172C2×C22⋊Q8—72no—
173C2×C22⋊Q8—141no—
174C2×C4×Q8—72no—
175C2×C4×Q8—141no—
176C2×#117—141no—
177C22×C42—71no—
178C2×C4⋊C8—71no—
179C2×C4⋊C8—71no—
180C2×C4⋊C8C2×D711yescharacteristic
181C2×C4⋊C8C2×D711yescharacteristic
182C2×C22⋊C8—141no—
183C2×C22⋊C8—141no—
184#336—141no—
185#336—141no—
186#333—22no—
187#333—142no—
188#332—142no—
189#332—142no—
190C23×C7C2×C22⋊C411yescharacteristic
191C22×D7—21no—
192C22×D7—21no—
193C22×D7—21no—
194C22×D7—21no—
195C22×D7—21no—
196C22×D7—21no—
197C22×D7#10312yes—
198C7×Q8—44no—
199C7×Q8—44no—
200C2×C4×C7—21no—
201C2×C4×C7—21no—
202C2×C4×C7—24no—
203C2×C4×C7—42no—
204C2×C4×C7—42no—
205C2×C4×C7C2×C22⋊C411yescharacteristic
206C2×C4×C7C2×C22⋊C411yescharacteristic
207C2×C4×C7#12011yescharacteristic
208C2×C4×C7#12011yescharacteristic
209C2×C4×C7#12011yescharacteristic
210C2×C4×C7#12011yescharacteristic
211C2×C4×C7C2×SD1611yescharacteristic
212C2×C4×C7C2×Q1611yescharacteristic
213C2×C4×C7#13511yescharacteristic
214C2×C4×C7#13511yescharacteristic
215C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
216C2×C4×C7#13711yescharacteristic
217C2×C4×C7#13711yescharacteristic
218C2×C4×C7#13711yescharacteristic
219C2×Dic7—21no—
220C2×Dic7—21no—
221C2×Dic7—21no—
222C2×Dic7—21no—
223C2×Dic7—24no—
224C2×Dic7—21no—
225C2×Dic7—21no—
226C2×Dic7—21no—
227C2×Dic7—21no—
228C2×Dic7—42no—
229C2×Dic7—42no—
230C2×Dic7#10312yes—
231C4×D7—22no—
232C4×D7—22no—
233C4×D7—22no—
234C4×D7—22no—
235C4×D7—42no—
236C4×D7—42no—
237C4×D7—41no—
238C4×D7—41no—
239C4×D7—41no—
240C4×D7—41no—
241Dic14—42no—
242Dic14—42no—
243Dic14—42no—
244Dic14—42no—
245C7×C8—81no—
246C7×C8—81no—
247C7⋊C8—81no—
248C7⋊C8—81no—
249C22×Q8—141no—
250C22×Q8C4×D712yes—
251C23×C4—71no—
252C23×C4—71no—
253C23×C4—71no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—141no—
257C22×C8—141no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—72no—
261C4⋊Q8—72no—
262C4⋊Q8—141no—
263C4⋊Q8—141no—
264C4⋊Q8D2812yes—
265C4⋊Q8C22⋊D712yes—
266#125—144no—
267#125—144no—
268C22⋊Q8—144no—
269C22⋊Q8—144no—
270C22⋊Q8—144no—
271C22⋊Q8—144no—
272C4×Q8—144no—
273C4×Q8—144no—
274C4×Q8—144no—
275C4×Q8—144no—
276#117—144no—
277#117—144no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—72no—
281C2×C4⋊C4—142no—
282C2×C4⋊C4—142no—
283C2×C4⋊C4—141no—
284C2×C22⋊C4—142no—
285C2×C42—71no—
286C2×C42—71no—
287C2×C42—71no—
288C2×C42—142no—
289C2×C42—141no—
290C2×C42—141no—
291C2×C42—141no—
292C2×C42—141no—
293C2×C42C22×D711yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8—21no—
298C4⋊C8—141no—
299C4⋊C8—141no—
300C4⋊C8—141no—
301C4⋊C8—141no—
302C22⋊C8—282no—
303C22⋊C8—282no—
304C22×C7#37911yescharacteristic
305C22×C7#41311yescharacteristic
306C22×C7#41311yescharacteristic
307C22×C7C2×#10311yescharacteristic
308C22×C7#41611yescharacteristic
309C22×C7#41711yescharacteristic
310C22×C7#41911yescharacteristic
311C2×D7—22no—
312C2×D7—22no—
313C2×D7—22no—
314C2×D7—41no—
315C2×D7—41no—
316C2×D7—41no—
317C2×D7—41no—
318C4×C7—21no—
319C4×C7—21no—
320C4×C7—44no—
321C4×C7#44811yescharacteristic
322C4×C7#44811yescharacteristic
323C4×C7#44911yescharacteristic
324C4×C7#44911yescharacteristic
325C4×C7#45111yescharacteristic
326C4×C7#45111yescharacteristic
327C4×C7#45211yescharacteristic
328C4×C7#45211yescharacteristic
329Dic7—22no—
330Dic7—41no—
331Dic7—44no—
332Dic7—41no—
333C24—71no—
334C2×Q8—22no—
335C2×Q8—42no—
336C2×Q8—42no—
337C2×Q8—142no—
338C2×Q8—142no—
339C2×Q8—281no—
340C2×Q8—281no—
341C2×Q8—281no—
342C2×Q8—281no—
343C2×Q8(C2×D7)⋊C414yes—
344C22×C4—22no—
345C22×C4—71no—
346C22×C4—72no—
347C22×C4—72no—
348C22×C4—71no—
349C22×C4—71no—
350C22×C4—141no—
351C22×C4—141no—
352C22×C4—141no—
353C22×C4—141no—
354C22×C4—142no—
355C22×C4—141no—
356C22×C4—141no—
357C22×C4—141no—
358C22×C4—141no—
359C22×C4—141no—
360C22×C4—141no—
361C22×C4—141no—
362C22×C4—141no—
363C22×C4—281no—
364C22×C4—281no—
365C22×C4C2×C4×D711yescharacteristic
366C22×C4D4×D711yescharacteristic
367C22×C4D4×D711yescharacteristic
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—41no—
374C2×C8—281no—
375C2×C8—281no—
376C2×C8—281no—
377C2×C8—281no—
378C2×C8—281no—
379C2×C8—281no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—74no—
385C4⋊C4—148no—
386C4⋊C4—148no—
387C4⋊C4—142no—
388C4⋊C4—142no—
389C4⋊C4—142no—
390C22⋊C4—148no—
391C42—148no—
392C42—141no—
393C42—141no—
394C42—141no—
395C42—141no—
396C42—141no—
397C42—141no—
398C42C2×D2811yescharacteristic
399C42D4×D711yescharacteristic
400C42D4×D711yescharacteristic
401C42C2×C22⋊D711yescharacteristic
402C2×C7#154211yescharacteristic
403C2×C7#155011yescharacteristic
404C2×C7#155411yescharacteristic
405C2×C7#155911yescharacteristic
406C2×C7#178511yescharacteristic
407C2×C7#178711yescharacteristic
408C2×C7#178811yescharacteristic
409D7—42no—
410C23—72no—
411C23—141no—
412C23—141no—
413C23—141no—
414C23—141no—
415C23—141no—
416C23—141no—
417C23D7×C22⋊C411yescharacteristic
418Q8—44no—
419Q8—44no—
420Q8—282no—
421Q8—282no—
422Q8—282no—
423Q8—282no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—24no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—72no—
430C2×C4—141no—
431C2×C4—141no—
432C2×C4—142no—
433C2×C4—142no—
434C2×C4—142no—
435C2×C4—142no—
436C2×C4—141no—
437C2×C4—141no—
438C2×C4—144no—
439C2×C4—141no—
440C2×C4—141no—
441C2×C4—141no—
442C2×C4—141no—
443C2×C4—282no—
444C2×C4—282no—
445C2×C4—282no—
446C2×C4—282no—
447C2×C4—281no—
448C2×C4—281no—
449C2×C4—281no—
450C2×C4—281no—
451C2×C4D7×C22⋊C411yescharacteristic
452C2×C4#644511yescharacteristic
453C2×C4#644511yescharacteristic
454C2×C4D7×SD1611yescharacteristic
455C2×C4#647711yescharacteristic
456C2×C4#647811yescharacteristic
457C2×C4#647911yescharacteristic
458C2×C4D7×Q1611yescharacteristic
459C2×C4#648111yescharacteristic
460C2×C4#648111yescharacteristic
461C2×C4#648211yescharacteristic
462C2×C4C2×(C2×D7)⋊C411yescharacteristic
463C2×C4#650011yescharacteristic
464C2×C4#650011yescharacteristic
465C8—81no—
466C8—81no—
467C8—561no—
468C8—561no—
469C7#834311yescharacteristic, complemented, Sylow
470C22—142no—
471C22—142no—
472C22—142no—
473C22—281no—
474C22—281no—
475C22—281no—
476C22—281no—
477C22#8951711yescharacteristic
478C22#8951711yescharacteristic
479C22D7×#10311yescharacteristic
480C22#8957411yescharacteristic
481C22#8957511yescharacteristic
482C22#8957611yescharacteristic
483C22#8972711yescharacteristic
484C4—21no—
485C4—21no—
486C4—44no—
487C4—142no—
488C4—281no—
489C4—284no—
490C4—281no—
491C4#8957811yescharacteristic
492C4#8958011yescharacteristic
493C4#8958211yescharacteristic
494C4#8958311yescharacteristic
495C4#8994211yescharacteristic
496C4#8994411yescharacteristic
497C4#8995811yescharacteristic
498C4#8995911yescharacteristic
499C2—282no—
500C2#1172623511yescharacteristic
501C2#1172623811yescharacteristic
502C2#1172624011yescharacteristic
503C2#1172624211yescharacteristic
504C2#1172783411yescharacteristic
505C2#1172802011yescharacteristic
506C2#1172802111yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC2×C7×#333C2
socleC23×C7C2×C22⋊C4
prime radicalC23×D7C22⋊C4
cosocleC2×C42×C7C23
hypercenterC2×#333D7
hypocenterC7#8343
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
2. C2×C7×#333C2semidirect
3. C2×#89341C2semidirect
6. C2×#89277C2semidirect
7. C2×#89281C2semidirect
93. C2×#333D7semidirect
469. C7#8343semidirect

Maximal subgroups

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

subgroupindex
C2×#904192
C2×C7×#3332
C2×#893412
#117282292
C2×#892772
C2×#892812
#83437