Finite Group Databasebeta

← #13252640

Subgroups — #13252640

Order 1792.

640 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89744C211yesmaximal, characteristic
2C2×C7×#324C211yesmaximal, characteristic
3C2×#89323C211yesmaximal, characteristic
4C2×#89264C211yesmaximal, characteristic
5C2×#89264C211yesmaximal, characteristic
6#11727662C211yesmaximal, characteristic
7#11727660C211yesmaximal, characteristic
8C22×C7×C4⋊C4C2211yescharacteristic
9C22×Dic7⋊C4C411yescharacteristic
10C22×Dic7⋊C4C411yescharacteristic
11C22×Dic7⋊C4C2211yescharacteristic
12C22×C4×Dic7C2211yescharacteristic
13C2×C7×C22⋊C8C2211yescharacteristic
14C2×C7×C22⋊C8C2211yescharacteristic
15C2×C7⋊#95C411yescharacteristic
16C2×C7⋊#95C411yescharacteristic
17C2×C22⋊(C7⋊C8)C2211yescharacteristic
18C2×C22⋊(C7⋊C8)C2211yescharacteristic
19C2×#6389—21no—
20C2×Dic7⋊C8—21no—
21#89744—21no—
22#89744—21no—
23#89744—21no—
24#89744—21no—
25C7×#324—22no—
26#89345—21no—
27#89345—21no—
28#89323—22no—
29#89264—22no—
30#89264—22no—
31#9654—71nomaximal, Sylow
32C23×C4×C7C2×C411yescharacteristic
33C23×C4×C7C2×C411yescharacteristic
34C23×C4×C7C2311yescharacteristic
35C23×Dic7C2×C411yescharacteristic
36C23×Dic7C2×C411yescharacteristic
37C23×Dic7C2×C411yescharacteristic
38C23×Dic7C2×C411yescharacteristic
39C22×C7×C8—21no—
40C22×C7×C8—21no—
41C2×C7×C4⋊C4—21no—
42C2×C7×C4⋊C4—21no—
43C2×C7×C4⋊C4—21no—
44C2×C7×C4⋊C4—21no—
45C2×C7×C4⋊C4—21no—
46C2×C7×C4⋊C4—21no—
47C2×Dic7⋊C4—22no—
48C2×Dic7⋊C4—21no—
49C2×Dic7⋊C4—21no—
50C2×Dic7⋊C4—22no—
51C2×Dic7⋊C4—21no—
52C2×Dic7⋊C4—21no—
53C2×Dic7⋊C4—21no—
54C2×Dic7⋊C4—21no—
55C2×Dic7⋊C4—21no—
56C2×Dic7⋊C4—21no—
57C2×Dic7⋊C4—21no—
58C2×Dic7⋊C4—21no—
59C2×Dic7⋊C4—42no—
60C2×C4×Dic7—42no—
61C2×C4×Dic7D411yescharacteristic
62C2×C4×Dic7D411yescharacteristic
63C2×C4×Dic7D411yescharacteristic
64C2×C4×Dic7D411yescharacteristic
65C22×C7⋊C8—21no—
66C22×C7⋊C8—21no—
67C7×C22⋊C8—21no—
68C7×C22⋊C8—21no—
69C7×C22⋊C8—21no—
70C7×C22⋊C8D412yes—
71C7⋊#95—21no—
72C7⋊#95—21no—
73C7⋊#95—21no—
74C7⋊#95—21no—
75C22⋊(C7⋊C8)—21no—
76C22⋊(C7⋊C8)—21no—
77C22⋊(C7⋊C8)—21no—
78C22⋊(C7⋊C8)D412yes—
79#6389—42no—
80Dic7⋊C8—42no—
81C2×#389—71no—
82#1797—71no—
83#1749—71no—
84C2×#324—71no—
85C2×#324—71no—
86C2×#324—71no—
87C2×#324D711yescharacteristic
88C24×C7C22×C411yescharacteristic
89C22×C4×C7—21no—
90C22×C4×C7—21no—
91C22×C4×C7—21no—
92C22×C4×C7—21no—
93C22×C4×C7—21no—
94C22×C4×C7—21no—
95C22×C4×C7—21no—
96C22×C4×C7—21no—
97C22×C4×C7—21no—
98C22×C4×C7—41no—
99C22×C4×C7—41no—
100C22×C4×C7—41no—
101C22×C4×C7—41no—
102C22×C4×C7M1612yes—
103C22×C4×C7C2×D411yescharacteristic
104C22×C4×C7C2×D411yescharacteristic
105C22×C4×C7C2×D411yescharacteristic
106C22×C4×C7C2×D411yescharacteristic
107C22×C4×C7#4111yescharacteristic
108C22×C4×C7#4111yescharacteristic
109C22×Dic7—21no—
110C22×Dic7—21no—
111C22×Dic7—22no—
112C22×Dic7—22no—
113C22×Dic7—21no—
114C22×Dic7—21no—
115C22×Dic7—21no—
116C22×Dic7—21no—
117C22×Dic7—21no—
118C22×Dic7—21no—
119C22×Dic7—21no—
120C22×Dic7—21no—
121C22×Dic7—22no—
122C22×Dic7—21no—
123C22×Dic7—21no—
124C22×Dic7—21no—
125C22×Dic7—41no—
126C22×Dic7—41no—
127C22×Dic7—41no—
128C22×Dic7C22⋊C411yescharacteristic
129C22×Dic7C22⋊C411yescharacteristic
130C22×Dic7C22⋊C411yescharacteristic
131C22×Dic7C22⋊C411yescharacteristic
132C22×Dic7M1612yes—
133C2×C7×C8—22no—
134C2×C7×C8—41no—
135C2×C7×C8—41no—
136C2×C7×C8—41no—
137C2×C7×C8—41no—
138C2×C7×C8—41no—
139C7×C4⋊C4—41no—
140C7×C4⋊C4—41no—
141C7×C4⋊C4—41no—
142C7×C4⋊C4—41no—
143Dic7⋊C4—24no—
144Dic7⋊C4—24no—
145Dic7⋊C4—42no—
146Dic7⋊C4—41no—
147Dic7⋊C4—41no—
148Dic7⋊C4—41no—
149Dic7⋊C4—41no—
150Dic7⋊C4—42no—
151C4×Dic7—22no—
152C4×Dic7—22no—
153C4×Dic7—41no—
154C4×Dic7—41no—
155C2×C7⋊C8—22no—
156C2×C7⋊C8—41no—
157C2×C7⋊C8—41no—
158C2×C7⋊C8—41no—
159C2×C7⋊C8—41no—
160C2×C7⋊C8—41no—
161C22×C4⋊C4—71no—
162C22×C4⋊C4—71no—
163C22×C4⋊C4—71no—
164C22×C4⋊C4C2×D711yescharacteristic
165C22×C42—71no—
166C2×C4⋊C8—141no—
167C2×C22⋊C8—71no—
168C2×C22⋊C8—71no—
169C2×C22⋊C8C2×D711yescharacteristic
170C2×C22⋊C8C2×D711yescharacteristic
171C2×#97—141no—
172#389—141no—
173#389—141no—
174#389—141no—
175#389—141no—
176C2×#95—71no—
177C2×#95—71no—
178#336—141no—
179#336—141no—
180#324—22no—
181#324—142no—
182#324—142no—
183#324—142no—
184C23×C7—21no—
185C23×C7—21no—
186C23×C7—21no—
187C23×C7—21no—
188C23×C7C2×C22⋊C411yescharacteristic
189C23×C7C4×D411yescharacteristic
190C23×C7C4×D411yescharacteristic
191C23×C7C2×M1611yescharacteristic
192C23×C7C2×M1611yescharacteristic
193C23×C7#13111yescharacteristic
194C23×C7#13111yescharacteristic
195C2×C4×C7—21no—
196C2×C4×C7—21no—
197C2×C4×C7—21no—
198C2×C4×C7—21no—
199C2×C4×C7—22no—
200C2×C4×C7—22no—
201C2×C4×C7—22no—
202C2×C4×C7—41no—
203C2×C4×C7—41no—
204C2×C4×C7—41no—
205C2×C4×C7—41no—
206C2×C4×C7—41no—
207C2×C4×C7—41no—
208C2×C4×C7—41no—
209C2×C4×C7—41no—
210C2×C4×C7—41no—
211C2×C4×C7—41no—
212C2×C4×C7—41no—
213C2×C4×C7—81no—
214C2×C4×C7—81no—
215C2×C4×C7#12111yescharacteristic
216C2×C4×C7#12111yescharacteristic
217C2×C4×C7#12411yescharacteristic
218C2×C4×C7#12711yescharacteristic
219C2×Dic7—24no—
220C2×Dic7—24no—
221C2×Dic7—21no—
222C2×Dic7—21no—
223C2×Dic7—21no—
224C2×Dic7—21no—
225C2×Dic7—21no—
226C2×Dic7—21no—
227C2×Dic7—22no—
228C2×Dic7—21no—
229C2×Dic7—21no—
230C2×Dic7—21no—
231C2×Dic7—22no—
232C2×Dic7—22no—
233C2×Dic7—42no—
234C2×Dic7—42no—
235C2×Dic7—41no—
236C2×Dic7—41no—
237C2×Dic7—41no—
238C2×Dic7—41no—
239C2×Dic7—41no—
240C2×Dic7—41no—
241C2×Dic7—41no—
242C2×Dic7—81no—
243C2×Dic7—81no—
244C2×Dic7#9912yes—
245C2×Dic7#10112yes—
246C2×Dic7#10112yes—
247C7×C8—42no—
248C7×C8—81no—
249C7⋊C8—42no—
250C7⋊C8—81no—
251C23×C4—71no—
252C23×C4—71no—
253C23×C4—71no—
254C23×C4—71no—
255C23×C4C4×D711yescharacteristic
256C23×C4C4×D711yescharacteristic
257C23×C4C22×D711yescharacteristic
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—141no—
261C22×C8—141no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—142no—
269C2×C4⋊C4—141no—
270C2×C4⋊C4—141no—
271C2×C4⋊C4—142no—
272C2×C4⋊C4—141no—
273C2×C4⋊C4—141no—
274C2×C4⋊C4—141no—
275C2×C4⋊C4—141no—
276C2×C4⋊C4—141no—
277C2×C4⋊C4—141no—
278C2×C4⋊C4—141no—
279C2×C4⋊C4—141no—
280C2×C4⋊C4—282no—
281C2×C42—71no—
282C2×C42—71no—
283C2×C42—71no—
284C2×C42—71no—
285C2×C42—282no—
286C4⋊C8—282no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—72no—
291C22⋊C8—141no—
292C22⋊C8—141no—
293C22⋊C8—141no—
294C22⋊C8C22⋊D712yes—
295#97—282no—
296#95—141no—
297#95—141no—
298#95—141no—
299#95—141no—
300C22×C7—21no—
301C22×C7—21no—
302C22×C7—21no—
303C22×C7—21no—
304C22×C7—21no—
305C22×C7—21no—
306C22×C7—21no—
307C22×C7—21no—
308C22×C7—21no—
309C22×C7—21no—
310C22×C7—21no—
311C22×C7—21no—
312C22×C7#39011yescharacteristic
313C22×C7#40711yescharacteristic
314C22×C7#40811yescharacteristic
315C22×C7C2×#9911yescharacteristic
316C22×C7#41011yescharacteristic
317C22×C7C2×#10111yescharacteristic
318C22×C7C2×#10111yescharacteristic
319C22×C7#43511yescharacteristic
320C22×C7#43511yescharacteristic
321C22×C7#43511yescharacteristic
322C22×C7#43511yescharacteristic
323C4×C7—21no—
324C4×C7—21no—
325C4×C7—21no—
326C4×C7—21no—
327C4×C7—42no—
328C4×C7—81no—
329Dic7—22no—
330Dic7—22no—
331Dic7—22no—
332Dic7—42no—
333Dic7—41no—
334Dic7—81no—
335C24C2×C4×D711yescharacteristic
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—71no—
350C22×C4—71no—
351C22×C4—71no—
352C22×C4—71no—
353C22×C4—72no—
354C22×C4—142no—
355C22×C4—142no—
356C22×C4—142no—
357C22×C4—141no—
358C22×C4—141no—
359C22×C4—141no—
360C22×C4—141no—
361C22×C4—141no—
362C22×C4—141no—
363C22×C4—141no—
364C22×C4—141no—
365C22×C4—141no—
366C22×C4—141no—
367C22×C4—141no—
368C22×C4—141no—
369C22×C4—141no—
370C22×C4—281no—
371C22×C4—281no—
372C22×C4—281no—
373C22×C4#113112yes—
374C22×C4#115711yescharacteristic
375C22×C4D4×D711yescharacteristic
376C22×C4D4×D711yescharacteristic
377C22×C4D4×D711yescharacteristic
378C22×C4#115911yescharacteristic
379C22×C4C2×C22⋊D711yescharacteristic
380C2×C8—22no—
381C2×C8—41no—
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—142no—
387C2×C8—281no—
388C2×C8—281no—
389C2×C8—281no—
390C2×C8—281no—
391C2×C8—281no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—144no—
397C4⋊C4—144no—
398C4⋊C4—282no—
399C4⋊C4—282no—
400C4⋊C4—281no—
401C4⋊C4—281no—
402C4⋊C4—281no—
403C4⋊C4—281no—
404C42—142no—
405C42—142no—
406C42—281no—
407C42—281no—
408C2×C7—21no—
409C2×C7—21no—
410C2×C7—21no—
411C2×C7—21no—
412C2×C7#146311yescharacteristic
413C2×C7#146711yescharacteristic
414C2×C7#147011yescharacteristic
415C2×C7#147211yescharacteristic
416C2×C7#195511yescharacteristic
417C2×C7#196411yescharacteristic
418C2×C7#196611yescharacteristic
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23D7×C22⋊C411yescharacteristic
424C23(C22⋊D7)⋊C411yescharacteristic
425C23C2×#113111yescharacteristic
426C23#646411yescharacteristic
427C23D7×M1611yescharacteristic
428C23#647011yescharacteristic
429C23C4×C22⋊D711yescharacteristic
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—72no—
449C2×C4—72no—
450C2×C4—72no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—144no—
454C2×C4—144no—
455C2×C4—141no—
456C2×C4—141no—
457C2×C4—141no—
458C2×C4—141no—
459C2×C4—141no—
460C2×C4—141no—
461C2×C4—142no—
462C2×C4—142no—
463C2×C4—141no—
464C2×C4—142no—
465C2×C4—141no—
466C2×C4—141no—
467C2×C4—282no—
468C2×C4—282no—
469C2×C4—281no—
470C2×C4—281no—
471C2×C4—281no—
472C2×C4—281no—
473C2×C4—281no—
474C2×C4—281no—
475C2×C4—281no—
476C2×C4—561no—
477C2×C4—561no—
478C2×C4#644711yescharacteristic
479C2×C4#644811yescharacteristic
480C2×C4#650211yescharacteristic
481C2×C4#650311yescharacteristic
482C8—42no—
483C8—81no—
484C8—282no—
485C8—561no—
486C7#965411yescharacteristic, complemented, Sylow
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22#8949811yescharacteristic
500C22#8949911yescharacteristic
501C22#8950011yescharacteristic
502C22#8950211yescharacteristic
503C22#8951211yescharacteristic
504C22D7×#9911yescharacteristic
505C22D7×#10111yescharacteristic
506C22D7×#10111yescharacteristic
507C22#8972911yescharacteristic
508C22#8988311yescharacteristic
509C22#8989911yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—42no—
515C4—81no—
516C4—142no—
517C4—142no—
518C4—142no—
519C4—282no—
520C4—281no—
521C4—561no—
522C2—21no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2#1172588111yescharacteristic
527C2#1172588211yescharacteristic
528C2#1172589811yescharacteristic
529C2#1172590111yescharacteristic
530C2#1172767111yescharacteristic
531C2#1172778411yescharacteristic
532C2#1172785211yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutator, prime radicalC24×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#324C2
socleC23×C7C2×C22⋊C4
cosocleC23×C4×C7C23
hypercenterC2×#324D7
hypocenterC7#9654
LCSG ▷ C24×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
486. C7#9654semidirect

Maximal subgroups

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

subgroupindex
C2×#897442
C2×C7×#3242
C2×#893232
C2×#892642
#117276622
#117276602
#96547