Finite Group Databasebeta

← #13248970

Subgroups — #13248970

Order 1792.

594 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#484C211yesmaximal, characteristic
2#11740190C211yesmaximal, characteristic
3C2×#89333C211yesmaximal, characteristic
4#11729323C211yesmaximal, characteristic
5#11729308C211yesmaximal, characteristic
6#11725481C211yesmaximal, characteristic
7#11725480C211yesmaximal, characteristic
8C2×C7×C22⋊Q8C2211yescharacteristic
9C22×C7×C4⋊C4C2211yescharacteristic
10C7×#484—22no—
11C7×#484C414yescomplemented
12C2×C7×#107—21no—
13C2×C7×#103—21no—
14C2×C7×C22⋊C8C2211yescharacteristic
15#90002—21no—
16#89984C2211yescharacteristic
17C2×C7⋊#95—21no—
18C2×C7⋊#95—21no—
19C2×C7⋊#95C2211yescharacteristic
20C2×C7⋊#95C2211yescharacteristic
21C2×C22⋊(C7⋊C8)C2211yescharacteristic
22#89757—21no—
23#89753—21no—
24#89753—21no—
25#89722—21no—
26C22⋊C4×Dic7—21no—
27#89333—22no—
28#89324—21no—
29#89324—21no—
30#9046—71nomaximal, Sylow
31C22×C7×Q8D411yescharacteristic
32C23×C4×C7—21no—
33C23×C4×C7C2311yescharacteristic
34C23×Dic7—21no—
35C23×Dic7D411yescharacteristic
36C23×Dic7D411yescharacteristic
37C22×C7×C8—21no—
38C7×C22⋊Q8—21no—
39C7×C22⋊Q8—21no—
40C7×C22⋊Q8C2×C412yes—
41C7×C22⋊Q8D412yes—
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×C7×C4⋊C4—21no—
48C2×C7×C4⋊C4C2×C412yes—
49C2×C7×C4⋊C4D411yescharacteristic
50C2×C7×C22⋊C4—21no—
51C2×C22⋊Dic7—21no—
52C2×C4⋊Dic7—21no—
53C2×C4⋊Dic7—21no—
54C2×C4⋊Dic7D411yescharacteristic
55C2×C4⋊Dic7D411yescharacteristic
56C2×C4×Dic7—21no—
57C2×C4×Dic7—21no—
58C22×C7⋊C8—21no—
59C7×#107—24no—
60C7×#103—24no—
61C7×C22⋊C8—21no—
62C7×C22⋊C8C2×C412yes—
63C7⋊#95—21no—
64C7⋊#95—21no—
65C7⋊#95—21no—
66C7⋊#95—21no—
67C7⋊#95—21no—
68C7⋊#95—21no—
69C7⋊#95—21no—
70C7⋊#95—21no—
71C7⋊#95—21no—
72C7⋊#95—42no—
73C7⋊#95—42no—
74C22⋊(C7⋊C8)—21no—
75C22⋊(C7⋊C8)—21no—
76C2×#484D711yescharacteristic
77#2329—71no—
78#1824—71no—
79C2×#328—71no—
80#1445—71no—
81#1294—71no—
82#1280—71no—
83C24×C7C2×D411yescharacteristic
84C2×C7×Q8—21no—
85C2×C7×Q8—41no—
86C2×C7×Q8—41no—
87C2×C7×Q8C22⋊C412yes—
88C22×C4×C7—21no—
89C22×C4×C7—21no—
90C22×C4×C7—22no—
91C22×C4×C7—41no—
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×C7—41no—
99C22×C4×C7C22×C411yescharacteristic
100C22×C4×C7C2×D411yescharacteristic
101C22×C4×C7C2×D411yescharacteristic
102C22×C4×C7C2×D411yescharacteristic
103C22×C4×C7#4111yescharacteristic
104C22×C4×C7#4111yescharacteristic
105C22×Dic7—21no—
106C22×Dic7—21no—
107C22×Dic7—22no—
108C22×Dic7—21no—
109C22×Dic7—21no—
110C22×Dic7—21no—
111C22×Dic7—21no—
112C22×Dic7—21no—
113C22×Dic7—41no—
114C22×Dic7—41no—
115C22×Dic7—41no—
116C22×Dic7—41no—
117C22×Dic7—41no—
118C22×Dic7—41no—
119C22×Dic7—41no—
120C22×Dic7—41no—
121C22×Dic7—41no—
122C22×Dic7—41no—
123C22×Dic7Q1612yes—
124C2×C7×C8—22no—
125C2×C7×C8—41no—
126C2×C7×C8—41no—
127C7×C4⋊C4—22no—
128C7×C4⋊C4—22no—
129C7×C4⋊C4—21no—
130C7×C4⋊C4—22no—
131C7×C4⋊C4—22no—
132C7×C4⋊C4—41no—
133C7×C4⋊C4—41no—
134C7×C4⋊C4C22⋊C412yes—
135C7×C22⋊C4—22no—
136C7×C22⋊C4—22no—
137C22⋊Dic7—41no—
138C22⋊Dic7—41no—
139C4⋊Dic7—41no—
140C4⋊Dic7—41no—
141C4⋊Dic7—81no—
142C4⋊Dic7—81no—
143C4×Dic7—81no—
144C4×Dic7—81no—
145C2×C7⋊C8—41no—
146C2×C7⋊C8—41no—
147C2×C7⋊C8—41no—
148C2×C22⋊Q8C2×D711yescharacteristic
149C22×C4⋊C4C2×D711yescharacteristic
150#484—22no—
151#484Dic714yescomplemented
152C2×#107—21no—
153C2×#103—21no—
154C2×C22⋊C8—71no—
155C2×C22⋊C8C2×D711yescharacteristic
156#391—141no—
157#389—141no—
158#387—141no—
159#387—141no—
160#385—141no—
161#380—71no—
162C4×C22⋊C4—141no—
163C2×#95—71no—
164C2×#95—71no—
165C2×#95—141no—
166C2×#95—141no—
167#340—141no—
168#340—141no—
169#328—142no—
170C23×C7—21no—
171C23×C7—21no—
172C23×C7—21no—
173C23×C7—21no—
174C23×C7C4×D411yescharacteristic
175C23×C7#12011yescharacteristic
176C23×C7#12111yescharacteristic
177C23×C7C2×Q1611yescharacteristic
178C23×C7#13511yescharacteristic
179C23×C7#13711yescharacteristic
180C23×C7#13711yescharacteristic
181C7×Q8—42no—
182C7×Q8—81no—
183C2×C4×C7—21no—
184C2×C4×C7—21no—
185C2×C4×C7—21no—
186C2×C4×C7—21no—
187C2×C4×C7—22no—
188C2×C4×C7—22no—
189C2×C4×C7—41no—
190C2×C4×C7—41no—
191C2×C4×C7—41no—
192C2×C4×C7—41no—
193C2×C4×C7—41no—
194C2×C4×C7—41no—
195C2×C4×C7—41no—
196C2×C4×C7—41no—
197C2×C4×C7—42no—
198C2×C4×C7—42no—
199C2×C4×C7—42no—
200C2×C4×C7—81no—
201C2×C4×C7—81no—
202C2×C4×C7—81no—
203C2×C4×C7—81no—
204C2×C4×C7C2×C22⋊C411yescharacteristic
205C2×C4×C7C4×D411yescharacteristic
206C2×C4×C7#12111yescharacteristic
207C2×C4×C7#12311yescharacteristic
208C2×Dic7—22no—
209C2×Dic7—41no—
210C2×Dic7—41no—
211C2×Dic7—42no—
212C2×Dic7—42no—
213C2×Dic7—42no—
214C2×Dic7—42no—
215C2×Dic7—42no—
216C2×Dic7—41no—
217C2×Dic7—41no—
218C2×Dic7—41no—
219C2×Dic7—41no—
220C2×Dic7—41no—
221C2×Dic7—41no—
222C2×Dic7—41no—
223C2×Dic7—41no—
224C2×Dic7—41no—
225C2×Dic7—81no—
226C2×Dic7—81no—
227C2×Dic7—81no—
228C2×Dic7—81no—
229C2×Dic7—81no—
230C2×Dic7—81no—
231C7×C8—42no—
232C7⋊C8—81no—
233C22×Q8C22⋊D711yescharacteristic
234C23×C4—21no—
235C23×C4—71no—
236C23×C4—71no—
237C23×C4—141no—
238C23×C4C22×D711yescharacteristic
239C22×C8—21no—
240C22×C8—141no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8C2×Dic712yes—
244C22⋊Q8C22⋊D712yes—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—71no—
252C2×C4⋊C4—71no—
253C2×C4⋊C4—141no—
254C2×C4⋊C4—141no—
255C2×C4⋊C4C2×Dic712yes—
256C2×C4⋊C4C22⋊D711yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—141no—
259C2×C42—141no—
260C2×C42—141no—
261#107—24no—
262#103—24no—
263C22⋊C8—21no—
264C22⋊C8—141no—
265C22⋊C8—141no—
266C22⋊C8C2×Dic712yes—
267#95—141no—
268#95—141no—
269#95—141no—
270#95—141no—
271#95—141no—
272#95—141no—
273#95—141no—
274#95—141no—
275#95—141no—
276#95—282no—
277#95—282no—
278C22×C7—21no—
279C22×C7—21no—
280C22×C7—21no—
281C22×C7—21no—
282C22×C7—21no—
283C22×C7—21no—
284C22×C7—21no—
285C22×C7—21no—
286C22×C7—21no—
287C22×C7—21no—
288C22×C7—21no—
289C22×C7—21no—
290C22×C7#38611yescharacteristic
291C22×C7C4×Q1611yescharacteristic
292C22×C7#44111yescharacteristic
293C22×C7#45111yescharacteristic
294C22×C7#45211yescharacteristic
295C22×C7#45311yescharacteristic
296C22×C7#45411yescharacteristic
297C22×C7#45811yescharacteristic
298C22×C7#45811yescharacteristic
299C22×C7#46211yescharacteristic
300C22×C7#46411yescharacteristic
301C4×C7—21no—
302C4×C7—21no—
303C4×C7—21no—
304C4×C7—21no—
305C4×C7—42no—
306C4×C7—42no—
307C4×C7—82no—
308Dic7—42no—
309Dic7—82no—
310Dic7—81no—
311Dic7—81no—
312Dic7—81no—
313C24D4×D711yescharacteristic
314C2×Q8—21no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×Q8C22⋊Dic712yes—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—72no—
330C22×C4—141no—
331C22×C4—141no—
332C22×C4—142no—
333C22×C4—141no—
334C22×C4—141no—
335C22×C4—141no—
336C22×C4—141no—
337C22×C4—141no—
338C22×C4—281no—
339C22×C4—281no—
340C22×C4—281no—
341C22×C4—281no—
342C22×C4—281no—
343C22×C4—281no—
344C22×C4—281no—
345C22×C4—281no—
346C22×C4—281no—
347C22×C4—281no—
348C22×C4D4×D711yescharacteristic
349C22×C4#115911yescharacteristic
350C22×C4#115911yescharacteristic
351C22×C4C22×Dic711yescharacteristic
352C22×C4C2×C22⋊D711yescharacteristic
353C22×C4C2×C22⋊D711yescharacteristic
354C2×C8—22no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—281no—
358C2×C8—281no—
359C2×C8—281no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—281no—
368C4⋊C4—281no—
369C4⋊C4—561no—
370C4⋊C4—561no—
371C4⋊C4C22⋊Dic712yes—
372C22⋊C4—22no—
373C22⋊C4—22no—
374C22⋊C4—281no—
375C22⋊C4—281no—
376C42—561no—
377C42—561no—
378C2×C7—21no—
379C2×C7—21no—
380C2×C7—21no—
381C2×C7—21no—
382C2×C7#161411yescharacteristic
383C2×C7#161511yescharacteristic
384C2×C7#161711yescharacteristic
385C2×C7#161811yescharacteristic
386C2×C7#187811yescharacteristic
387C2×C7#188311yescharacteristic
388C2×C7#189011yescharacteristic
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23D7×Q1611yescharacteristic
394C23#648111yescharacteristic
395C23#648111yescharacteristic
396C23#648211yescharacteristic
397C23D4×Dic711yescharacteristic
398C23#650011yescharacteristic
399C23#650211yescharacteristic
400Q8—42no—
401Q8—81no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—142no—
424C2×C4—281no—
425C2×C4—281no—
426C2×C4—282no—
427C2×C4—282no—
428C2×C4—282no—
429C2×C4—282no—
430C2×C4—282no—
431C2×C4—281no—
432C2×C4—281no—
433C2×C4—281no—
434C2×C4—281no—
435C2×C4—281no—
436C2×C4—281no—
437C2×C4—281no—
438C2×C4—281no—
439C2×C4—281no—
440C2×C4—561no—
441C2×C4—561no—
442C2×C4—561no—
443C2×C4—561no—
444C2×C4—561no—
445C2×C4—561no—
446C2×C4D4×Dic711yescharacteristic
447C2×C4#649811yescharacteristic
448C2×C4#650211yescharacteristic
449C2×C4C2×C22⋊Dic711yescharacteristic
450C8—42no—
451C8—561no—
452C7#904611yescharacteristic, complemented, Sylow
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22#8982511yescharacteristic
466C22#8982511yescharacteristic
467C22#8995411yescharacteristic
468C22Q16×Dic711yescharacteristic
469C22#8995611yescharacteristic
470C22#8995711yescharacteristic
471C22#8995811yescharacteristic
472C22#8995911yescharacteristic
473C22#8997011yescharacteristic
474C22#8997311yescharacteristic
475C22#8999211yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—42no—
481C4—42no—
482C4—82no—
483C4—282no—
484C4—562no—
485C4—561no—
486C4—561no—
487C4—561no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2#1172893011yescharacteristic
493C2#1172893111yescharacteristic
494C2#1172893211yescharacteristic
495C2#1172893311yescharacteristic
496C2#1172945811yescharacteristic
497C2#1172981911yescharacteristic
498C2#1172984211yescharacteristic
subgroupG/H
centerC23#6500
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#484C2
socleC23×C7#120
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenterC2×#484D7
hypocenterC7#9046
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
11. C7×#484C4semidirect
151. #484Dic7semidirect
452. C7#9046semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4842
#117401902
C2×#893332
#117293232
#117293082
#117254812
#117254802
#90467