Finite Group Databasebeta

← #13252929

Subgroups — #13252929

Order 1792.

624 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740256C211yesmaximal, characteristic
2C2×C7×#328C211yesmaximal, characteristic
3C2×#89333C211yesmaximal, characteristic
4C2×#89262C211yesmaximal, characteristic
5#11727662C211yesmaximal, characteristic
6#11727155C211yesmaximal, characteristic
7C2×#89247C211yesmaximal, characteristic
8C2×C7×C22⋊Q8C2211yescharacteristic
9C2×#6507C411yescharacteristic, complemented
10C2×#6487C2211yescharacteristic
11C22×C4×Dic7C2211yescharacteristic
12C2×C7×C22⋊C8C2211yescharacteristic
13C2×C7×#95C2211yescharacteristic
14#90002C411yescharacteristic, complemented
15C2×C7⋊#95—21no—
16C2×C7⋊#95—21no—
17C2×C7⋊#95C2211yescharacteristic
18C2×C22⋊(C7⋊C8)C2211yescharacteristic
19C2×Dic7⋊C8—21no—
20#89748C411yescharacteristic, complemented
21#89746C411yescharacteristic, complemented
22#89744—21no—
23#89744—21no—
24#89714—21no—
25#89714—21no—
26C7×#328—22no—
27#89345—21no—
28#89333—22no—
29#89262—22no—
30#89247—22no—
31#9714—71nomaximal, Sylow
32C22×C7×Q8C2×C411yescharacteristic
33C23×C4×C7—21no—
34C23×C4×C7C2311yescharacteristic
35C23×Dic7—21no—
36C23×Dic7D411yescharacteristic
37C23×Dic7D411yescharacteristic
38C22×Dic14C2×C411yescharacteristic
39C22×C7×C8—21no—
40C7×C22⋊Q8—21no—
41C7×C22⋊Q8—21no—
42C7×C22⋊Q8—21no—
43C7×C22⋊Q8—21no—
44C2×C7×C4⋊C4—21no—
45C2×C7×C4⋊C4C2×C411yescharacteristic
46C2×C7×C22⋊C4—21no—
47C2×C22⋊Dic7—21no—
48#6507—42no—
49C2×C4⋊Dic7C2×C411yescharacteristic
50#6487—21no—
51#6487—21no—
52#6487—21no—
53#6487—21no—
54C2×Dic7⋊C4—21no—
55C2×Dic7⋊C4—21no—
56C2×Dic7⋊C4—21no—
57C2×Dic7⋊C4—21no—
58C2×Dic7⋊C4—21no—
59C2×C4×Dic7—42no—
60C2×C4×Dic7C2×C411yescharacteristic
61C2×C4×Dic7C2×C411yescharacteristic
62C2×C4×Dic7D411yescharacteristic
63C2×C4×Dic7D411yescharacteristic
64C22×C7⋊C8—21no—
65C7×C22⋊C8—21no—
66C7×C22⋊C8—21no—
67C7×#95—21no—
68C7×#95D412yes—
69C7⋊#95—21no—
70C7⋊#95—21no—
71C7⋊#95—21no—
72C7⋊#95—21no—
73C7⋊#95—21no—
74C7⋊#95—42no—
75C7⋊#95—42no—
76C7⋊#95D412yes—
77C22⋊(C7⋊C8)—21no—
78C22⋊(C7⋊C8)—21no—
79Dic7⋊C8—42no—
80#2857—71no—
81#1797—71no—
82C2×#328—71no—
83C2×#328—71no—
84C2×#328—71no—
85C2×#328D711yescharacteristic
86#1434—71no—
87C24×C7C2×D411yescharacteristic
88C2×C7×Q8—21no—
89C2×C7×Q8—21no—
90C2×C7×Q8—41no—
91C2×C7×Q8—41no—
92C22×C4×C7—21no—
93C22×C4×C7—21no—
94C22×C4×C7—22no—
95C22×C4×C7—41no—
96C22×C4×C7—41no—
97C22×C4×C7—41no—
98C22×C4×C7—41no—
99C22×C4×C7—41no—
100C22×C4×C7—41no—
101C22×C4×C7—41no—
102C22×C4×C7—41no—
103C22×C4×C7C22×C411yescharacteristic
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—21no—
113C22×Dic7—21no—
114C22×Dic7—22no—
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×Dic7—41no—
124C22×Dic7C22⋊C411yescharacteristic
125C22×Dic7C22⋊C411yescharacteristic
126C22×Dic7C22⋊C411yescharacteristic
127C22×Dic7C22⋊C411yescharacteristic
128C22×Dic7SD1612yes—
129C22×Dic7Q1612yes—
130C2×Dic14—21no—
131C2×Dic14—21no—
132C2×Dic14—41no—
133C2×Dic14—41no—
134C2×C7×C8—41no—
135C2×C7×C8—41no—
136C2×C7×C8—41no—
137C7×C4⋊C4—21no—
138C7×C4⋊C4—21no—
139C7×C4⋊C4—41no—
140C7×C4⋊C4—41no—
141C7×C22⋊C4—41no—
142C7×C22⋊C4—41no—
143C22⋊Dic7—41no—
144C22⋊Dic7—41no—
145C4⋊Dic7—21no—
146C4⋊Dic7—21no—
147Dic7⋊C4—42no—
148Dic7⋊C4—42no—
149Dic7⋊C4—42no—
150Dic7⋊C4—41no—
151Dic7⋊C4—41no—
152Dic7⋊C4—42no—
153C4×Dic7—22no—
154C4×Dic7—22no—
155C4×Dic7—41no—
156C4×Dic7—41no—
157C2×C7⋊C8—41no—
158C2×C7⋊C8—41no—
159C2×C7⋊C8—41no—
160C2×C4⋊Q8—71no—
161C2×C22⋊Q8—71no—
162C2×C22⋊Q8C2×D711yescharacteristic
163C22×C42—71no—
164C2×C4⋊C8—141no—
165C2×C22⋊C8—71no—
166C2×C22⋊C8C2×D711yescharacteristic
167#391—71no—
168#391—71no—
169#389—141no—
170#389—141no—
171#384—71no—
172#380—141no—
173#380—141no—
174C2×#95—71no—
175C2×#95—141no—
176C2×#95—141no—
177C2×#95C2×D711yescharacteristic
178#336—141no—
179#328—22no—
180#328—142no—
181#328—142no—
182#328—142no—
183C23×C7—21no—
184C23×C7—21no—
185C23×C7—21no—
186C23×C7—21no—
187C23×C7C2×C22⋊C411yescharacteristic
188C23×C7#12111yescharacteristic
189C23×C7#12111yescharacteristic
190C23×C7C2×SD1611yescharacteristic
191C23×C7C2×Q1611yescharacteristic
192C23×C7#13711yescharacteristic
193C23×C7#13711yescharacteristic
194C7×Q8—81no—
195C7×Q8—81no—
196C2×C4×C7—21no—
197C2×C4×C7—21no—
198C2×C4×C7—21no—
199C2×C4×C7—21no—
200C2×C4×C7—41no—
201C2×C4×C7—41no—
202C2×C4×C7—41no—
203C2×C4×C7—41no—
204C2×C4×C7—42no—
205C2×C4×C7—42no—
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—42no—
213C2×C4×C7—81no—
214C2×C4×C7—81no—
215C2×C4×C7—81no—
216C2×C4×C7—81no—
217C2×C4×C7C4×D411yescharacteristic
218C2×C4×C7C4×D411yescharacteristic
219C2×C4×C7#12411yescharacteristic
220C2×C4×C7#12711yescharacteristic
221C2×Dic7—21no—
222C2×Dic7—21no—
223C2×Dic7—21no—
224C2×Dic7—21no—
225C2×Dic7—21no—
226C2×Dic7—21no—
227C2×Dic7—21no—
228C2×Dic7—21no—
229C2×Dic7—21no—
230C2×Dic7—42no—
231C2×Dic7—42no—
232C2×Dic7—42no—
233C2×Dic7—42no—
234C2×Dic7—42no—
235C2×Dic7—42no—
236C2×Dic7—41no—
237C2×Dic7—41no—
238C2×Dic7—41no—
239C2×Dic7—41no—
240C2×Dic7—41no—
241C2×Dic7—41no—
242C2×Dic7—42no—
243C2×Dic7—81no—
244C2×Dic7—81no—
245C2×Dic7—81no—
246C2×Dic7—81no—
247C2×Dic7#9912yes—
248C2×Dic7#10312yes—
249C2×Dic7#10312yes—
250Dic14—81no—
251Dic14—81no—
252C7×C8—81no—
253C7⋊C8—81no—
254C22×Q8—71no—
255C22×Q8C4×D711yescharacteristic
256C23×C4—21no—
257C23×C4—71no—
258C23×C4—71no—
259C23×C4—141no—
260C23×C4C22×D711yescharacteristic
261C22×C8—21no—
262C22×C8—141no—
263C4⋊Q8—282no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—141no—
269C22⋊Q8—141no—
270C22⋊Q8—141no—
271C22⋊Q8—141no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—71no—
274C2×C4⋊C4—141no—
275C2×C4⋊C4—141no—
276C2×C4⋊C4—141no—
277C2×C4⋊C4—141no—
278C2×C4⋊C4—141no—
279C2×C4⋊C4C4×D711yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—141no—
282C2×C42—71no—
283C2×C42—71no—
284C2×C42—71no—
285C2×C42—71no—
286C2×C42—282no—
287C4⋊C8—282no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—141no—
291C22⋊C8—141no—
292#95—21no—
293#95—72no—
294#95—141no—
295#95—141no—
296#95—141no—
297#95—141no—
298#95—141no—
299#95—282no—
300#95—282no—
301#95C22⋊D712yes—
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—21no—
313C22×C7—21no—
314C22×C7#39011yescharacteristic
315C22×C7C2×#9911yescharacteristic
316C22×C7#41011yescharacteristic
317C22×C7C2×#10311yescharacteristic
318C22×C7#41911yescharacteristic
319C22×C7#42111yescharacteristic
320C22×C7#42111yescharacteristic
321C22×C7#46111yescharacteristic
322C22×C7#46111yescharacteristic
323C22×C7#46211yescharacteristic
324C22×C7#46211yescharacteristic
325C4×C7—21no—
326C4×C7—21no—
327C4×C7—21no—
328C4×C7—21no—
329C4×C7—82no—
330C4×C7—81no—
331C4×C7—81no—
332Dic7—22no—
333Dic7—22no—
334Dic7—22no—
335Dic7—41no—
336Dic7—82no—
337Dic7—81no—
338Dic7—81no—
339C24D4×D711yescharacteristic
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—141no—
345C2×Q8—141no—
346C2×Q8—281no—
347C2×Q8—281no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—71no—
360C22×C4—71no—
361C22×C4—71no—
362C22×C4—72no—
363C22×C4—72no—
364C22×C4—71no—
365C22×C4—142no—
366C22×C4—141no—
367C22×C4—141no—
368C22×C4—141no—
369C22×C4—141no—
370C22×C4—142no—
371C22×C4—281no—
372C22×C4—281no—
373C22×C4—281no—
374C22×C4—281no—
375C22×C4—281no—
376C22×C4—281no—
377C22×C4—281no—
378C22×C4—281no—
379C22×C4—281no—
380C22×C4C2×C4×D711yescharacteristic
381C22×C4#115711yescharacteristic
382C22×C4D4×D711yescharacteristic
383C22×C4D4×D711yescharacteristic
384C22×C4#115911yescharacteristic
385C22×C4C2×C22⋊D711yescharacteristic
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—41no—
389C2×C8—281no—
390C2×C8—281no—
391C2×C8—281no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—141no—
397C4⋊C4—141no—
398C4⋊C4—282no—
399C4⋊C4—282no—
400C4⋊C4—282no—
401C4⋊C4—282no—
402C4⋊C4—281no—
403C4⋊C4—281no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—281no—
407C22⋊C4—281no—
408C42—142no—
409C42—142no—
410C42—281no—
411C42—281no—
412C2×C7—21no—
413C2×C7—21no—
414C2×C7—21no—
415C2×C7—21no—
416C2×C7#151111yescharacteristic
417C2×C7#151511yescharacteristic
418C2×C7#151811yescharacteristic
419C2×C7#152011yescharacteristic
420C2×C7#196311yescharacteristic
421C2×C7#196411yescharacteristic
422C2×C7#198111yescharacteristic
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23D7×C22⋊C411yescharacteristic
428C23#644711yescharacteristic
429C23D7×SD1611yescharacteristic
430C23#647811yescharacteristic
431C23D7×Q1611yescharacteristic
432C23#648111yescharacteristic
433C23#650211yescharacteristic
434Q8—81no—
435Q8—81no—
436Q8—561no—
437Q8—561no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—72no—
456C2×C4—72no—
457C2×C4—72no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—141no—
463C2×C4—141no—
464C2×C4—141no—
465C2×C4—141no—
466C2×C4—141no—
467C2×C4—141no—
468C2×C4—141no—
469C2×C4—141no—
470C2×C4—141no—
471C2×C4—282no—
472C2×C4—282no—
473C2×C4—282no—
474C2×C4—282no—
475C2×C4—282no—
476C2×C4—282no—
477C2×C4—281no—
478C2×C4—281no—
479C2×C4—281no—
480C2×C4—281no—
481C2×C4—282no—
482C2×C4—281no—
483C2×C4—281no—
484C2×C4—561no—
485C2×C4—561no—
486C2×C4—561no—
487C2×C4—561no—
488C2×C4(C22⋊D7)⋊C411yescharacteristic
489C2×C4#644811yescharacteristic
490C2×C4C4×C22⋊D711yescharacteristic
491C2×C4#650311yescharacteristic
492C8—81no—
493C8—561no—
494C7#971411yescharacteristic, complemented, Sylow
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22#8951211yescharacteristic
508C22D7×#9911yescharacteristic
509C22#8956511yescharacteristic
510C22D7×#10311yescharacteristic
511C22#8957411yescharacteristic
512C22#8959011yescharacteristic
513C22#8959311yescharacteristic
514C22#8959311yescharacteristic
515C22#8972911yescharacteristic
516C22#8993411yescharacteristic
517C22#8995411yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—82no—
523C4—81no—
524C4—81no—
525C4—142no—
526C4—142no—
527C4—142no—
528C4—281no—
529C4—562no—
530C4—561no—
531C4—561no—
532C2—21no—
533C2—21no—
534C2—21no—
535C2—21no—
536C2#1172606711yescharacteristic
537C2#1172606811yescharacteristic
538C2#1172609011yescharacteristic
539C2#1172609311yescharacteristic
540C2#1172778411yescharacteristic
541C2#1172798311yescharacteristic
542C2#1172811111yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#328C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC23×C4×C7C23
hypercenterC2×#328D7
hypocenterC7#9714
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
9. C2×#6507C4semidirect
14. #90002C4semidirect
20. #89748C4semidirect
21. #89746C4semidirect
494. C7#9714semidirect

Maximal subgroups

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

subgroupindex
#117402562
C2×C7×#3282
C2×#893332
C2×#892622
#117276622
#117271552
C2×#892472
#97147