Finite Group Databasebeta

← #13371533

Subgroups — #13371533

Order 1792.

782 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2346C211yesmaximal, characteristic
2C2×#89767C211yesmaximal, characteristic
3#11730902C211yesmaximal, characteristic
4#11729329C211yesmaximal, characteristic
5#11727374C211yesmaximal, characteristic, complemented
6#11727373C211yesmaximal, characteristic, complemented
7#11727357C211yesmaximal, characteristic, complemented
8#11727354C211yesmaximal, characteristic, complemented
9#11727267C211yesmaximal, characteristic
10#11727255C211yesmaximal, characteristic
11#11727235C211yesmaximal, characteristic, complemented
12C4×#6382C211yesmaximal, characteristic, complemented
13#11727214C211yesmaximal, characteristic, complemented
14#11727213C211yesmaximal, characteristic, complemented
15#11727202C211yesmaximal, characteristic
16C2×C7×#117C2211yescharacteristic
17C22×C4⋊Dic7C2211yescharacteristic
18C22×#1136C2211yescharacteristic
19C7×#389C2211yescharacteristic
20C7×#389C2211yescharacteristic
21C7×#388—21no—
22C7×#388—21no—
23C7×#382—21no—
24C7×#380C2211yescharacteristic
25C4×C7×C4⋊C4C2211yescharacteristic
26C4×C7×C4⋊C4C2211yescharacteristic
27C4×C7×C22⋊C4C2211yescharacteristic
28C7×#376—21no—
29#89984C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31#89767C418yescomplemented
32C2×#6382C2211yescharacteristic
33C2×#6382C2211yescharacteristic
34C2×#6382C2211yescharacteristic
35C2×#6381C2211yescharacteristic
36C2×#6381C2211yescharacteristic
37C2×#6381C2211yescharacteristic
38#89714—21no—
39C22⋊C4×Dic7—21no—
40C4×C4⋊Dic7C2211yescharacteristic
41C4×C4⋊Dic7C2211yescharacteristic
42#89700C2211yescharacteristic
43#89700C2211yescharacteristic
44C2×#6377C2211yescharacteristic
45C2×C4×C7⋊C8C2211yescharacteristic
46#89426—21no—
47#89426—21no—
48#89324C2211yescharacteristic
49#89324C2211yescharacteristic
50#89324C2211yescharacteristic
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89319C2211yescharacteristic
59#89319C2211yescharacteristic
60#22621—71nomaximal, Sylow
61C23×C4×C7C2311yescharacteristic
62C23×Dic7—21no—
63C7×#117—22no—
64C7×#117C2×C414yes—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C22⋊C4—21no—
72C2×C7×C22⋊C4—21no—
73C2×C7×C22⋊C4D411yescharacteristic
74C2×C7×C22⋊C4D411yescharacteristic
75C2×C42×C7—21no—
76C2×C42×C7—21no—
77C2×C42×C7—21no—
78C2×C42×C7C2311yescharacteristic
79C2×C42×C7C2311yescharacteristic
80C2×C22⋊Dic7—21no—
81C2×C4⋊Dic7—21no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7C2×C414yes—
84C2×C4⋊Dic7C2311yescharacteristic
85C2×C4⋊Dic7C2311yescharacteristic
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—21no—
90C2×C4×Dic7—21no—
91C2×C4×Dic7—21no—
92C2×#1136—22no—
93C2×#1136—22no—
94C2×#1136C2×C414yes—
95C22×C7⋊C8C2311yescharacteristic
96C22×C7⋊C8C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98C22×C7⋊C8C2311yescharacteristic
99C7×#95—21no—
100C7×#95—21no—
101C7×#95—21no—
102C7×#95—21no—
103C7×#95—21no—
104C7×#95D411yescharacteristic
105C7×#95D411yescharacteristic
106C7⋊#95—21no—
107C7⋊#95—21no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C22⋊(C7⋊C8)—22no—
112#6382—22no—
113#6382C2×C414yes—
114#6382C2×C414yes—
115#6381—22no—
116#6381C2×C414yes—
117#6381C2×C414yes—
118#6377—22no—
119C4×C7⋊C8—22no—
120C2×#428—71no—
121#2346D711yescharacteristic
122#2345—71no—
123#1943—71no—
124#1942—71no—
125#1921—71no—
126#1920—71no—
127#1919—71no—
128#1918—71no—
129#1825—71no—
130#1823—71no—
131#1809—71no—
132#1776—71no—
133C4×#106—71no—
134#1753—71no—
135C24×C7C2×D411yescharacteristic
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7C22×C412yes—
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2×D411yescharacteristic
147C22×C4×C7C2×D411yescharacteristic
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7#4112yes—
151C22×C4×C7C2411yescharacteristic
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—24no—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—81no—
158C22×Dic7—81no—
159C7×C4⋊C4—21no—
160C7×C4⋊C4—21no—
161C7×C4⋊C4—21no—
162C7×C4⋊C4—21no—
163C7×C4⋊C4—21no—
164C7×C4⋊C4—21no—
165C7×C4⋊C4—81no—
166C7×C4⋊C4—81no—
167C7×C4⋊C4C22×C412yes—
168C7×C4⋊C4C22×C412yes—
169C7×C22⋊C4—24no—
170C7×C22⋊C4—22no—
171C7×C22⋊C4—41no—
172C7×C22⋊C4—81no—
173C42×C7—24no—
174C42×C7—21no—
175C42×C7—21no—
176C42×C7—21no—
177C42×C7—21no—
178C42×C7—42no—
179C42×C7—42no—
180C22⋊Dic7—42no—
181C4⋊Dic7—24no—
182C4⋊Dic7—21no—
183C4⋊Dic7—21no—
184C4⋊Dic7—21no—
185C4⋊Dic7—21no—
186C4⋊Dic7—21no—
187C4⋊Dic7—21no—
188C4⋊Dic7C22×C412yes—
189C4⋊Dic7C22×C412yes—
190Dic7⋊C4—81no—
191Dic7⋊C4—81no—
192C4×Dic7—81no—
193C4×Dic7—81no—
194#1136—28no—
195C2×C7⋊C8—21no—
196C2×C7⋊C8—21no—
197C2×C7⋊C8—21no—
198C2×C7⋊C8—21no—
199C2×C7⋊C8—21no—
200C2×C7⋊C8—21no—
201C2×C7⋊C8—21no—
202C2×C7⋊C8—21no—
203C2×C7⋊C8C22×C412yes—
204C2×C7⋊C8C22×C412yes—
205C2×C7⋊C8#4112yes—
206C2×C7⋊C8#4112yes—
207C22×M16—71no—
208C2×#117C2×D711yescharacteristic
209C22×C4⋊C4—71no—
210#428—78no—
211C2×#107—71no—
212C2×#107—71no—
213C2×#107—71no—
214C2×#106—71no—
215C2×#106—71no—
216C2×#106—71no—
217C2×C22⋊C8—71no—
218C2×#97—71no—
219C2×C4×C8—71no—
220#389—71no—
221#389—71no—
222#389C2×D711yescharacteristic
223#389C2×D711yescharacteristic
224#388—21no—
225#388—21no—
226#387—141no—
227#387—141no—
228#382—21no—
229#380—71no—
230#380—141no—
231#380C2×D711yescharacteristic
232C4×C4⋊C4—71no—
233C4×C4⋊C4—71no—
234C4×C4⋊C4C2×D711yescharacteristic
235C4×C4⋊C4C2×D711yescharacteristic
236C4×C22⋊C4—141no—
237C4×C22⋊C4C2×D711yescharacteristic
238#376—21no—
239#340—71no—
240#340—71no—
241#340—71no—
242#340—71no—
243#340—71no—
244#340—71no—
245#340—71no—
246#340—71no—
247#340—71no—
248#340—71no—
249#336—71no—
250#336—71no—
251C23×C7—21no—
252C23×C7—21no—
253C23×C7—21no—
254C23×C7—21no—
255C23×C7—21no—
256C23×C7—21no—
257C23×C7C4×D412yes—
258C23×C7C22×D411yescharacteristic
259C2×C4×C7—21no—
260C2×C4×C7—21no—
261C2×C4×C7—21no—
262C2×C4×C7—21no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—21no—
270C2×C4×C7—21no—
271C2×C4×C7—21no—
272C2×C4×C7—21no—
273C2×C4×C7—21no—
274C2×C4×C7—21no—
275C2×C4×C7—21no—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7—41no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7C4×D412yes—
289C2×C4×C7#13712yes—
290C2×C4×C7C23×C411yescharacteristic
291C2×C4×C7C2×#4111yescharacteristic
292C2×C4×C7C2×#4111yescharacteristic
293C2×C4×C7C2×#4111yescharacteristic
294C2×C4×C72−1+411yescharacteristic
295C2×C4×C72−1+411yescharacteristic
296C2×Dic7—22no—
297C2×Dic7—22no—
298C2×Dic7—41no—
299C2×Dic7—41no—
300C2×Dic7—41no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—84no—
309C7⋊C8—22no—
310C7⋊C8—41no—
311C7⋊C8—41no—
312C7⋊C8#11714yes—
313C23×C4—141no—
314C23×C4C22×D711yescharacteristic
315C2×M16—74no—
316C2×M16—142no—
317C2×M16—142no—
318C22×C8—71no—
319C22×C8—71no—
320C22×C8—71no—
321C22×C8—71no—
322#117—22no—
323#117C4×D714yes—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—74no—
327C2×C4⋊C4—71no—
328C2×C4⋊C4—71no—
329C2×C4⋊C4—71no—
330C2×C4⋊C4—71no—
331C2×C4⋊C4—142no—
332C2×C4⋊C4—141no—
333C2×C4⋊C4—141no—
334C2×C4⋊C4—141no—
335C2×C4⋊C4C22×D711yescharacteristic
336C2×C4⋊C4C22×D711yescharacteristic
337C2×C4⋊C4C22×D711yescharacteristic
338C2×C4⋊C4C22×D711yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—141no—
342C2×C22⋊C4C22⋊D711yescharacteristic
343C2×C22⋊C4C22⋊D711yescharacteristic
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—141no—
348C2×C42—141no—
349C2×C42C22×D711yescharacteristic
350C2×C42C22×D711yescharacteristic
351#107—74no—
352#107—74no—
353#107—142no—
354#106—74no—
355#106—74no—
356#106—142no—
357C22⋊C8—142no—
358#97—142no—
359C4×C8—142no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—141no—
366#95—141no—
367#95—141no—
368#95—141no—
369#95—141no—
370#95C22⋊D711yescharacteristic
371#95C22⋊D711yescharacteristic
372C22×C7—22no—
373C22×C7—22no—
374C22×C7—22no—
375C22×C7—41no—
376C22×C7—41no—
377C22×C7—41no—
378C22×C7—41no—
379C22×C7C2×C4×D411yescharacteristic
380C22×C7#54711yescharacteristic
381C22×C7#54711yescharacteristic
382C22×C7C2×#13711yescharacteristic
383C22×C7#57511yescharacteristic
384C22×C7#57611yescharacteristic
385C22×C7#57711yescharacteristic
386C4×C7—22no—
387C4×C7—22no—
388C4×C7—41no—
389C4×C7—41no—
390C4×C7—41no—
391C4×C7—42no—
392C4×C7—42no—
393C4×C7—81no—
394C4×C7—81no—
395C4×C7C2×#11711yescharacteristic
396C4×C7#51911yescharacteristic
397C4×C7#55211yescharacteristic
398C4×C7#55211yescharacteristic
399Dic7—42no—
400Dic7—42no—
401Dic7—81no—
402Dic7—81no—
403C24C2×C22⋊D711yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—141no—
413C22×C4—141no—
414C22×C4—144no—
415C22×C4—141no—
416C22×C4—141no—
417C22×C4—561no—
418C22×C4—561no—
419C22×C4C2×C4×D712yes—
420C22×C4#115712yes—
421C22×C4C2×C22⋊D711yescharacteristic
422C22×C4C2×C22⋊D711yescharacteristic
423C22×C4C2×C22⋊D711yescharacteristic
424C22×C4C2×C22⋊D711yescharacteristic
425C22×C4C2×C22⋊D711yescharacteristic
426C22×C4C23×D711yescharacteristic
427M16—148no—
428C2×C8—72no—
429C2×C8—72no—
430C2×C8—72no—
431C2×C8—72no—
432C2×C8—141no—
433C2×C8—141no—
434C2×C8—141no—
435C2×C8—141no—
436C2×C8—141no—
437C2×C8—141no—
438C2×C8—141no—
439C2×C8—141no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—72no—
447C4⋊C4—72no—
448C4⋊C4—81no—
449C4⋊C4—81no—
450C4⋊C4—144no—
451C4⋊C4—141no—
452C4⋊C4—141no—
453C4⋊C4—141no—
454C4⋊C4—141no—
455C4⋊C4—141no—
456C4⋊C4—141no—
457C4⋊C4—561no—
458C4⋊C4—561no—
459C4⋊C4C2×C4×D712yes—
460C4⋊C4C2×C4×D712yes—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—41no—
464C22⋊C4—81no—
465C22⋊C4—282no—
466C42—24no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—42no—
472C42—42no—
473C42—561no—
474C42—561no—
475C2×C7—42no—
476C2×C7#234411yescharacteristic
477C2×C7C4×#13711yescharacteristic
478C2×C7#294611yescharacteristic
479C2×C7#334411yescharacteristic
480C2×C7#334711yescharacteristic
481C2×C7#335111yescharacteristic
482C2×C7#335711yescharacteristic
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23C4×C22⋊D712yes—
490C23C22×C22⋊D711yescharacteristic
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—142no—
521C2×C4—142no—
522C2×C4—281no—
523C2×C4—281no—
524C2×C4—281no—
525C2×C4—281no—
526C2×C4—281no—
527C2×C4—281no—
528C2×C4—281no—
529C2×C4—281no—
530C2×C4—281no—
531C2×C4—281no—
532C2×C4—564no—
533C2×C4C4×C22⋊D712yes—
534C2×C4#651412yes—
535C2×C4C22×C4×D711yescharacteristic
536C2×C4C2×#115711yescharacteristic
537C2×C4D7×#4111yescharacteristic
538C2×C4D7×#4111yescharacteristic
539C2×C4#655411yescharacteristic
540C2×C4#655411yescharacteristic
541C8—74no—
542C8—142no—
543C8—281no—
544C8—281no—
545C7#2262111yescharacteristic, complemented, Sylow
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22C2×C4×C22⋊D711yescharacteristic
554C22#9051311yescharacteristic
555C22C2×#651411yescharacteristic
556C22#9051511yescharacteristic
557C22#9051511yescharacteristic
558C22#9052611yescharacteristic
559C22#9052811yescharacteristic
560C4—22no—
561C4—22no—
562C4—42no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—282no—
570C4—282no—
571C4—561no—
572C4—561no—
573C4#9020711yescharacteristic
574C4D7×#11711yescharacteristic
575C4#9022211yescharacteristic
576C4#9022211yescharacteristic
577C2—42no—
578C2#1173968311yescharacteristic
579C2C4×#651411yescharacteristic
580C2#1174000911yescharacteristic
581C2#1174103811yescharacteristic
582C2#1174104111yescharacteristic
583C2#1174109311yescharacteristic
584C2#1174109611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2346C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
cosocleC22×C4×C7C24
hypercenter#2346D7
hypocenterC7#22621
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2346

Complements

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

NH ≅ G/Ntype
5. #11727374C2semidirect
6. #11727373C2semidirect
7. #11727357C2semidirect
8. #11727354C2semidirect
11. #11727235C2semidirect
12. C4×#6382C2semidirect
13. #11727214C2semidirect
14. #11727213C2semidirect
31. #89767C4semidirect
545. C7#22621semidirect

Maximal subgroups

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

subgroupindex
C7×#23462
C2×#897672
#117309022
#117293292
#117273742
#117273732
#117273572
#117273542
#117272672
#117272552
#117272352
C4×#63822
#117272142
#117272132
#117272022
#226217