Finite Group Databasebeta

← #13325024

Subgroups — #13325024

Order 1792.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11736781C211yesmaximal, characteristic, complemented
2#11736745C211yesmaximal, characteristic
3#11736462C211yesmaximal, characteristic, complemented
4C7×#1573C211yesmaximal, characteristic, complemented
5#11728554C211yesmaximal, characteristic, complemented
6#11728496C211yesmaximal, characteristic, complemented
7C2×#89278C211yesmaximal, characteristic, complemented
8#11726319C211yesmaximal, characteristic, complemented
9#11726313C211yesmaximal, characteristic, complemented
10#11726313C211yesmaximal, characteristic, complemented
11#11726312C211yesmaximal, characteristic, complemented
12#11726279C211yesmaximal, characteristic, complemented
13#11726274C211yesmaximal, characteristic, complemented
14#11726273C211yesmaximal, characteristic, complemented
15#11726272C211yesmaximal, characteristic, complemented
16#90170C2211yescharacteristic
17C2×C4×D28C2211yescharacteristic
18C7×#432C2211yescharacteristic
19C7×#431C2211yescharacteristic
20C2×C7×C4⋊C8C2211yescharacteristic
21#89883—21no—
22C8×C22⋊D7—21no—
23#89697C2211yescharacteristic
24C2×C4×C7⋊C8C2211yescharacteristic
25#89619C411yescharacteristic
26#89619C411yescharacteristic
27#89616C411yescharacteristic
28#89616C411yescharacteristic
29#89612—21no—
30#89611—21no—
31#89610C2211yescharacteristic
32#89610C2211yescharacteristic
33#89610C2211yescharacteristic, complemented
34#89606C2211yescharacteristic
35#89606C2211yescharacteristic
36#89606C2211yescharacteristic, complemented
37#89603C2211yescharacteristic, complemented
38#89602C2211yescharacteristic, complemented
39#89507C411yescharacteristic
40#89504C411yescharacteristic
41#89503C411yescharacteristic
42#89498—21no—
43D7×C22⋊C8—21no—
44#89494C411yescharacteristic
45#89478—21no—
46#89478—21no—
47C4×D56C2211yescharacteristic
48C4×D56C2211yescharacteristic
49C4×#1132C2211yescharacteristic
50C4×#1132C2211yescharacteristic
51C7×#335C2211yescharacteristic, complemented
52C7×#335C2211yescharacteristic, complemented
53C7×#334C2211yescharacteristic, complemented
54C7×#334C2211yescharacteristic, complemented
55#89279C2211yescharacteristic, complemented
56#89279C2211yescharacteristic, complemented
57#89278C2211yescharacteristic
58#89278C2211yescharacteristic
59#89278C2211yescharacteristic
60#89278C2211yescharacteristic
61#89278C2211yescharacteristic, complemented
62#89278C2211yescharacteristic, complemented
63#89250C2211yescharacteristic, complemented
64#89250C2211yescharacteristic, complemented
65#89249C2211yescharacteristic, complemented
66#89249C2211yescharacteristic, complemented
67#18020—71nomaximal, Sylow
68C22×D28C2×C411yescharacteristic
69C22×C4×D7—21no—
70C22×C7×C8—21no—
71C2×C42×C7C2311yescharacteristic
72#6493C2×C411yescharacteristic
73#6492—21no—
74C4×C22⋊D7—21no—
75C2×(C2×D7)⋊C4—21no—
76C2×C4⋊Dic7C2×C411yescharacteristic
77#6487C2×C411yescharacteristic
78C22×C7⋊C8—21no—
79C2×D56C2×C411yescharacteristic
80C2×D56C2×C411yescharacteristic
81C2×#1132C2×C411yescharacteristic
82C2×#1132C2×C411yescharacteristic
83C2×#1131—21no—
84C2×#1131—21no—
85C2×#1131—21no—
86C2×C8×D7—21no—
87C2×C8×D7—21no—
88C2×C8×D7—21no—
89#6439—21no—
90#6438C2×C411yescharacteristic
91C4×D28—21no—
92C4×D28—21no—
93C4×D28C2×C411yescharacteristic
94C4×D28C2×C411yescharacteristic
95C4×D28C2311yescharacteristic
96C4×D28C2311yescharacteristic
97C4×D28C2311yescharacteristic
98#6435—21no—
99#6433C2×C411yescharacteristic
100C4×Dic14C2311yescharacteristic
101C7×C4⋊C8—21no—
102C7×C4⋊C8C2×C411yescharacteristic
103C7×C4⋊C8C2×C411yescharacteristic
104C7×C4⋊C8C2311yescharacteristic
105C7×C4⋊C8C2311yescharacteristic
106C7×C4⋊C8C2311yescharacteristic
107C7×C4⋊C8C2311yescharacteristic
108C7×C22⋊C8—21no—
109C7×C22⋊C8C2×C411yescharacteristic
110C7×C22⋊C8C2×C411yescharacteristic
111C7×#97—21no—
112C4×C7×C8C2311yescharacteristic
113C4×C7×C8C2311yescharacteristic
114C22⋊(C7⋊C8)D411yescharacteristic
115C22⋊(C7⋊C8)D411yescharacteristic
116#6395C2×C411yescharacteristic
117#6395C2×C411yescharacteristic
118#6395C2×C411yescharacteristic
119#6395C2×C411yescharacteristic
120#6395C2×C411yescharacteristic
121#6395C2×C411yescharacteristic
122(C2×D7)⋊C8—21no—
123(C2×D7)⋊C8—21no—
124(C2×D7)⋊C8—21no—
125(C2×D7)⋊C8—21no—
126(C2×D7)⋊C8—21no—
127(C2×D7)⋊C8—21no—
128#6392C2×C411yescharacteristic
129#6392C2×C411yescharacteristic
130#6391C2×C411yescharacteristic
131#6391C2×C411yescharacteristic
132#6390C2×C411yescharacteristic
133#6390C2×C411yescharacteristic
134#6389—21no—
135Dic7⋊C8—21no—
136Dic7⋊C8—21no—
137C8×Dic7—21no—
138C4⋊(C7⋊C8)D411yescharacteristic
139C4⋊(C7⋊C8)D411yescharacteristic
140C4×C7⋊C8—21no—
141C4×C7⋊C8C2311yescharacteristic
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3105—71no—
146#2994—71no—
147#2974—71no—
148#1594—71no—
149#1592—71no—
150#1583—71no—
151#1582—71no—
152#1581—71no—
153#1581—71no—
154#1580—71no—
155SD16⋊C8—71no—
156#1573D711yescharacteristic, complemented
157#1494—71no—
158C2×D4⋊C8—71no—
159#1452—71no—
160C23×D7—21no—
161C22×C4×C7C22×C411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7#4111yescharacteristic
164C2×C22⋊D7—21no—
165C22×Dic7—21no—
166C2×D28—22no—
167C2×D28—21no—
168C2×D28—41no—
169C2×D28C22×C411yescharacteristic
170C2×D28C22×C411yescharacteristic
171C2×D28C22×C411yescharacteristic
172C2×C4×D7—21no—
173C2×C4×D7—21no—
174C2×C4×D7—21no—
175C2×C4×D7—21no—
176C2×C4×D7—21no—
177C2×C4×D7—81no—
178C2×C4×D7—81no—
179C2×Dic14C22×C411yescharacteristic
180C2×C7×C8—21no—
181C2×C7×C8—21no—
182C2×C7×C8—21no—
183C2×C7×C8—21no—
184C2×C7×C8—81no—
185C2×C7×C8C22×C411yescharacteristic
186C2×C7×C8C22×C411yescharacteristic
187C2×C7×C8C22×C411yescharacteristic
188C2×C7×C8C22×C411yescharacteristic
189C42×C7C22×C411yescharacteristic
190C42×C7C2×D411yescharacteristic
191C42×C7#4111yescharacteristic
192C42×C7C2411yescharacteristic
193C22⋊Dic7—21no—
194(C2×D7)⋊C4—21no—
195(C2×D7)⋊C4—21no—
196(C2×D7)⋊C4—21no—
197(C2×D7)⋊C4—21no—
198(C2×D7)⋊C4—21no—
199(C2×D7)⋊C4—21no—
200(C2×D7)⋊C4—21no—
201(C2×D7)⋊C4—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7C22×C411yescharacteristic
204C4⋊Dic7C22×C411yescharacteristic
205C4⋊Dic7C22×C411yescharacteristic
206C4⋊Dic7C22×C411yescharacteristic
207Dic7⋊C4—21no—
208Dic7⋊C4—21no—
209Dic7⋊C4—21no—
210Dic7⋊C4—21no—
211C4×Dic7—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—42no—
215C2×C7⋊C8C2×D411yescharacteristic
216C2×C7⋊C8C2×D411yescharacteristic
217C2×C7⋊C8C2×D411yescharacteristic
218C2×C7⋊C8C2×D411yescharacteristic
219D56—22no—
220D56—41no—
221#1132—22no—
222#1132—41no—
223#1131—81no—
224#1131—81no—
225#1131—81no—
226C8×D7—81no—
227C8×D7—81no—
228C8×D7—81no—
229#529—71no—
230C2×C4×D4—71no—
231#484—71no—
232#481—71no—
233#478—71no—
234#478—71no—
235#463—71no—
236#463—71no—
237#450—71no—
238#447—71no—
239#446—71no—
240C8×Q8—71no—
241C4×SD16—71no—
242C4×SD16—71no—
243C4×D8—71no—
244C4×D8—71no—
245#436—71no—
246#436—71no—
247#436—71no—
248#435—141no—
249#435—141no—
250#435—141no—
251C8×D4—71no—
252C8×D4—71no—
253C8×D4—71no—
254C8×D4—141no—
255#433—141no—
256#432C2×D711yescharacteristic
257#431—71no—
258#431C2×D711yescharacteristic
259#424—141no—
260C2×C4⋊C8C2×D711yescharacteristic
261#407—141no—
262C2×C22⋊C8—141no—
263C2×C4×C8—71no—
264#335C2×D711yescharacteristic, complemented
265#335C2×D711yescharacteristic, complemented
266#334C2×D711yescharacteristic, complemented
267#334C2×D711yescharacteristic, complemented
268Q8⋊C8—71no—
269Q8⋊C8—71no—
270D4⋊C8—71no—
271D4⋊C8—71no—
272D4⋊C8—71no—
273D4⋊C8—71no—
274D4⋊C8—71no—
275D4⋊C8—71no—
276#322—71no—
277#322—71no—
278#322—71no—
279#322—71no—
280C23×C7C4×D411yescharacteristic
281C22×D7—21no—
282C22×D7—21no—
283C22×D7—21no—
284C22×D7—42no—
285C22×D7—42no—
286C22×D7—81no—
287C2×C4×C7—22no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—21no—
291C2×C4×C7—21no—
292C2×C4×C7C4×D411yescharacteristic
293C2×C4×C7C4×D411yescharacteristic
294C2×C4×C7C4×D411yescharacteristic
295C2×C4×C7C23×C411yescharacteristic
296C2×C4×C7C22×D411yescharacteristic
297C2×C4×C7C2×#4111yescharacteristic
298C22⋊D7—42no—
299C2×Dic7—21no—
300C2×Dic7—21no—
301C2×Dic7—21no—
302C2×Dic7—21no—
303C2×Dic7—21no—
304C2×Dic7—81no—
305D28—21no—
306D28—21no—
307D28—21no—
308D28—21no—
309D28—21no—
310D28—42no—
311D28#13112yes—
312C4×D7—41no—
313C4×D7—41no—
314C4×D7—41no—
315C4×D7—41no—
316C4×D7—41no—
317C4×D7—41no—
318C4×D7—81no—
319C4×D7—81no—
320Dic14—21no—
321Dic14—21no—
322C7×C8—21no—
323C7×C8—21no—
324C7×C8—21no—
325C7×C8—21no—
326C7×C8—41no—
327C7×C8—41no—
328C7×C8—41no—
329C7×C8—41no—
330C7⋊C8—21no—
331C7⋊C8—21no—
332C7⋊C8—21no—
333C7⋊C8—21no—
334C7⋊C8—41no—
335C7⋊C8—41no—
336C22×D4—71no—
337C23×C4—141no—
338C2×SD16—71no—
339C2×SD16—71no—
340C2×D8—71no—
341C2×D8—71no—
342C2×M16—141no—
343C2×M16—141no—
344C2×M16—141no—
345C22×C8—21no—
346C22×C8—141no—
347C22×C8—141no—
348C22×C8—141no—
349C22×C8—141no—
350#126—141no—
351#125—71no—
352#124—71no—
353#123—141no—
354C22⋊Q8—71no—
355#121—71no—
356C4×Q8—71no—
357C4×D4—71no—
358C4×D4—71no—
359C4×D4—71no—
360C4×D4—71no—
361C4×D4—71no—
362C4×D4—141no—
363C4×D4—141no—
364C4×D4—141no—
365#117—141no—
366C2×C4⋊C4—71no—
367C2×C22⋊C4—141no—
368C2×C42C22×D711yescharacteristic
369#107—71no—
370#107—71no—
371#106—71no—
372#106—71no—
373C4⋊C8—21no—
374C4⋊C8—71no—
375C4⋊C8—71no—
376C4⋊C8—141no—
377C4⋊C8—141no—
378C4⋊C8C4×D711yescharacteristic
379C4⋊C8C4×D711yescharacteristic
380C4⋊C8C22×D711yescharacteristic
381C4⋊C8C22×D711yescharacteristic
382C4⋊C8C22×D711yescharacteristic
383C4⋊C8C22×D711yescharacteristic
384#103—71no—
385#103—71no—
386#102—71no—
387#102—71no—
388#102—71no—
389#102—71no—
390#102—71no—
391#102—71no—
392C22⋊C8—21no—
393C22⋊C8—71no—
394C22⋊C8—71no—
395C22⋊C8—141no—
396C22⋊C8—141no—
397C22⋊C8—141no—
398C22⋊C8—141no—
399C22⋊C8—141no—
400C22⋊C8—141no—
401C22⋊C8C4×D711yescharacteristic
402C22⋊C8C4×D711yescharacteristic
403#97—21no—
404#97—141no—
405C4×C8—71no—
406C4×C8—71no—
407C4×C8—71no—
408C4×C8—71no—
409C4×C8—141no—
410C4×C8—141no—
411C4×C8C22×D711yescharacteristic
412C4×C8C22×D711yescharacteristic
413C22×C7—21no—
414C22×C7—21no—
415C22×C7#44412yes—
416C22×C7C2×C4×D411yescharacteristic
417C2×D7—22no—
418C2×D7—41no—
419C2×D7—41no—
420C2×D7—41no—
421C2×D7—41no—
422C2×D7—41no—
423C2×D7—41no—
424C2×D7—41no—
425C2×D7—41no—
426C2×D7—84no—
427C4×C7—21no—
428C4×C7—21no—
429C4×C7—21no—
430C4×C7—21no—
431C4×C7C2×#13111yescharacteristic
432C4×C7#56811yescharacteristic
433C4×C7#57611yescharacteristic
434C4×C7#57711yescharacteristic
435Dic7—41no—
436Dic7—41no—
437Dic7—41no—
438Dic7—41no—
439Dic7—41no—
440C24—141no—
441C2×Q8—71no—
442C2×D4—71no—
443C2×D4—71no—
444C2×D4—71no—
445C2×D4—142no—
446C2×D4—141no—
447C2×D4—141no—
448C2×D4—281no—
449C22×C4—141no—
450C22×C4—141no—
451C22×C4—141no—
452C22×C4—141no—
453C22×C4—141no—
454C22×C4—141no—
455C22×C4—561no—
456C22×C4—561no—
457C22×C4C2×C4×D711yescharacteristic
458C22×C4D4×D711yescharacteristic
459C22×C4#116111yescharacteristic
460SD16—142no—
461SD16—281no—
462D8—142no—
463D8—281no—
464M16—561no—
465M16—561no—
466M16—561no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—71no—
472C2×C8—71no—
473C2×C8—71no—
474C2×C8—71no—
475C2×C8—81no—
476C2×C8—141no—
477C2×C8—141no—
478C2×C8—282no—
479C2×C8—561no—
480C2×C8—561no—
481C2×C8—561no—
482C2×C8C2×C4×D711yescharacteristic
483C2×C8C2×C4×D711yescharacteristic
484C2×C8C2×C4×D711yescharacteristic
485C2×C8C2×C4×D711yescharacteristic
486C4⋊C4—71no—
487C4⋊C4—71no—
488C4⋊C4—71no—
489C4⋊C4—71no—
490C4⋊C4—141no—
491C4⋊C4—141no—
492C4⋊C4—141no—
493C4⋊C4—141no—
494C4⋊C4—141no—
495C22⋊C4—141no—
496C22⋊C4—141no—
497C22⋊C4—141no—
498C22⋊C4—141no—
499C22⋊C4—141no—
500C22⋊C4—141no—
501C22⋊C4—141no—
502C22⋊C4—141no—
503C22⋊C4—141no—
504C42—141no—
505C42C2×C4×D711yescharacteristic
506C42D4×D711yescharacteristic
507C42#116111yescharacteristic
508C42C23×D711yescharacteristic
509C2×C7—22no—
510C2×C7#293311yescharacteristic
511C2×C7#294611yescharacteristic
512C2×C7C2×#44411yescharacteristic
513D7—42no—
514D7—81no—
515D7—81no—
516C23—141no—
517C23—141no—
518C23—141no—
519C23—282no—
520C23—282no—
521C23—561no—
522C23#645611yescharacteristic
523Q8—141no—
524Q8—141no—
525D4—72no—
526D4—141no—
527D4—141no—
528D4—141no—
529D4—141no—
530D4—141no—
531D4—282no—
532D4—282no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—141no—
539C2×C4—141no—
540C2×C4—141no—
541C2×C4—141no—
542C2×C4—141no—
543C2×C4—281no—
544C2×C4—281no—
545C2×C4—281no—
546C2×C4—281no—
547C2×C4—281no—
548C2×C4—281no—
549C2×C4—561no—
550C2×C4—561no—
551C2×C4—561no—
552C2×C4#645611yescharacteristic
553C2×C4#645611yescharacteristic
554C2×C4#645611yescharacteristic
555C2×C4C22×C4×D711yescharacteristic
556C2×C4C2×D4×D711yescharacteristic
557C2×C4C2×#116111yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—141no—
567C8—141no—
568C8—141no—
569C8—141no—
570C8—281no—
571C8—281no—
572C7#1802011yescharacteristic, complemented, Sylow
573C22—21no—
574C22—21no—
575C22—142no—
576C22—281no—
577C22—281no—
578C22—281no—
579C22—281no—
580C22—281no—
581C22—281no—
582C22—281no—
583C22—281no—
584C22—564no—
585C22#8966612yes—
586C22C2×#645611yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—281no—
592C4—281no—
593C4—281no—
594C4—281no—
595C4—281no—
596C4D7×#13111yescharacteristic
597C4#9044111yescharacteristic
598C4#9046511yescharacteristic
599C4#9046911yescharacteristic
600C2—22no—
601C2—282no—
602C2—561no—
603C2—561no—
604C2#1173652011yescharacteristic
605C2#1173664611yescharacteristic
606C2C2×#8966611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1573C2
socleC22×C7C2×C4×D4
prime radical#89504C4
cosocleC42×C7C24
hypercenter#1573D7
hypocenterC7#18020
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
1. #11736781C2semidirect
3. #11736462C2semidirect
4. C7×#1573C2semidirect
5. #11728554C2semidirect
6. #11728496C2semidirect
7. C2×#89278C2semidirect
8. #11726319C2semidirect
9. #11726313C2semidirect
10. #11726313C2semidirect
11. #11726312C2semidirect
12. #11726279C2semidirect
13. #11726274C2semidirect
14. #11726273C2semidirect
15. #11726272C2semidirect
33. #89610C22semidirect
36. #89606C22semidirect
37. #89603C22semidirect
38. #89602C22semidirect
51. C7×#335C22semidirect
52. C7×#335C22semidirect
53. C7×#334C22semidirect
54. C7×#334C22semidirect
55. #89279C22semidirect
56. #89279C22semidirect
61. #89278C22semidirect
62. #89278C22semidirect
63. #89250C22semidirect
64. #89250C22semidirect
65. #89249C22semidirect
66. #89249C22semidirect
156. #1573D7semidirect
264. #335C2×D7semidirect
265. #335C2×D7semidirect
266. #334C2×D7semidirect
267. #334C2×D7semidirect
572. C7#18020semidirect

Maximal subgroups

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

subgroupindex
#117367812
#117367452
#117364622
C7×#15732
#117285542
#117284962
C2×#892782
#117263192
#117263132
#117263122
#117262792
#117262742
#117262732
#117262722
#180207