Finite Group Databasebeta

← #13356984

Subgroups — #13356984

Order 1792.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic7C211yesmaximal, characteristic
2#11739762C211yesmaximal, characteristic, complemented
3#11733740C211yesmaximal, characteristic, complemented
4C7×#1879C211yesmaximal, characteristic
5#11729791C211yesmaximal, characteristic
6#11729361C211yesmaximal, characteristic, complemented
7#11727928C211yesmaximal, characteristic, complemented
8#11727923C211yesmaximal, characteristic, complemented
9#11727906C211yesmaximal, characteristic, complemented
10#11727906C211yesmaximal, characteristic, complemented
11#11727391C211yesmaximal, characteristic, complemented
12#11726568C211yesmaximal, characteristic, complemented
13#11726538C211yesmaximal, characteristic, complemented
14#11726375C211yesmaximal, characteristic, complemented
15#11726352C211yesmaximal, characteristic, complemented
16C22×C7×D8C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×D4×Dic7C2211yescharacteristic
19C2×D4×Dic7C2211yescharacteristic
20C2×D4×Dic7C2211yescharacteristic
21C2×C7×#102C2211yescharacteristic
22C2×C7×#102C2211yescharacteristic
23C7×#390C2211yescharacteristic
24#89993C2211yescharacteristic
25C2×#6406C2211yescharacteristic
26C2×#6406C2211yescharacteristic
27C2×#6406C2211yescharacteristic
28C2×#6406C2211yescharacteristic
29C4×C22⋊Dic7—21no—
30C2×C7⋊#95—21no—
31D8×Dic7C418yescomplemented
32C2×#6392C2211yescharacteristic
33C2×#6389C2211yescharacteristic
34C2×C8×Dic7C2211yescharacteristic
35C4⋊C4×Dic7C2211yescharacteristic
36C4⋊C4×Dic7C2211yescharacteristic
37C4⋊C4×Dic7C2211yescharacteristic
38#89745C2211yescharacteristic
39C2×#6382C2211yescharacteristic
40C2×#6382C2211yescharacteristic
41#89717—21no—
42#89716—21no—
43#89715—21no—
44#89714—21no—
45C22⋊C4×Dic7—21no—
46C22⋊C4×Dic7—21no—
47C4×C4⋊Dic7C2211yescharacteristic
48#89704C2211yescharacteristic
49#89700C2211yescharacteristic
50C7×#340C2211yescharacteristic
51C7×#336C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89345C2211yescharacteristic
56#89345C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89319C2211yescharacteristic
60#21134—71nomaximal, Sylow
61C22×C7×D4C2311yescharacteristic
62C22×C7×D4C2311yescharacteristic
63C23×C4×C7—21no—
64C23×Dic7—21no—
65C23×Dic7—21no—
66C23×Dic7—21no—
67C2×C7×D8—22no—
68C2×C7×D8—22no—
69C2×C7×D8C2×C414yes—
70C22×C7×C8C2311yescharacteristic
71C22×C7×C8C2311yescharacteristic
72C4×C7×D4—22no—
73C4×C7×D4—22no—
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C22⋊C4—21no—
77C2×C7×C22⋊C4—21no—
78C2×C7×C22⋊C4—21no—
79C2×C42×C7C2311yescharacteristic
80C2×C22⋊Dic7—21no—
81C2×C22⋊Dic7—21no—
82C2×C22⋊Dic7—21no—
83C2×C22⋊Dic7—21no—
84C2×C22⋊Dic7—21no—
85D4×Dic7—22no—
86D4×Dic7—22no—
87D4×Dic7—22no—
88D4×Dic7—22no—
89D4×Dic7C2×C414yes—
90D4×Dic7C2×C414yescomplemented
91C2×C4⋊Dic7C2311yescharacteristic
92C2×C4⋊Dic7C2311yescharacteristic
93C2×C4⋊Dic7C2311yescharacteristic
94C2×C4⋊Dic7C2311yescharacteristic
95C2×Dic7⋊C4—21no—
96C2×Dic7⋊C4—21no—
97C2×C4×Dic7—21no—
98C2×C4×Dic7—21no—
99C2×C4×Dic7—21no—
100C2×C4×Dic7—21no—
101C2×C4×Dic7C2311yescharacteristic
102C2×C4×Dic7C2311yescharacteristic
103C22×C7⋊C8C2311yescharacteristic
104C22×C7⋊C8C2311yescharacteristic
105C7×#102—22no—
106C7×#102—22no—
107#6406—22no—
108#6406—22no—
109#6406C2×C414yes—
110#6406C2×C414yescomplemented
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95D411yescharacteristic
118C7⋊#95D411yescharacteristic
119C7⋊#95D411yescharacteristic
120C7⋊#95D411yescharacteristic
121#6392C2×C414yescomplemented
122#6389—22no—
123C8×Dic7C2×C414yescomplemented
124#6382—22no—
125#6382—22no—
126C2×C4×D8—71no—
127#2319—71no—
128#2275—71no—
129#1926—71no—
130#1926—71no—
131#1918—71no—
132#1918—71no—
133#1879—71no—
134#1879D711yescharacteristic
135#1864—71no—
136#1864—71no—
137C4×#106—71no—
138#1762—71no—
139#1762—71no—
140#1746—71no—
141C24×C7—21no—
142C24×C7—21no—
143C2×C7×D4—21no—
144C2×C7×D4—21no—
145C2×C7×D4—21no—
146C2×C7×D4—21no—
147C2×C7×D4—21no—
148C2×C7×D4—21no—
149C2×C7×D4—21no—
150C2×C7×D4—21no—
151C2×C7×D4C22×C412yes—
152C2×C7×D4C22×C412yes—
153C2×C7×D4#4112yes—
154C2×C7×D4#4112yes—
155C22×C4×C7—21no—
156C22×C4×C7—24no—
157C22×C4×C7—21no—
158C22×C4×C7—81no—
159C22×C4×C7—81no—
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2411yescharacteristic
163C22×Dic7—21no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—24no—
167C22×Dic7—24no—
168C22×Dic7—24no—
169C22×Dic7—21no—
170C22×Dic7—81no—
171C22×Dic7—81no—
172C22×Dic7—81no—
173C22×Dic7—81no—
174C22×Dic7—81no—
175C22×Dic7—81no—
176C22×Dic7C2×D411yescharacteristic
177C22×Dic7C2×D411yescharacteristic
178C22×Dic7C2×D411yescharacteristic
179C22×Dic7C2×D411yescharacteristic
180C7×D8—28no—
181C2×C7×C8—21no—
182C2×C7×C8—21no—
183C2×C7×C8—21no—
184C2×C7×C8—21no—
185C2×C7×C8—21no—
186C2×C7×C8C22×C412yes—
187C7×C4⋊C4—21no—
188C7×C4⋊C4—21no—
189C7×C4⋊C4—21no—
190C7×C4⋊C4#4112yes—
191C7×C22⋊C4—24no—
192C7×C22⋊C4—81no—
193C7×C22⋊C4—81no—
194C42×C7—21no—
195C42×C7—21no—
196C22⋊Dic7—24no—
197C22⋊Dic7—24no—
198C22⋊Dic7—24no—
199C22⋊Dic7—81no—
200C22⋊Dic7—81no—
201C4⋊Dic7—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7—21no—
204C4⋊Dic7—21no—
205C4⋊Dic7—21no—
206C4⋊Dic7C22×C412yes—
207C4⋊Dic7C22×C412yes—
208C4⋊Dic7#4112yes—
209Dic7⋊C4—81no—
210Dic7⋊C4—81no—
211C4×Dic7—21no—
212C4×Dic7—21no—
213C4×Dic7—81no—
214C4×Dic7—81no—
215C4×Dic7—81no—
216C4×Dic7—81no—
217C4×Dic7C22×C412yes—
218C4×Dic7#4112yes—
219C2×C7⋊C8—21no—
220C2×C7⋊C8—21no—
221C2×C7⋊C8—21no—
222C2×C7⋊C8—21no—
223C2×C7⋊C8—21no—
224C2×C7⋊C8C22×C412yes—
225C22×D8C2×D711yescharacteristic
226C2×C4×D4—71no—
227C2×C4×D4—71no—
228C2×C4×D4—71no—
229C2×C4×D4C2×D711yescharacteristic
230C4×D8—78no—
231C2×#107—71no—
232C2×#106—71no—
233C2×#106—71no—
234C2×#102—71no—
235C2×#102—71no—
236C2×#102—71no—
237C2×#102—71no—
238C2×#102C2×D711yescharacteristic
239C2×#102C2×D711yescharacteristic
240C2×#97—71no—
241C2×C4×C8—71no—
242#390—71no—
243#390C2×D711yescharacteristic
244#389—71no—
245#389—71no—
246#388—141no—
247#388—141no—
248#381—141no—
249#380—141no—
250C4×C4⋊C4—71no—
251C4×C4⋊C4—71no—
252C4×C4⋊C4—71no—
253C4×C4⋊C4—71no—
254C4×C22⋊C4—141no—
255C4×C22⋊C4—141no—
256C4×C22⋊C4—141no—
257#376—71no—
258C2×#95—141no—
259#340—71no—
260#340—71no—
261#340—71no—
262#340—71no—
263#340—71no—
264#340C2×D711yescharacteristic
265#336—71no—
266#336—71no—
267#336—71no—
268#336C2×D711yescharacteristic
269C23×C7—22no—
270C23×C7—22no—
271C23×C7—22no—
272C23×C7—22no—
273C23×C7—41no—
274C23×C7—41no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7C22×D411yescharacteristic
284C7×D4—22no—
285C7×D4—22no—
286C7×D4—22no—
287C7×D4—22no—
288C7×D4—22no—
289C7×D4—41no—
290C7×D4—41no—
291C7×D4#11714yes—
292C2×C4×C7—21no—
293C2×C4×C7—21no—
294C2×C4×C7—22no—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
302C2×C4×C7—41no—
303C2×C4×C7—41no—
304C2×C4×C7—84no—
305C2×C4×C7C23×C411yescharacteristic
306C2×C4×C7C2×#4111yescharacteristic
307C2×C4×C7C2×#4111yescharacteristic
308C2×C4×C7C2×#4111yescharacteristic
309C2×C4×C7C2×#4111yescharacteristic
310C2×C4×C7C2×#4111yescharacteristic
311C2×Dic7—21no—
312C2×Dic7—21no—
313C2×Dic7—21no—
314C2×Dic7—21no—
315C2×Dic7—22no—
316C2×Dic7—22no—
317C2×Dic7—21no—
318C2×Dic7—21no—
319C2×Dic7—22no—
320C2×Dic7—21no—
321C2×Dic7—21no—
322C2×Dic7—21no—
323C2×Dic7—21no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326C2×Dic7—41no—
327C2×Dic7—41no—
328C2×Dic7—41no—
329C2×Dic7—41no—
330C2×Dic7—41no—
331C2×Dic7—41no—
332C2×Dic7—41no—
333C2×Dic7—84no—
334C2×Dic7—84no—
335C2×Dic7—84no—
336C2×Dic7C4×D412yes—
337C2×Dic7C4×D412yes—
338C7×C8—22no—
339C7×C8—41no—
340C7⋊C8—22no—
341C7⋊C8—41no—
342C22×D4C22×D711yescharacteristic
343C22×D4C22×D711yescharacteristic
344C23×C4—21no—
345C23×C4—141no—
346C23×C4—141no—
347C23×C4—141no—
348C2×D8—22no—
349C2×D8—22no—
350C2×D8C4×D714yes—
351C22×C8—71no—
352C22×C8—71no—
353C22×C8C22×D711yescharacteristic
354C22×C8C22×D711yescharacteristic
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—74no—
358C4×D4—74no—
359C4×D4—142no—
360C4×D4—142no—
361C4×D4—142no—
362C4×D4—142no—
363C2×C4⋊C4—71no—
364C2×C4⋊C4—71no—
365C2×C4⋊C4—71no—
366C2×C4⋊C4—71no—
367C2×C4⋊C4—141no—
368C2×C4⋊C4—141no—
369C2×C4⋊C4C22×D711yescharacteristic
370C2×C4⋊C4C22×D711yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—141no—
375C2×C22⋊C4—141no—
376C2×C22⋊C4—141no—
377C2×C22⋊C4—141no—
378C2×C22⋊C4—141no—
379C2×C42—71no—
380C2×C42—71no—
381C2×C42—141no—
382C2×C42—141no—
383C2×C42—141no—
384C2×C42—141no—
385C2×C42C22×D711yescharacteristic
386#107—74no—
387#106—142no—
388#106—142no—
389#102—22no—
390#102—22no—
391#102—74no—
392#102—74no—
393#102—142no—
394#102—142no—
395#97—142no—
396C4×C8—74no—
397#95—71no—
398#95—71no—
399#95—71no—
400#95—71no—
401#95—141no—
402#95—141no—
403#95—141no—
404#95—141no—
405#95—141no—
406#95—141no—
407C22×C7—24no—
408C22×C7—42no—
409C22×C7—42no—
410C22×C7—42no—
411C22×C7—42no—
412C22×C7—42no—
413C22×C7—42no—
414C22×C7—42no—
415C22×C7—42no—
416C22×C7—42no—
417C22×C7—81no—
418C22×C7—81no—
419C22×C7—81no—
420C22×C7—81no—
421C22×C7C2×C4×D411yescharacteristic
422C22×C7#52511yescharacteristic
423C22×C7#52511yescharacteristic
424C22×C7#57611yescharacteristic
425C22×C7#57611yescharacteristic
426C22×C7#57711yescharacteristic
427C22×C7#57711yescharacteristic
428C4×C7—41no—
429C4×C7—42no—
430C4×C7—41no—
431C4×C7—81no—
432C4×C7C2×#11711yescharacteristic
433C4×C7C4×#4111yescharacteristic
434C4×C7#52911yescharacteristic
435C4×C7#52911yescharacteristic
436Dic7—22no—
437Dic7—22no—
438Dic7—41no—
439Dic7—42no—
440Dic7—41no—
441Dic7—42no—
442Dic7—42no—
443Dic7—81no—
444C24—21no—
445C24—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4C2×C4×D712yes—
455C2×D4C2×C4×D712yes—
456C2×D4#115912yes—
457C2×D4#115912yes—
458C22×C4—21no—
459C22×C4—24no—
460C22×C4—21no—
461C22×C4—71no—
462C22×C4—71no—
463C22×C4—71no—
464C22×C4—71no—
465C22×C4—81no—
466C22×C4—81no—
467C22×C4—144no—
468C22×C4—144no—
469C22×C4—141no—
470C22×C4—141no—
471C22×C4—141no—
472C22×C4—144no—
473C22×C4—141no—
474C22×C4—561no—
475C22×C4—561no—
476C22×C4—561no—
477C22×C4—561no—
478C22×C4—561no—
479C22×C4—561no—
480C22×C4D4×D711yescharacteristic
481C22×C4D4×D711yescharacteristic
482C22×C4C23×D711yescharacteristic
483D8—28no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—72no—
490C2×C8—141no—
491C2×C8—141no—
492C2×C8—141no—
493C2×C8—141no—
494C2×C8—141no—
495C2×C8C2×C4×D712yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—72no—
500C4⋊C4—72no—
501C4⋊C4—72no—
502C4⋊C4—141no—
503C4⋊C4—141no—
504C4⋊C4—141no—
505C4⋊C4—141no—
506C4⋊C4—141no—
507C4⋊C4—561no—
508C4⋊C4—561no—
509C4⋊C4#115912yes—
510C22⋊C4—24no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C22⋊C4—144no—
514C22⋊C4—144no—
515C22⋊C4—144no—
516C22⋊C4—561no—
517C22⋊C4—561no—
518C42—21no—
519C42—21no—
520C42—72no—
521C42—72no—
522C42—141no—
523C42—141no—
524C42—561no—
525C42—561no—
526C42—561no—
527C42—561no—
528C2×C7—44no—
529C2×C7—82no—
530C2×C7#229011yescharacteristic
531C2×C7#294811yescharacteristic
532C2×C7#295211yescharacteristic
533C2×C7#311811yescharacteristic
534C2×C7#311811yescharacteristic
535C2×C7#311911yescharacteristic
536C2×C7#311911yescharacteristic
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23C2×D4×D711yescharacteristic
552D4—22no—
553D4—22no—
554D4—22no—
555D4—22no—
556D4—22no—
557D4—41no—
558D4—41no—
559D4#644014yes—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—72no—
573C2×C4—72no—
574C2×C4—84no—
575C2×C4—141no—
576C2×C4—141no—
577C2×C4—141no—
578C2×C4—141no—
579C2×C4—141no—
580C2×C4—141no—
581C2×C4—141no—
582C2×C4—141no—
583C2×C4—142no—
584C2×C4—142no—
585C2×C4—141no—
586C2×C4—141no—
587C2×C4—142no—
588C2×C4—281no—
589C2×C4—281no—
590C2×C4—281no—
591C2×C4—281no—
592C2×C4—281no—
593C2×C4—281no—
594C2×C4—281no—
595C2×C4—281no—
596C2×C4—281no—
597C2×C4—564no—
598C2×C4—564no—
599C2×C4—564no—
600C2×C4C22×C4×D711yescharacteristic
601C2×C4C2×#115911yescharacteristic
602C2×C4C2×#115911yescharacteristic
603C2×C4C2×#115911yescharacteristic
604C2×C4D7×#4111yescharacteristic
605C2×C4D7×#4111yescharacteristic
606C8—22no—
607C8—41no—
608C8—142no—
609C8—281no—
610C7#2113411yescharacteristic, complemented, Sylow
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22C4×D4×D711yescharacteristic
626C22#9027711yescharacteristic
627C22#9029711yescharacteristic
628C22#9044811yescharacteristic
629C22#9046011yescharacteristic
630C22#9046611yescharacteristic
631C22#9046611yescharacteristic
632C4—41no—
633C4—42no—
634C4—41no—
635C4—81no—
636C4—142no—
637C4—142no—
638C4—281no—
639C4—282no—
640C4—281no—
641C4—282no—
642C4—282no—
643C4—561no—
644C4C2×#644011yescharacteristic
645C4C4×#115911yescharacteristic
646C4#9029111yescharacteristic
647C4#9034011yescharacteristic
648C2—44no—
649C2—82no—
650C2#1173210211yescharacteristic
651C2#1173703311yescharacteristic
652C2#1173731311yescharacteristic
653C2#1173743711yescharacteristic
654C2#1173751711yescharacteristic
655C2#1173776111yescharacteristic
656C2#1173795311yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1879C2
socleC23×C7C22×D4
prime radicalC22×C7×D8C22
cosocleC22×C4×C7C24
hypercenter#1879D7
hypocenterC7#21134
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. #11739762C2semidirect
3. #11733740C2semidirect
6. #11729361C2semidirect
7. #11727928C2semidirect
8. #11727923C2semidirect
9. #11727906C2semidirect
10. #11727906C2semidirect
11. #11727391C2semidirect
12. #11726568C2semidirect
13. #11726538C2semidirect
14. #11726375C2semidirect
15. #11726352C2semidirect
31. D8×Dic7C4semidirect
90. D4×Dic7C2×C4semidirect
110. #6406C2×C4semidirect
121. #6392C2×C4semidirect
123. C8×Dic7C2×C4semidirect
610. C7#21134semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic72
#117397622
#117337402
C7×#18792
#117297912
#117293612
#117279282
#117279232
#117279062
#117273912
#117265682
#117265382
#117263752
#117263522
#211347