Finite Group Databasebeta

← #13358647

Subgroups — #13358647

Order 1792.

870 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89605C211yesmaximal, characteristic
2#11731592C211yesmaximal, characteristic
3C4×#6455C211yesmaximal, characteristic
4C7×#1949C211yesmaximal, characteristic, complemented
5#11728387C211yesmaximal, characteristic
6Dic7×#107C211yesmaximal, characteristic, complemented
7#11728334C211yesmaximal, characteristic
8Dic7×#106C211yesmaximal, characteristic, complemented
9#11728209C211yesmaximal, characteristic, complemented
10#11727294C211yesmaximal, characteristic, complemented
11#11727222C211yesmaximal, characteristic, complemented
12#11726631C211yesmaximal, characteristic
13#11726630C211yesmaximal, characteristic
14#11726539C211yesmaximal, characteristic, complemented
15#11726538C211yesmaximal, characteristic, complemented
16C2×#6455C2211yescharacteristic
17C2×#6455C2211yescharacteristic
18C2×C42×D7C2211yescharacteristic
19C2×C7×#107C2211yescharacteristic
20C2×C7×#106C2211yescharacteristic
21C2×C7×C4⋊C8C2211yescharacteristic
22C7×#382C2211yescharacteristic
23C4×C7×C4⋊C4C2211yescharacteristic
24C2×(C2×D7)⋊C8C2211yescharacteristic
25C2×(C2×D7)⋊C8C2211yescharacteristic
26C2×#6392C2211yescharacteristic
27C2×#6391C2211yescharacteristic
28C2×C8×Dic7C2211yescharacteristic
29C2×C8×Dic7C2211yescharacteristic
30#89759C2211yescharacteristic
31#89759C2211yescharacteristic
32C4⋊C4×Dic7C2211yescharacteristic
33C4⋊C4×Dic7C2211yescharacteristic
34C4⋊C4×Dic7C2211yescharacteristic
35C4⋊C4×Dic7C2211yescharacteristic
36C2×#6382C2211yescharacteristic
37C2×#6382C2211yescharacteristic
38C2×#6381C2211yescharacteristic
39C2×#6381C2211yescharacteristic
40C4×(C2×D7)⋊C4—21no—
41#89708C2211yescharacteristic
42C4×C4⋊Dic7C2211yescharacteristic
43C42×Dic7—21no—
44C2×C4⋊(C7⋊C8)C2211yescharacteristic
45#89605C418yescomplemented
46#89438—21no—
47#89438—21no—
48#89436—21no—
49#89423—21no—
50#89420—21no—
51#89420—21no—
52C7×#340C2211yescharacteristic
53C7×#340C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#21360—71nomaximal, Sylow
61C22×C4×D7D411yescharacteristic
62C22×C4×D7D411yescharacteristic
63C22×C4×D7C2311yescharacteristic
64C22×C7×C8C2311yescharacteristic
65C22×C7×C8C2311yescharacteristic
66C2×C7×C4⋊C4C2311yescharacteristic
67C2×C7×C4⋊C4C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C42×C7—21no—
71C2×C42×C7C2311yescharacteristic
72C2×(C2×D7)⋊C4—21no—
73C2×(C2×D7)⋊C4—21no—
74C2×(C2×D7)⋊C4—21no—
75C2×(C2×D7)⋊C4—21no—
76C2×C4⋊Dic7C2311yescharacteristic
77C2×C4⋊Dic7C2311yescharacteristic
78C2×C4⋊Dic7C2311yescharacteristic
79C2×C4⋊Dic7C2311yescharacteristic
80C2×C4×Dic7—21no—
81C2×C4×Dic7—21no—
82C2×C4×Dic7—21no—
83C2×C4×Dic7—21no—
84C2×C4×Dic7—21no—
85C2×C4×Dic7—21no—
86C2×C4×Dic7—21no—
87C2×C4×Dic7D411yescharacteristic
88C2×C4×Dic7D411yescharacteristic
89C2×C4×Dic7C2311yescharacteristic
90C22×C7⋊C8C2311yescharacteristic
91C22×C7⋊C8C2311yescharacteristic
92#6455—22no—
93#6455—22no—
94#6455—22no—
95#6455—22no—
96C42×D7C2×C414yes—
97C42×D7Q814yes—
98C7×#107—22no—
99C7×#106—22no—
100C7×C4⋊C8C2×C414yes—
101C7×#95—21no—
102C7×#95—21no—
103C7×#95—21no—
104C7⋊#95—21no—
105C7⋊#95—21no—
106C7⋊#95—21no—
107C7⋊#95—21no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113(C2×D7)⋊C8C2×C414yes—
114(C2×D7)⋊C8C2×C414yes—
115#6392—22no—
116#6391—22no—
117C8×Dic7C2×C414yes—
118C8×Dic7C2×C414yes—
119#6382—22no—
120#6382—22no—
121#6381—22no—
122#6381—22no—
123C4⋊(C7⋊C8)C2×C414yes—
124C2×#431—71no—
125#2283—71no—
126C4×#117—71no—
127#1949—71no—
128#1949—71no—
129#1949—71no—
130#1949D711yescharacteristic, complemented
131#1854—71no—
132#1854—71no—
133#1854—71no—
134#1854—71no—
135C4×#107—71no—
136C4×#107—71no—
137C4×#106—71no—
138C4×#106—71no—
139C23×D7C2×D411yescharacteristic
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2411yescharacteristic
147C22×Dic7—21no—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7C2×D411yescharacteristic
152C22×Dic7C2×D411yescharacteristic
153C22×Dic7C2×D411yescharacteristic
154C2×C4×D7—21no—
155C2×C4×D7—21no—
156C2×C4×D7—21no—
157C2×C4×D7—21no—
158C2×C4×D7—22no—
159C2×C4×D7—22no—
160C2×C4×D7—41no—
161C2×C4×D7—41no—
162C2×C4×D7C4⋊C414yes—
163C2×C4×D7C4⋊C414yes—
164C2×C4×D7C22×C412yes—
165C2×C4×D7C2×Q812yes—
166C2×C7×C8—21no—
167C2×C7×C8—21no—
168C2×C7×C8—21no—
169C2×C7×C8—21no—
170C2×C7×C8C22×C412yes—
171C2×C7×C8C22×C412yes—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—21no—
177C7×C4⋊C4—21no—
178C7×C4⋊C4#4112yes—
179C7×C4⋊C4#4112yes—
180C42×C7—42no—
181C42×C7C22×C412yes—
182C42×C7C2×Q812yes—
183(C2×D7)⋊C4—24no—
184(C2×D7)⋊C4—24no—
185(C2×D7)⋊C4—42no—
186(C2×D7)⋊C4—42no—
187C4⋊Dic7—21no—
188C4⋊Dic7—21no—
189C4⋊Dic7—21no—
190C4⋊Dic7—21no—
191C4⋊Dic7—21no—
192C4⋊Dic7—21no—
193C4⋊Dic7#4112yes—
194C4⋊Dic7#4112yes—
195C4×Dic7—24no—
196C4×Dic7—24no—
197C4×Dic7—42no—
198C4×Dic7—42no—
199C4×Dic7—42no—
200C4×Dic7—42no—
201C4×Dic7—42no—
202C4×Dic7C4⋊C414yes—
203C4×Dic7C4⋊C414yes—
204C4×Dic7C22×C412yes—
205C4×Dic7C2×Q812yes—
206C2×C7⋊C8—21no—
207C2×C7⋊C8—21no—
208C2×C7⋊C8—21no—
209C2×C7⋊C8—21no—
210C2×C7⋊C8C22×C412yes—
211C2×C7⋊C8C22×C412yes—
212C2×#117—71no—
213C2×#117—71no—
214C22×C42—71no—
215#431—78no—
216C2×#107—71no—
217C2×#107—71no—
218C2×#107—71no—
219C2×#107C2×D711yescharacteristic
220C2×#106—71no—
221C2×#106—71no—
222C2×#106—71no—
223C2×#106C2×D711yescharacteristic
224C2×C4⋊C8—71no—
225C2×C4⋊C8C2×D711yescharacteristic
226C2×C22⋊C8—71no—
227C2×C22⋊C8—71no—
228C2×C4×C8—71no—
229C2×C4×C8—71no—
230#383—141no—
231#382—71no—
232#382C2×D711yescharacteristic
233#381—141no—
234#380—71no—
235#380—71no—
236C4×C4⋊C4—71no—
237C4×C4⋊C4—71no—
238C4×C4⋊C4—71no—
239C4×C4⋊C4—71no—
240C4×C4⋊C4—71no—
241C4×C4⋊C4C2×D711yescharacteristic
242C4×C22⋊C4—141no—
243C4×C22⋊C4—141no—
244C4×C22⋊C4—141no—
245#376—141no—
246#376—141no—
247C43—141no—
248#340—71no—
249#340—71no—
250#340—71no—
251#340—71no—
252#340—71no—
253#340—71no—
254#340C2×D711yescharacteristic
255#340C2×D711yescharacteristic
256C23×C7C22×D411yescharacteristic
257C22×D7—21no—
258C22×D7—21no—
259C22×D7—21no—
260C22×D7—21no—
261C22×D7—21no—
262C22×D7—21no—
263C22×D7C2×C4⋊C412yes—
264C2×C4×C7—21no—
265C2×C4×C7—21no—
266C2×C4×C7—21no—
267C2×C4×C7—21no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—41no—
271C2×C4×C7—41no—
272C2×C4×C7—41no—
273C2×C4×C7—41no—
274C2×C4×C7—41no—
275C2×C4×C7—41no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7C2×C4⋊C412yes—
281C2×C4×C7C2×C4⋊C412yes—
282C2×C4×C7C23×C411yescharacteristic
283C2×C4×C7C22×Q811yescharacteristic
284C2×C4×C7C2×#4111yescharacteristic
285C2×C4×C7C2×#4111yescharacteristic
286C2×C4×C7C2×#4111yescharacteristic
287C2×C4×C7C2×#4111yescharacteristic
288C2×Dic7—21no—
289C2×Dic7—21no—
290C2×Dic7—21no—
291C2×Dic7—21no—
292C2×Dic7—22no—
293C2×Dic7—22no—
294C2×Dic7—41no—
295C2×Dic7—41no—
296C2×Dic7—41no—
297C2×Dic7—41no—
298C2×Dic7—41no—
299C2×Dic7—41no—
300C2×Dic7—41no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7C2×C4⋊C412yes—
305C2×Dic7C2×C4⋊C412yes—
306C2×Dic7C2×C4⋊C412yes—
307C2×Dic7#13512yes—
308C2×Dic7#13512yes—
309C4×D7—22no—
310C4×D7—22no—
311C4×D7—22no—
312C4×D7—22no—
313C4×D7—28no—
314C4×D7—44no—
315C7×C8—22no—
316C7×C8—22no—
317C7⋊C8—22no—
318C7⋊C8—22no—
319C23×C4—71no—
320C23×C4—71no—
321C23×C4—71no—
322C22×C8—71no—
323C22×C8—71no—
324C22×C8C22×D711yescharacteristic
325C22×C8C22×D711yescharacteristic
326#117—142no—
327#117—142no—
328#117—142no—
329#117—142no—
330C2×C4⋊C4—71no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—71no—
333C2×C4⋊C4—71no—
334C2×C4⋊C4C22×D711yescharacteristic
335C2×C4⋊C4C22×D711yescharacteristic
336C2×C4⋊C4C22×D711yescharacteristic
337C2×C4⋊C4C22×D711yescharacteristic
338C2×C22⋊C4—141no—
339C2×C22⋊C4—141no—
340C2×C22⋊C4—141no—
341C2×C22⋊C4—141no—
342C2×C42—21no—
343C2×C42—71no—
344C2×C42—71no—
345C2×C42—71no—
346C2×C42—74no—
347C2×C42—74no—
348C2×C42—141no—
349C2×C42—141no—
350C2×C42—141no—
351C2×C42—141no—
352C2×C42—141no—
353C2×C42—141no—
354C2×C42—141no—
355C2×C42C22×D711yescharacteristic
356#107—22no—
357#107—142no—
358#107—142no—
359#107—142no—
360#106—22no—
361#106—142no—
362#106—142no—
363#106—142no—
364C4⋊C8—74no—
365C4⋊C8C4×D714yes—
366C22⋊C8—74no—
367C22⋊C8—74no—
368C4×C8—74no—
369C4×C8—74no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—141no—
374#95—141no—
375#95—141no—
376#95—141no—
377#95—141no—
378#95—141no—
379#95—141no—
380#95—141no—
381#95—141no—
382C22×C7C22×C4⋊C411yescharacteristic
383C22×C7#52511yescharacteristic
384C22×C7#52511yescharacteristic
385C22×C7C2×#13511yescharacteristic
386C22×C7C2×#13511yescharacteristic
387C22×C7#57511yescharacteristic
388C22×C7#57511yescharacteristic
389C2×D7—22no—
390C2×D7—22no—
391C2×D7—22no—
392C2×D7—41no—
393C2×D7—41no—
394C2×D7—41no—
395C2×D7—41no—
396C4×C7—22no—
397C4×C7—22no—
398C4×C7—42no—
399C4×C7—42no—
400C4×C7—81no—
401C4×C7—81no—
402C4×C7C4×#4111yescharacteristic
403C4×C7C4×#4111yescharacteristic
404C4×C7#53311yescharacteristic
405C4×C7#53311yescharacteristic
406Dic7—22no—
407Dic7—22no—
408Dic7—42no—
409Dic7—42no—
410Dic7—81no—
411Dic7—81no—
412Dic7#42714yes—
413C24—71no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—71no—
419C22×C4—71no—
420C22×C4—71no—
421C22×C4—74no—
422C22×C4—72no—
423C22×C4—72no—
424C22×C4—74no—
425C22×C4—142no—
426C22×C4—142no—
427C22×C4—141no—
428C22×C4—141no—
429C22×C4—141no—
430C22×C4—141no—
431C22×C4—141no—
432C22×C4—141no—
433C22×C4—141no—
434C22×C4—141no—
435C22×C4—281no—
436C22×C4—281no—
437C22×C4D4×D711yescharacteristic
438C22×C4D4×D711yescharacteristic
439C22×C4C23×D711yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—72no—
445C2×C8—72no—
446C2×C8—141no—
447C2×C8—141no—
448C2×C8—141no—
449C2×C8—141no—
450C2×C8C2×C4×D712yes—
451C2×C8C2×C4×D712yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—72no—
459C4⋊C4—72no—
460C4⋊C4—141no—
461C4⋊C4—141no—
462C4⋊C4—141no—
463C4⋊C4—141no—
464C4⋊C4—141no—
465C4⋊C4—141no—
466C4⋊C4#115912yes—
467C4⋊C4#116112yes—
468C22⋊C4—144no—
469C22⋊C4—144no—
470C22⋊C4—282no—
471C22⋊C4—282no—
472C42—42no—
473C42—74no—
474C42—74no—
475C42—72no—
476C42—72no—
477C42—144no—
478C42—144no—
479C42—282no—
480C42—282no—
481C42—282no—
482C42—282no—
483C42—282no—
484C42C2×C4×D712yes—
485C42Q8×D712yes—
486C2×C7#229611yescharacteristic
487C2×C7C2×#42711yescharacteristic
488C2×C7#291111yescharacteristic
489C2×C7#310211yescharacteristic
490C2×C7#310211yescharacteristic
491C2×C7#310211yescharacteristic
492C2×C7#310211yescharacteristic
493D7—42no—
494C23—72no—
495C23—141no—
496C23—141no—
497C23—141no—
498C23—141no—
499C23—141no—
500C23—141no—
501C23C2×D4×D711yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
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—72no—
519C2×C4—72no—
520C2×C4—72no—
521C2×C4—72no—
522C2×C4—72no—
523C2×C4—148no—
524C2×C4—141no—
525C2×C4—141no—
526C2×C4—141no—
527C2×C4—141no—
528C2×C4—142no—
529C2×C4—142no—
530C2×C4—142no—
531C2×C4—142no—
532C2×C4—142no—
533C2×C4—142no—
534C2×C4—284no—
535C2×C4—281no—
536C2×C4—281no—
537C2×C4—281no—
538C2×C4—281no—
539C2×C4—281no—
540C2×C4—281no—
541C2×C4—281no—
542C2×C4—281no—
543C2×C4—281no—
544C2×C4—281no—
545C2×C4D7×C4⋊C412yes—
546C2×C4D7×C4⋊C412yes—
547C2×C4C22×C4×D711yescharacteristic
548C2×C4C2×#115911yescharacteristic
549C2×C4C2×Q8×D711yescharacteristic
550C2×C4C2×#116111yescharacteristic
551C2×C4D7×#4111yescharacteristic
552C2×C4D7×#4111yescharacteristic
553C8—22no—
554C8—22no—
555C8—142no—
556C8—142no—
557C7#2136011yescharacteristic, complemented, Sylow
558C22—142no—
559C22—142no—
560C22—142no—
561C22—281no—
562C22—281no—
563C22—281no—
564C22—281no—
565C22C2×D7×C4⋊C411yescharacteristic
566C22#9029711yescharacteristic
567C22#9031811yescharacteristic
568C22D7×#13511yescharacteristic
569C22D7×#13511yescharacteristic
570C22#9046411yescharacteristic
571C22#9046811yescharacteristic
572C4—22no—
573C4—22no—
574C4—42no—
575C4—42no—
576C4—74no—
577C4—81no—
578C4—81no—
579C4—142no—
580C4—142no—
581C4—282no—
582C4—282no—
583C4—561no—
584C4—561no—
585C4C4×#115911yescharacteristic
586C4C4×#116111yescharacteristic
587C4#9037911yescharacteristic
588C4#9041911yescharacteristic
589C2—282no—
590C2#1173340811yescharacteristic
591C2D7×#42711yescharacteristic
592C2#1173665311yescharacteristic
593C2#1173794911yescharacteristic
594C2#1173801311yescharacteristic
595C2#1173858511yescharacteristic
596C2#1173864911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1949C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
cosocleC22×C4×C7C24
hypercenter#1949D7
hypocenterC7#21360
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. C7×#1949C2semidirect
6. Dic7×#107C2semidirect
8. Dic7×#106C2semidirect
9. #11728209C2semidirect
10. #11727294C2semidirect
11. #11727222C2semidirect
14. #11726539C2semidirect
15. #11726538C2semidirect
45. #89605C4semidirect
130. #1949D7semidirect
557. C7#21360semidirect

Maximal subgroups

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

subgroupindex
C2×#896052
#117315922
C4×#64552
C7×#19492
#117283872
Dic7×#1072
#117283342
Dic7×#1062
#117282092
#117272942
#117272222
#117266312
#117266302
#117265392
#117265382
#213607