Finite Group Databasebeta

← #13372172

Subgroups — #13372172

Order 1792.

906 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×Q8×C4⋊C4C211yesmaximal, characteristic
2C2×#89802C211yesmaximal, characteristic
3C2×#89802C211yesmaximal, characteristic
4C2×C4×#1144C211yesmaximal, characteristic
5#11731082C211yesmaximal, characteristic
6#11729383C211yesmaximal, characteristic
7#11729382C211yesmaximal, characteristic
8#11729381C211yesmaximal, characteristic
9#11727386C211yesmaximal, characteristic
10#11727385C211yesmaximal, characteristic
11#11727375C211yesmaximal, characteristic
12#11727372C211yesmaximal, characteristic
13#11727342C211yesmaximal, characteristic
14#11727332C211yesmaximal, characteristic
15#11727232C211yesmaximal, characteristic
16C2×C4×C7×Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C22×#1144C2211yescharacteristic
20C2×C4×Dic14C2211yescharacteristic
21C2×C4×Dic14C2211yescharacteristic
22C2×C4×Dic14C2211yescharacteristic
23C7×#389—21no—
24C7×#389—21no—
25C7×#389C2211yescharacteristic
26C7×#389C2211yescharacteristic
27C7×#384—21no—
28C7×#384C2211yescharacteristic
29C4×C7×C4⋊C4—21no—
30C4×C7×C4⋊C4C2211yescharacteristic
31C2×#6409C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34#89802—24no—
35#89802C418yescomplemented
36C4×#1144—24no—
37#89744—21no—
38#89744—21no—
39C2×#6384C2211yescharacteristic
40C2×#6384C2211yescharacteristic
41C2×#6384C2211yescharacteristic
42C2×#6382C2211yescharacteristic
43C2×#6382C2211yescharacteristic
44C2×#6382C2211yescharacteristic
45C2×#6381C2211yescharacteristic
46C2×#6381C2211yescharacteristic
47#89708C2211yescharacteristic
48#89700C2211yescharacteristic
49#89700C2211yescharacteristic
50C2×C4⋊(C7⋊C8)C2211yescharacteristic
51C2×#6377C2211yescharacteristic
52C2×#6377C2211yescharacteristic
53C2×C4×C7⋊C8C2211yescharacteristic
54#89422—21no—
55#89421—21no—
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89319C2211yescharacteristic
61#89319C2211yescharacteristic
62#22679—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C22×Dic14C2311yescharacteristic
65C4×C7×Q8—22no—
66C4×C7×Q8—22no—
67C4×C7×Q8—22no—
68C4×C7×Q8—41no—
69C4×C7×Q8—41no—
70C4×C7×Q8C2×C414yes—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4—21no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4D411yescharacteristic
79C2×C7×C4⋊C4D411yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C42×C7—21no—
84C2×C42×C7—21no—
85C2×C42×C7—21no—
86C2×C42×C7C2311yescharacteristic
87C2×C42×C7C2311yescharacteristic
88C2×C42×C7C2311yescharacteristic
89C2×#1144C2×C414yes—
90C2×#1144D414yes—
91C2×#1144Q814yes—
92C2×C4⋊Dic7C2311yescharacteristic
93C2×C4⋊Dic7C2311yescharacteristic
94C2×C4⋊Dic7C2311yescharacteristic
95C2×Dic7⋊C4—21no—
96C2×Dic7⋊C4—21no—
97C2×Dic7⋊C4—21no—
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—21no—
100C2×C4×Dic7—21no—
101C2×C4×Dic7—21no—
102C2×C4×Dic7—21no—
103C22×C7⋊C8C2311yescharacteristic
104C22×C7⋊C8C2311yescharacteristic
105C22×C7⋊C8C2311yescharacteristic
106C22×C7⋊C8C2311yescharacteristic
107C4×Dic14—22no—
108C4×Dic14—22no—
109C4×Dic14—22no—
110C4×Dic14—41no—
111C4×Dic14—41no—
112C4×Dic14C2×C414yes—
113C7×#95—21no—
114C7×#95—21no—
115C7×#95D411yescharacteristic
116C7×#95D411yescharacteristic
117#6409—22no—
118#6409—22no—
119#6409C2×C414yes—
120C7⋊#95—21no—
121C7⋊#95—21no—
122C7⋊#95—21no—
123C7⋊#95—21no—
124#6384—22no—
125#6384—22no—
126#6384C2×C414yes—
127#6382—22no—
128#6382—41no—
129#6382C2×C414yes—
130#6381—22no—
131#6381—41no—
132C4⋊(C7⋊C8)—22no—
133#6377—22no—
134#6377C2×C414yes—
135C4×C7⋊C8—22no—
136C2×#441—71no—
137C2×#441—71no—
138C2×C4×Q16—71no—
139#2351—71no—
140Q8×C4⋊C4D711yescharacteristic
141#1944—71no—
142#1941—71no—
143#1865—71no—
144#1865—71no—
145#1863—71no—
146#1863—71no—
147#1847—71no—
148#1805—71no—
149#1803—71no—
150#1771—71no—
151C2×C7×Q8—21no—
152C2×C7×Q8—21no—
153C2×C7×Q8—21no—
154C2×C7×Q8C22×C412yes—
155C2×C7×Q8C2×D412yes—
156C2×C7×Q8C2×Q812yes—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2411yescharacteristic
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C2×Dic14—21no—
173C2×Dic14—21no—
174C2×Dic14—21no—
175C2×Dic14C22×C412yes—
176C2×Dic14C2×D412yes—
177C2×Dic14C2×Q812yes—
178C7×C4⋊C4—24no—
179C7×C4⋊C4—22no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4—41no—
186C7×C4⋊C4—42no—
187C7×C4⋊C4—42no—
188C7×C4⋊C4—42no—
189C7×C4⋊C4—81no—
190C7×C4⋊C4—81no—
191C7×C4⋊C4—81no—
192C7×C4⋊C4C22×C412yes—
193C42×C7—24no—
194C42×C7—21no—
195C42×C7—21no—
196C42×C7—21no—
197C42×C7—21no—
198C42×C7—42no—
199C42×C7—42no—
200C42×C7C22×C412yes—
201C42×C7#4112yes—
202#1144C4⋊C4116yescomplemented
203C4⋊Dic7—21no—
204C4⋊Dic7—21no—
205C4⋊Dic7—21no—
206C4⋊Dic7—21no—
207C4⋊Dic7—21no—
208C4⋊Dic7C22×C412yes—
209Dic7⋊C4—24no—
210Dic7⋊C4—42no—
211Dic7⋊C4—42no—
212Dic7⋊C4—42no—
213Dic7⋊C4—42no—
214C4×Dic7—24no—
215C4×Dic7—42no—
216C4×Dic7—42no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8—21no—
219C2×C7⋊C8—21no—
220C2×C7⋊C8—21no—
221C2×C7⋊C8—21no—
222C2×C7⋊C8—21no—
223C2×C7⋊C8—21no—
224C2×C7⋊C8—21no—
225C2×C7⋊C8C22×C412yes—
226C2×C7⋊C8C22×C412yes—
227C2×C7⋊C8C2×D412yes—
228C2×C7⋊C8C2×Q812yes—
229C22×Q16—71no—
230C2×C4×Q8—71no—
231C2×C4×Q8—71no—
232C2×C4×Q8—71no—
233C2×C4×Q8C2×D711yescharacteristic
234C2×C4×Q8C2×D711yescharacteristic
235C2×C4×Q8C2×D711yescharacteristic
236#441—78no—
237#441—144no—
238C4×Q16—144no—
239C2×#107—71no—
240C2×#107—71no—
241C2×#106—71no—
242C2×#106—71no—
243C2×#106—71no—
244C2×C4⋊C8—71no—
245C2×#103—71no—
246C2×#103—71no—
247C2×#103—71no—
248C2×#103—71no—
249C2×#103—71no—
250C2×#103—71no—
251C2×#97—71no—
252C2×#97—71no—
253C2×C4×C8—71no—
254#389—21no—
255#389—21no—
256#389—71no—
257#389—71no—
258#389—141no—
259#389—141no—
260#389C2×D711yescharacteristic
261#389C2×D711yescharacteristic
262#384—21no—
263#384C2×D711yescharacteristic
264#382—71no—
265#382—141no—
266C4×C4⋊C4—21no—
267C4×C4⋊C4—141no—
268C4×C4⋊C4C2×D711yescharacteristic
269#340—71no—
270#340—71no—
271#340—71no—
272#340—71no—
273#336—71no—
274#336—71no—
275C23×C7C22×D411yescharacteristic
276C7×Q8—22no—
277C7×Q8—22no—
278C7×Q8—22no—
279C7×Q8C2×C4⋊C414yes—
280C2×C4×C7—22no—
281C2×C4×C7—21no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—22no—
290C2×C4×C7—21no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—21no—
294C2×C4×C7—21no—
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—41no—
305C2×C4×C7—41no—
306C2×C4×C7—41no—
307C2×C4×C7C4×D412yes—
308C2×C4×C7C4×D412yes—
309C2×C4×C7#13712yes—
310C2×C4×C7C23×C411yescharacteristic
311C2×C4×C7C22×D411yescharacteristic
312C2×C4×C7C22×Q811yescharacteristic
313C2×C4×C7C2×#4111yescharacteristic
314C2×C4×C7H(5,𝔽2)11yescharacteristic
315C2×C4×C72−1+411yescharacteristic
316C2×Dic7—22no—
317C2×Dic7—22no—
318C2×Dic7—22no—
319C2×Dic7—22no—
320C2×Dic7—41no—
321C2×Dic7—41no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326C2×Dic7—41no—
327C2×Dic7—41no—
328Dic14—22no—
329Dic14—22no—
330Dic14—22no—
331Dic14C2×C4⋊C414yes—
332C7⋊C8—22no—
333C7⋊C8—41no—
334C7⋊C8—41no—
335C7⋊C8C2×C4⋊C414yes—
336C22×Q8—71no—
337C22×Q8C22×D711yescharacteristic
338C2×Q16—74no—
339C2×Q16—74no—
340C2×Q16—74no—
341C22×C8—71no—
342C22×C8—71no—
343C22×C8—71no—
344C22×C8—71no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—41no—
349C4×Q8—41no—
350C4×Q8—74no—
351C4×Q8—142no—
352C4×Q8—142no—
353C4×Q8—142no—
354C4×Q8—281no—
355C4×Q8—281no—
356C4×Q8C4×D714yes—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—71no—
365C2×C4⋊C4—71no—
366C2×C4⋊C4—71no—
367C2×C4⋊C4—141no—
368C2×C4⋊C4—141no—
369C2×C4⋊C4—141no—
370C2×C4⋊C4—141no—
371C2×C4⋊C4—141no—
372C2×C4⋊C4C22⋊D711yescharacteristic
373C2×C4⋊C4C22⋊D711yescharacteristic
374C2×C4⋊C4C22×D711yescharacteristic
375C2×C4⋊C4C22×D711yescharacteristic
376C2×C4⋊C4C22×D711yescharacteristic
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—141no—
381C2×C42—141no—
382C2×C42—141no—
383C2×C42C22×D711yescharacteristic
384C2×C42C22×D711yescharacteristic
385C2×C42C22×D711yescharacteristic
386#107—142no—
387#107—281no—
388#106—74no—
389#106—142no—
390#106—281no—
391C4⋊C8—142no—
392#103—74no—
393#103—74no—
394#103—142no—
395#103—142no—
396#103—142no—
397#103—142no—
398#97—74no—
399#97—142no—
400C4×C8—142no—
401#95—21no—
402#95—21no—
403#95—141no—
404#95—141no—
405#95—141no—
406#95—141no—
407#95C22⋊D711yescharacteristic
408#95C22⋊D711yescharacteristic
409C22×C7C2×C4×D411yescharacteristic
410C22×C7D4211yescharacteristic
411C22×C7D4×Q811yescharacteristic
412C22×C7C2×#13711yescharacteristic
413C22×C7#57511yescharacteristic
414C22×C7#57711yescharacteristic
415C22×C7#57811yescharacteristic
416C4×C7—24no—
417C4×C7—22no—
418C4×C7—22no—
419C4×C7—22no—
420C4×C7—42no—
421C4×C7—41no—
422C4×C7—41no—
423C4×C7—41no—
424C4×C7—81no—
425C4×C7—81no—
426C4×C7C22×C4⋊C411yescharacteristic
427C4×C7#52011yescharacteristic
428C4×C7#54711yescharacteristic
429C4×C7#55411yescharacteristic
430Dic7—24no—
431Dic7—42no—
432Dic7—81no—
433Dic7—81no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—72no—
438C2×Q8—72no—
439C2×Q8—72no—
440C2×Q8—141no—
441C2×Q8—141no—
442C2×Q8—141no—
443C2×Q8C2×C4×D712yes—
444C2×Q8D4×D712yes—
445C2×Q8Q8×D712yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—141no—
451C22×C4—141no—
452C22×C4—141no—
453C22×C4—141no—
454C22×C4C2×C22⋊D711yescharacteristic
455C22×C4C2×C22⋊D711yescharacteristic
456C22×C4C2×C22⋊D711yescharacteristic
457C22×C4C2×C22⋊D711yescharacteristic
458C22×C4C2×C22⋊D711yescharacteristic
459C22×C4C2×C22⋊D711yescharacteristic
460C22×C4C23×D711yescharacteristic
461Q16—716no—
462C2×C8—72no—
463C2×C8—72no—
464C2×C8—72no—
465C2×C8—72no—
466C2×C8—141no—
467C2×C8—141no—
468C2×C8—141no—
469C2×C8—141no—
470C2×C8—141no—
471C2×C8—141no—
472C2×C8—141no—
473C2×C8—141no—
474C4⋊C4—24no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—72no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4—81no—
489C4⋊C4—144no—
490C4⋊C4—141no—
491C4⋊C4—141no—
492C4⋊C4—141no—
493C4⋊C4—141no—
494C4⋊C4—141no—
495C4⋊C4—282no—
496C4⋊C4—282no—
497C4⋊C4—282no—
498C4⋊C4—282no—
499C4⋊C4C2×C4×D712yes—
500C42—24no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—42no—
507C42—144no—
508C42—282no—
509C42—282no—
510C42C2×C4×D712yes—
511C42#115712yes—
512C2×C7D4×C4⋊C411yescharacteristic
513C2×C7C4×#13711yescharacteristic
514C2×C7#294711yescharacteristic
515C2×C7#327011yescharacteristic
516C2×C7#327111yescharacteristic
517C2×C7#338711yescharacteristic
518C2×C7#339011yescharacteristic
519C23C22×C22⋊D711yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8—74no—
524Q8—142no—
525Q8—142no—
526Q8—142no—
527Q8D7×C4⋊C414yes—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—142no—
556C2×C4—142no—
557C2×C4—142no—
558C2×C4—142no—
559C2×C4—281no—
560C2×C4—281no—
561C2×C4—281no—
562C2×C4—281no—
563C2×C4—281no—
564C2×C4—281no—
565C2×C4—281no—
566C2×C4—281no—
567C2×C4C4×C22⋊D712yes—
568C2×C4C4×C22⋊D712yes—
569C2×C4#650512yes—
570C2×C4C22×C4×D711yescharacteristic
571C2×C4C2×#115711yescharacteristic
572C2×C4C2×D4×D711yescharacteristic
573C2×C4#654811yescharacteristic
574C2×C4C2×Q8×D711yescharacteristic
575C2×C4#655111yescharacteristic
576C8—74no—
577C8—142no—
578C8—281no—
579C8—281no—
580C7#2267911yescharacteristic, complemented, Sylow
581C22C2×C4×C22⋊D711yescharacteristic
582C22D4×C22⋊D711yescharacteristic
583C22C2×#650511yescharacteristic
584C22Q8×C22⋊D711yescharacteristic
585C22#9051311yescharacteristic
586C22#9052711yescharacteristic
587C22#9052911yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—24no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—144no—
599C4—282no—
600C4—561no—
601C4—561no—
602C4C2×D7×C4⋊C411yescharacteristic
603C4#9019511yescharacteristic
604C4#9019811yescharacteristic
605C4#9020211yescharacteristic
606C2C4⋊C4×C22⋊D711yescharacteristic
607C2C4×#650511yescharacteristic
608C2#1174001611yescharacteristic
609C2#1174101011yescharacteristic
610C2#1174102811yescharacteristic
611C2#1174112911yescharacteristic
612C2#1174115411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×Q8×C4⋊C4C2
socle, prime radicalC23×C7C22×D4
cosocleC22×C4×C7C24
hypercenterQ8×C4⋊C4D7
hypocenterC7#22679
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
35. #89802C4semidirect
202. #1144C4⋊C4semidirect
580. C7#22679semidirect

Maximal subgroups

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

subgroupindex
C7×Q8×C4⋊C42
C2×#898022
C2×C4×#11442
#117310822
#117293832
#117293822
#117293812
#117273862
#117273852
#117273752
#117273722
#117273422
#117273322
#117272322
#226797