Finite Group Databasebeta

← #13371445

Subgroups — #13371445

Order 1792.

822 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×#107C211yesmaximal, characteristic
2#11733646C211yesmaximal, characteristic
3#11731213C211yesmaximal, characteristic
4C7×#1921C211yesmaximal, characteristic, complemented
5#11728364C211yesmaximal, characteristic, complemented
6#11727373C211yesmaximal, characteristic, complemented
7C4×#6381C211yesmaximal, characteristic, complemented
8#11726626C211yesmaximal, characteristic
9#11726626C211yesmaximal, characteristic
10#11726623C211yesmaximal, characteristic
11#11726613C211yesmaximal, characteristic, complemented
12#11726574C211yesmaximal, characteristic, complemented
13#11726539C211yesmaximal, characteristic, complemented
14#11726401C211yesmaximal, characteristic
15#11726378C211yesmaximal, characteristic, complemented
16C22×C8×D7C2211yescharacteristic
17C2×D7×C4⋊C4C2211yescharacteristic
18C2×D7×C4⋊C4C2211yescharacteristic
19C2×C7×#107C2211yescharacteristic
20C7×#389C2211yescharacteristic
21C4×C7×C4⋊C4C2211yescharacteristic
22C2×(C2×D7)⋊C8C2211yescharacteristic
23C2×#6392C2211yescharacteristic
24C2×C8×Dic7C2211yescharacteristic
25#89759—21no—
26#89759C2211yescharacteristic
27#89759C2211yescharacteristic
28#89757C2211yescharacteristic
29#89750—21no—
30C4⋊C4×Dic7C2211yescharacteristic
31C4⋊C4×Dic7C2211yescharacteristic
32#89745C2211yescharacteristic
33C2×#6381C2211yescharacteristic
34C2×#6381C2211yescharacteristic
35C2×#6381C2211yescharacteristic
36C2×#6381C2211yescharacteristic
37C4×(C2×D7)⋊C4—21no—
38C4×(C2×D7)⋊C4C2211yescharacteristic
39C4×C4⋊Dic7C2211yescharacteristic
40#89705—21no—
41#89700C2211yescharacteristic
42C2×C4×C7⋊C8C2211yescharacteristic
43D7×#107C418yescomplemented
44#89439—21no—
45#89438—21no—
46#89427—21no—
47#89424—21no—
48C7×#340C2211yescharacteristic
49C7×#340C2211yescharacteristic
50C7×#340C2211yescharacteristic
51C7×#336C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89345C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#22612—71nomaximal, Sylow
61C22×C4×D7—21no—
62C22×C4×D7—21no—
63C22×C4×D7C2311yescharacteristic
64C22×C7×C8C2311yescharacteristic
65C22×C7×C8C2311yescharacteristic
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C42×C7—21no—
72C2×C42×C7C2311yescharacteristic
73C2×(C2×D7)⋊C4—21no—
74C2×(C2×D7)⋊C4—21no—
75C2×(C2×D7)⋊C4D411yescharacteristic
76C2×(C2×D7)⋊C4D411yescharacteristic
77C2×C4⋊Dic7—21no—
78C2×C4⋊Dic7C2311yescharacteristic
79C2×C4⋊Dic7C2311yescharacteristic
80C2×C4⋊Dic7C2311yescharacteristic
81C2×C4⋊Dic7C2311yescharacteristic
82C2×Dic7⋊C4—21no—
83C2×Dic7⋊C4—21no—
84C2×Dic7⋊C4—21no—
85C2×Dic7⋊C4—21no—
86C2×C4×Dic7—21no—
87C2×C4×Dic7—21no—
88C2×C4×Dic7—21no—
89C2×C4×Dic7C2311yescharacteristic
90C22×C7⋊C8C2311yescharacteristic
91C22×C7⋊C8C2311yescharacteristic
92C2×C8×D7—22no—
93C2×C8×D7—22no—
94C2×C8×D7C2×C414yes—
95D7×C4⋊C4—22no—
96D7×C4⋊C4—22no—
97D7×C4⋊C4C2×C414yes—
98D7×C4⋊C4C2×C414yes—
99C7×#107C2×C414yes—
100C7×#95—21no—
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⋊#95D411yescharacteristic
111C7⋊#95D411yescharacteristic
112(C2×D7)⋊C8—22no—
113#6392C2×C414yes—
114C8×Dic7—22no—
115#6381—22no—
116#6381—22no—
117#6381C2×C414yes—
118#6381C2×C414yes—
119C4×C7⋊C8—22no—
120C22×#107—71no—
121#2345—71no—
122#2345—71no—
123#1942—71no—
124#1942—71no—
125#1921—71no—
126#1921—71no—
127#1921—71no—
128#1921D711yescharacteristic, complemented
129#1824—71no—
130#1824—71no—
131#1808—71no—
132C4×#107—71no—
133C4×#107—71no—
134C8×C22⋊C4—71no—
135C23×D7C2×D411yescharacteristic
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7C2×D411yescharacteristic
141C22×C4×C7C2×D411yescharacteristic
142C22×C4×C7C2411yescharacteristic
143C22×Dic7—21no—
144C22×Dic7—21no—
145C22×Dic7—21no—
146C22×Dic7—21no—
147C22×Dic7C2×D411yescharacteristic
148C22×Dic7C2×D411yescharacteristic
149C22×Dic7C2×D411yescharacteristic
150C2×C4×D7—21no—
151C2×C4×D7—21no—
152C2×C4×D7—21no—
153C2×C4×D7—21no—
154C2×C4×D7—24no—
155C2×C4×D7—24no—
156C2×C4×D7—81no—
157C2×C4×D7—81no—
158C2×C4×D7—81no—
159C2×C4×D7—81no—
160C2×C4×D7C22×C412yes—
161C2×C4×D7#4112yes—
162C2×C7×C8—21no—
163C2×C7×C8—21no—
164C2×C7×C8—21no—
165C2×C7×C8—21no—
166C2×C7×C8—21no—
167C2×C7×C8C22×C412yes—
168C7×C4⋊C4—21no—
169C7×C4⋊C4—21no—
170C7×C4⋊C4—21no—
171C7×C4⋊C4—21no—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—81no—
175C7×C4⋊C4C22×C412yes—
176C7×C4⋊C4C22×C412yes—
177C42×C7—21no—
178C42×C7—21no—
179C42×C7—81no—
180(C2×D7)⋊C4—22no—
181(C2×D7)⋊C4—42no—
182(C2×D7)⋊C4—42no—
183(C2×D7)⋊C4Q1614yes—
184C4⋊Dic7—21no—
185C4⋊Dic7—21no—
186C4⋊Dic7—21no—
187C4⋊Dic7—21no—
188C4⋊Dic7—21no—
189C4⋊Dic7—21no—
190C4⋊Dic7—81no—
191C4⋊Dic7C22×C412yes—
192C4⋊Dic7C22×C412yes—
193Dic7⋊C4—24no—
194Dic7⋊C4—24no—
195Dic7⋊C4—81no—
196Dic7⋊C4—81no—
197C4×Dic7—21no—
198C4×Dic7—21no—
199C4×Dic7—81no—
200C4×Dic7—81no—
201C4×Dic7—81no—
202C2×C7⋊C8—21no—
203C2×C7⋊C8—21no—
204C2×C7⋊C8—21no—
205C2×C7⋊C8C22×C412yes—
206C2×C7⋊C8#4112yes—
207C2×C7⋊C8#4112yes—
208C8×D7—28no—
209C23×C8—71no—
210C22×C4⋊C4—71no—
211C22×C4⋊C4—71no—
212C2×#107—71no—
213C2×#107—71no—
214C2×#107—71no—
215C2×#107—78no—
216C2×#107—71no—
217C2×#107—71no—
218C2×#107C2×D711yescharacteristic
219C2×C22⋊C8—71no—
220C2×C4×C8—71no—
221C2×C4×C8—71no—
222#389—71no—
223#389—71no—
224#389—71no—
225#389C2×D711yescharacteristic
226#387—141no—
227#387—141no—
228#387—141no—
229#387—141no—
230#380—71no—
231#380—71no—
232#380—141no—
233#380—141no—
234C4×C4⋊C4—71no—
235C4×C4⋊C4—71no—
236C4×C4⋊C4—71no—
237C4×C4⋊C4C2×D711yescharacteristic
238C4×C22⋊C4—71no—
239C4×C22⋊C4—141no—
240C4×C22⋊C4—141no—
241#340—71no—
242#340—71no—
243#340—71no—
244#340—71no—
245#340—71no—
246#340—71no—
247#340—71no—
248#340C2×D711yescharacteristic
249#340C2×D711yescharacteristic
250#340C2×D711yescharacteristic
251#336—71no—
252#336C2×D711yescharacteristic
253C23×C7C22×D411yescharacteristic
254C22×D7—21no—
255C22×D7—21no—
256C22×D7—21no—
257C22×D7—21no—
258C22×D7C4×D412yes—
259C22×D7C2×Q1612yes—
260C22×D7#13512yes—
261C2×C4×C7—21no—
262C2×C4×C7—21no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—21no—
266C2×C4×C7—21no—
267C2×C4×C7—21no—
268C2×C4×C7—41no—
269C2×C4×C7—41no—
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×C7C2×Q1612yes—
279C2×C4×C7C23×C411yescharacteristic
280C2×C4×C7C2×#4111yescharacteristic
281C2×C4×C7C2×#4111yescharacteristic
282C2×C4×C7C2×#4111yescharacteristic
283C2×C4×C72−1+411yescharacteristic
284C2×C4×C72−1+411yescharacteristic
285C2×Dic7—21no—
286C2×Dic7—21no—
287C2×Dic7—21no—
288C2×Dic7—21no—
289C2×Dic7—22no—
290C2×Dic7—22no—
291C2×Dic7—21no—
292C2×Dic7—21no—
293C2×Dic7—21no—
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×Dic7C4×D412yes—
305C2×Dic7C2×Q1612yes—
306C4×D7—22no—
307C4×D7—22no—
308C4×D7—22no—
309C4×D7—22no—
310C4×D7—84no—
311C4×D7—84no—
312C7×C8—22no—
313C7×C8—41no—
314C7⋊C8—41no—
315C7⋊C8#11714yes—
316C23×C4—71no—
317C23×C4—141no—
318C23×C4—141no—
319C22×C8—71no—
320C22×C8—74no—
321C22×C8—71no—
322C22×C8—142no—
323C22×C8—142no—
324C22×C8C22×D711yescharacteristic
325C22×C8C22×D711yescharacteristic
326C2×C4⋊C4—21no—
327C2×C4⋊C4—71no—
328C2×C4⋊C4—71no—
329C2×C4⋊C4—74no—
330C2×C4⋊C4—74no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—71no—
333C2×C4⋊C4—142no—
334C2×C4⋊C4—142no—
335C2×C4⋊C4—141no—
336C2×C4⋊C4—141no—
337C2×C4⋊C4—141no—
338C2×C4⋊C4—141no—
339C2×C4⋊C4—141no—
340C2×C4⋊C4C22×D711yescharacteristic
341C2×C4⋊C4C22×D711yescharacteristic
342C2×C4⋊C4C22×D711yescharacteristic
343C2×C4⋊C4C22×D711yescharacteristic
344C2×C22⋊C4—71no—
345C2×C22⋊C4—71no—
346C2×C22⋊C4—141no—
347C2×C22⋊C4—141no—
348C2×C42—21no—
349C2×C42—71no—
350C2×C42—141no—
351C2×C42—141no—
352C2×C42—141no—
353C2×C42C22×D711yescharacteristic
354#107—74no—
355#107—74no—
356#107—74no—
357#107—142no—
358#107—142no—
359#107C4×D714yes—
360C22⋊C8—142no—
361C4×C8—142no—
362C4×C8—142no—
363#95—21no—
364#95—21no—
365#95—71no—
366#95—71no—
367#95—141no—
368#95—141no—
369#95—141no—
370#95—141no—
371#95—141no—
372#95—141no—
373#95—141no—
374#95—141no—
375C22×C7C2×C4×D411yescharacteristic
376C22×C7#54711yescharacteristic
377C22×C7#54711yescharacteristic
378C22×C7C22×Q1611yescharacteristic
379C22×C7C2×#13511yescharacteristic
380C22×C7#57611yescharacteristic
381C22×C7#57611yescharacteristic
382C2×D7—22no—
383C2×D7—22no—
384C2×D7—22no—
385C2×D7—22no—
386C2×D7—22no—
387C2×D7—22no—
388C2×D7C4×Q1614yes—
389C4×C7—22no—
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—22no—
400Dic7—22no—
401Dic7—41no—
402Dic7—42no—
403Dic7—42no—
404Dic7—81no—
405Dic7—81no—
406C24—71no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—71no—
412C22×C4—71no—
413C22×C4—72no—
414C22×C4—72no—
415C22×C4—71no—
416C22×C4—144no—
417C22×C4—144no—
418C22×C4—141no—
419C22×C4—141no—
420C22×C4—141no—
421C22×C4—141no—
422C22×C4—141no—
423C22×C4—141no—
424C22×C4—141no—
425C22×C4—141no—
426C22×C4—561no—
427C22×C4—561no—
428C22×C4—561no—
429C22×C4—561no—
430C22×C4D4×D711yescharacteristic
431C22×C4D4×D711yescharacteristic
432C22×C4C23×D711yescharacteristic
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—72no—
439C2×C8—72no—
440C2×C8—72no—
441C2×C8—148no—
442C2×C8—141no—
443C2×C8—141no—
444C2×C8—141no—
445C2×C8C2×C4×D712yes—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—72no—
453C4⋊C4—72no—
454C4⋊C4—81no—
455C4⋊C4—144no—
456C4⋊C4—144no—
457C4⋊C4—141no—
458C4⋊C4—141no—
459C4⋊C4—141no—
460C4⋊C4—141no—
461C4⋊C4—141no—
462C4⋊C4—141no—
463C4⋊C4—561no—
464C4⋊C4—561no—
465C4⋊C4—561no—
466C4⋊C4C2×C4×D712yes—
467C4⋊C4C2×C4×D712yes—
468C22⋊C4—74no—
469C22⋊C4—142no—
470C22⋊C4—282no—
471C22⋊C4—282no—
472C42—21no—
473C42—21no—
474C42—81no—
475C42—141no—
476C42—141no—
477C42—561no—
478C42—561no—
479C42—561no—
480C2×C7#234411yescharacteristic
481C2×C7C2×C4×Q1611yescharacteristic
482C2×C7#294811yescharacteristic
483C2×C7#333811yescharacteristic
484C2×C7#333811yescharacteristic
485C2×C7#333911yescharacteristic
486C2×C7#333911yescharacteristic
487D7—24no—
488C23—72no—
489C23—72no—
490C23—72no—
491C23—141no—
492C23—141no—
493C23—141no—
494C23—141no—
495C23C2×D4×D711yescharacteristic
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—72no—
514C2×C4—72no—
515C2×C4—141no—
516C2×C4—141no—
517C2×C4—141no—
518C2×C4—141no—
519C2×C4—142no—
520C2×C4—142no—
521C2×C4—142no—
522C2×C4—142no—
523C2×C4—141no—
524C2×C4—141no—
525C2×C4—142no—
526C2×C4—142no—
527C2×C4—141no—
528C2×C4—281no—
529C2×C4—281no—
530C2×C4—281no—
531C2×C4—281no—
532C2×C4—281no—
533C2×C4—281no—
534C2×C4—281no—
535C2×C4—281no—
536C2×C4—281no—
537C2×C4—281no—
538C2×C4—564no—
539C2×C4—564no—
540C2×C4D7×Q1612yes—
541C2×C4C22×C4×D711yescharacteristic
542C2×C4#655111yescharacteristic
543C2×C4D7×#4111yescharacteristic
544C2×C4D7×#4111yescharacteristic
545C2×C4D7×#4111yescharacteristic
546C2×C4#655411yescharacteristic
547C8—22no—
548C8—41no—
549C8—74no—
550C8—281no—
551C7#2261211yescharacteristic, complemented, Sylow
552C22—74no—
553C22—142no—
554C22—142no—
555C22—142no—
556C22—142no—
557C22—142no—
558C22—142no—
559C22C4×D4×D711yescharacteristic
560C22#9032211yescharacteristic
561C22#9034611yescharacteristic
562C22C2×D7×Q1611yescharacteristic
563C22D7×#13511yescharacteristic
564C22#9046511yescharacteristic
565C22#9046511yescharacteristic
566C4—22no—
567C4—41no—
568C4—42no—
569C4—42no—
570C4—81no—
571C4—81no—
572C4—142no—
573C4—142no—
574C4—281no—
575C4—282no—
576C4—282no—
577C4—561no—
578C4—561no—
579C4D7×#11711yescharacteristic
580C4#9026311yescharacteristic
581C4#9038411yescharacteristic
582C4#9039911yescharacteristic
583C2—144no—
584C2#1173240611yescharacteristic
585C2C4×D7×Q1611yescharacteristic
586C2#1173731211yescharacteristic
587C2#1173857011yescharacteristic
588C2#1173864011yescharacteristic
589C2#1173883311yescharacteristic
590C2#1173892111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1921C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
cosocleC22×C4×C7C24
hypercenter#1921D7
hypocenterC7#22612
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
4. C7×#1921C2semidirect
5. #11728364C2semidirect
6. #11727373C2semidirect
7. C4×#6381C2semidirect
11. #11726613C2semidirect
12. #11726574C2semidirect
13. #11726539C2semidirect
15. #11726378C2semidirect
43. D7×#107C4semidirect
128. #1921D7semidirect
551. C7#22612semidirect

Maximal subgroups

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

subgroupindex
C2×D7×#1072
#117336462
#117312132
C7×#19212
#117283642
#117273732
C4×#63812
#117266262
#117266232
#117266132
#117265742
#117265392
#117264012
#117263782
#226127