Finite Group Databasebeta

← #13277968

Subgroups — #13277968

Order 1792.

1578 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89745C211yesmaximal, characteristic, complemented
2C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
3C2×#89442C211yesmaximal, characteristic
4C2×#89441C211yesmaximal, characteristic
5C2×#89441C211yesmaximal, characteristic
6C7×#1436C211yesmaximal, characteristic, complemented
7#11729324C211yesmaximal, characteristic
8#11729291C211yesmaximal, characteristic
9#11727182C211yesmaximal, characteristic
10#11727171C211yesmaximal, characteristic, complemented
11#11727165C211yesmaximal, characteristic, complemented
12#11727162C211yesmaximal, characteristic
13#11727160C211yesmaximal, characteristic, complemented
14#11727156C211yesmaximal, characteristic, complemented
15Dic7×#95C211yesmaximal, characteristic, complemented
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C22×(C2×D7)⋊C4C2211yescharacteristic
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51#89745—24no—
52C4×Dic7⋊C4—24no—
53#89442C418yescomplemented
54#89441—24no—
55#89441—24no—
56#14077—71nomaximal, Sylow
57C24×D7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—41no—
75C2×C42×C7—22no—
76C2×C42×C7—41no—
77C2×C42×C7—41no—
78C2×(C2×D7)⋊C4—22no—
79C2×(C2×D7)⋊C4—22no—
80C2×(C2×D7)⋊C4—22no—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4—22no—
84C2×(C2×D7)⋊C4—22no—
85C2×(C2×D7)⋊C4—22no—
86C2×(C2×D7)⋊C4—22no—
87C2×(C2×D7)⋊C4—22no—
88C2×(C2×D7)⋊C4—22no—
89C2×(C2×D7)⋊C4—22no—
90C2×(C2×D7)⋊C4—22no—
91C2×(C2×D7)⋊C4—22no—
92C2×(C2×D7)⋊C4—41no—
93C2×(C2×D7)⋊C4—41no—
94C2×(C2×D7)⋊C4—41no—
95C2×(C2×D7)⋊C4—41no—
96C2×(C2×D7)⋊C4C2×C414yes—
97C2×(C2×D7)⋊C4C2×C414yes—
98C2×(C2×D7)⋊C4C2×C414yes—
99C2×C4⋊Dic7—22no—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7C2×C414yes—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—22no—
105C2×Dic7⋊C4—22no—
106C2×Dic7⋊C4—22no—
107C2×Dic7⋊C4—22no—
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—22no—
110C2×Dic7⋊C4D414yes—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—22no—
113C2×C4×Dic7—22no—
114C2×C4×Dic7—22no—
115C2×C4×Dic7—22no—
116C2×C4×Dic7—22no—
117C2×C4×Dic7—41no—
118C2×C4×Dic7—41no—
119C2×C4×Dic7—41no—
120C2×C4×Dic7—41no—
121C2×C4×Dic7C2×C414yes—
122C2×C4×Dic7D414yes—
123C7×#95—22no—
124C7×#95—22no—
125C7×#95—22no—
126C7×#95—41no—
127C7×#95C2×C414yes—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95C2×C414yes—
141C2×#389—71no—
142C2×#388—71no—
143C2×#388—71no—
144C2×#388—71no—
145C2×C4×C4⋊C4—71no—
146#1443—71no—
147#1441—71no—
148#1439—71no—
149#1439—71no—
150#1437—71no—
151#1437—71no—
152#1436—71no—
153#1436D711yescharacteristic, complemented
154#1434—71no—
155C4×#95—71no—
156C24×C7C2411yescharacteristic
157C23×D7—21no—
158C23×D7—21no—
159C23×D7—21no—
160C23×D7—21no—
161C23×D7—21no—
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
165C23×D7—21no—
166C23×D7—21no—
167C23×D7—21no—
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7C22×C412yes—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7#4112yes—
218C22×C4×C7#4112yes—
219C22×C4×C7#4112yes—
220C22×C4×C7#4112yes—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7C22×C412yes—
260C22×Dic7C22×C412yes—
261C22×Dic7C22×C412yes—
262C22×Dic7C2×D412yes—
263C22×Dic7C2×D412yes—
264C22×Dic7C2×D412yes—
265C22×Dic7C2×D412yes—
266C22×Dic7#4112yes—
267C22×Dic7#4112yes—
268C22×Dic7#4112yes—
269C22×Dic7#4112yes—
270C7×C4⋊C4—44no—
271C42×C7—44no—
272(C2×D7)⋊C4—28no—
273(C2×D7)⋊C4—28no—
274(C2×D7)⋊C4—28no—
275(C2×D7)⋊C4—44no—
276(C2×D7)⋊C4—44no—
277(C2×D7)⋊C4—44no—
278(C2×D7)⋊C4—44no—
279C4⋊Dic7—28no—
280Dic7⋊C4—28no—
281Dic7⋊C4—28no—
282Dic7⋊C4—44no—
283C4×Dic7—28no—
284C4×Dic7—44no—
285C4×Dic7—44no—
286C4×Dic7—44no—
287C22×C4⋊C4—71no—
288C22×C4⋊C4—71no—
289C22×C4⋊C4—71no—
290C22×C4⋊C4—71no—
291C22×C4⋊C4C2×D711yescharacteristic
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C42—71no—
300C22×C42—71no—
301C22×C42—71no—
302C22×C42—71no—
303C22×C42C2×D711yescharacteristic
304#389—144no—
305#388—78no—
306#388—144no—
307#388—144no—
308C4×C4⋊C4—144no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95C2×D711yescharacteristic
323C2×#95C2×D711yescharacteristic
324C2×#95C2×D711yescharacteristic
325C2×#95C2×D711yescharacteristic
326C2×#95C2×D711yescharacteristic
327C23×C7C23×C411yescharacteristic
328C23×C7C22×D411yescharacteristic
329C23×C7C22×D411yescharacteristic
330C23×C7C2×#4111yescharacteristic
331C23×C7C2×#4111yescharacteristic
332C23×C7C2×#4111yescharacteristic
333C23×C7C2×#4111yescharacteristic
334C23×C7C2×#4111yescharacteristic
335C23×C7C2×#4111yescharacteristic
336C23×C7C2×#4111yescharacteristic
337C23×C7C2×#4111yescharacteristic
338C23×C7H(5,𝔽2)11yescharacteristic
339C23×C7H(5,𝔽2)11yescharacteristic
340C23×C72−1+411yescharacteristic
341C23×C72−1+411yescharacteristic
342C22×D7—22no—
343C22×D7—22no—
344C22×D7—22no—
345C22×D7—22no—
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—41no—
350C22×D7—41no—
351C22×D7—41no—
352C22×D7—41no—
353C22×D7—41no—
354C22×D7—41no—
355C22×D7—41no—
356C22×D7—41no—
357C22×D7—41no—
358C22×D7—41no—
359C22×D7—41no—
360C22×D7—41no—
361C22×D7—41no—
362C22×D7—41no—
363C22×D7—41no—
364C22×D7—41no—
365C22×D7—41no—
366C22×D7—41no—
367C22×D7—41no—
368C22×D7—41no—
369C22×D7—41no—
370C22×D7—41no—
371C22×D7—41no—
372C22×D7—41no—
373C22×D7—41no—
374C22×D7—41no—
375C22×D7—41no—
376C22×D7—41no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7#11714yes—
425C2×C4×C7C4×D414yes—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—41no—
454C2×Dic7—41no—
455C2×Dic7—41no—
456C2×Dic7—41no—
457C2×Dic7—41no—
458C2×Dic7—41no—
459C2×Dic7—41no—
460C2×Dic7—41no—
461C2×Dic7—41no—
462C2×Dic7—41no—
463C2×Dic7—41no—
464C2×Dic7—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7—41no—
469C2×Dic7—41no—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7C4×D414yes—
474C2×Dic7#12114yes—
475C25—71no—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486C23×C4C22×D711yescharacteristic
487C23×C4C22×D711yescharacteristic
488C23×C4C22×D711yescharacteristic
489C23×C4C22×D711yescharacteristic
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4—74no—
494C2×C4⋊C4—74no—
495C2×C4⋊C4—142no—
496C2×C4⋊C4—142no—
497C2×C4⋊C4—142no—
498C2×C4⋊C4—142no—
499C2×C4⋊C4—142no—
500C2×C4⋊C4—142no—
501C2×C4⋊C4—142no—
502C2×C4⋊C4—142no—
503C2×C4⋊C4—142no—
504C2×C4⋊C4—142no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—74no—
507C2×C22⋊C4—74no—
508C2×C22⋊C4—142no—
509C2×C22⋊C4—142no—
510C2×C22⋊C4—142no—
511C2×C22⋊C4—142no—
512C2×C22⋊C4—142no—
513C2×C22⋊C4—142no—
514C2×C22⋊C4—142no—
515C2×C22⋊C4—142no—
516C2×C22⋊C4—142no—
517C2×C22⋊C4—142no—
518C2×C22⋊C4—142no—
519C2×C22⋊C4—142no—
520C2×C22⋊C4—142no—
521C2×C22⋊C4—142no—
522C2×C22⋊C4—281no—
523C2×C22⋊C4—281no—
524C2×C22⋊C4—281no—
525C2×C22⋊C4—281no—
526C2×C42—22no—
527C2×C42—41no—
528C2×C42—41no—
529C2×C42—74no—
530C2×C42—74no—
531C2×C42—142no—
532C2×C42—142no—
533C2×C42—142no—
534C2×C42—142no—
535C2×C42—142no—
536C2×C42—142no—
537C2×C42—281no—
538C2×C42—281no—
539C2×C42—281no—
540C2×C42—281no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—41no—
545#95—74no—
546#95—142no—
547#95—142no—
548#95—142no—
549#95—142no—
550#95—142no—
551#95—142no—
552#95—142no—
553#95—142no—
554#95—142no—
555#95—142no—
556#95—142no—
557#95—142no—
558#95C4×D714yes—
559C22×C7C2×#11711yescharacteristic
560C22×C7C2×C4×D411yescharacteristic
561C22×C7C2×C4×D411yescharacteristic
562C22×C7C4×#4111yescharacteristic
563C22×C7C4×#4111yescharacteristic
564C22×C7#52011yescharacteristic
565C22×C7#52011yescharacteristic
566C22×C7C2×#12111yescharacteristic
567C22×C7#52511yescharacteristic
568C22×C7#52911yescharacteristic
569C22×C7#52911yescharacteristic
570C22×C7#52911yescharacteristic
571C22×C7#53211yescharacteristic
572C22×C7#53211yescharacteristic
573C22×C7#53211yescharacteristic
574C22×C7#53411yescharacteristic
575C22×C7#53611yescharacteristic
576C22×C7#53911yescharacteristic
577C22×C7#53911yescharacteristic
578C22×C7#54611yescharacteristic
579C22×C7#54611yescharacteristic
580C22×C7#54811yescharacteristic
581C22×C7#54811yescharacteristic
582C22×C7#55111yescharacteristic
583C22×C7#55211yescharacteristic
584C22×C7#55211yescharacteristic
585C22×C7#55311yescharacteristic
586C22×C7#55311yescharacteristic
587C22×C7#55311yescharacteristic
588C22×C7#55311yescharacteristic
589C22×C7#55611yescharacteristic
590C22×C7#55611yescharacteristic
591C22×C7#55611yescharacteristic
592C22×C7#55611yescharacteristic
593C22×C7#55911yescharacteristic
594C2×D7—42no—
595C2×D7—42no—
596C2×D7—42no—
597C2×D7—42no—
598C2×D7—42no—
599C2×D7—42no—
600C2×D7—42no—
601C2×D7—81no—
602C2×D7—81no—
603C2×D7—81no—
604C2×D7—81no—
605C2×D7—81no—
606C2×D7—81no—
607C2×D7—81no—
608C2×D7—81no—
609C4×C7—24no—
610C4×C7—24no—
611C4×C7—42no—
612C4×C7—42no—
613C4×C7—42no—
614C4×C7—81no—
615C4×C7—81no—
616Dic7—24no—
617Dic7—24no—
618Dic7—42no—
619Dic7—42no—
620Dic7—42no—
621Dic7—42no—
622Dic7—42no—
623C24—72no—
624C24—141no—
625C24—141no—
626C24—141no—
627C24—141no—
628C24—141no—
629C24—141no—
630C24—141no—
631C24—141no—
632C24—141no—
633C24—141no—
634C24—141no—
635C24—141no—
636C24—141no—
637C24—141no—
638C24C23×D711yescharacteristic
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—72no—
680C22×C4—72no—
681C22×C4—72no—
682C22×C4—72no—
683C22×C4—72no—
684C22×C4—72no—
685C22×C4—72no—
686C22×C4—72no—
687C22×C4—72no—
688C22×C4—72no—
689C22×C4—72no—
690C22×C4—141no—
691C22×C4—141no—
692C22×C4—141no—
693C22×C4—141no—
694C22×C4—141no—
695C22×C4—141no—
696C22×C4—141no—
697C22×C4—141no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—141no—
724C22×C4—141no—
725C22×C4—141no—
726C22×C4—141no—
727C22×C4—141no—
728C22×C4C2×C4×D712yes—
729C22×C4C2×C4×D712yes—
730C22×C4C2×C4×D712yes—
731C22×C4#115712yes—
732C22×C4#115712yes—
733C22×C4D4×D712yes—
734C22×C4D4×D712yes—
735C22×C4#116112yes—
736C22×C4#116112yes—
737C4⋊C4—44no—
738C4⋊C4—148no—
739C4⋊C4—148no—
740C4⋊C4—148no—
741C4⋊C4—284no—
742C22⋊C4—148no—
743C22⋊C4—148no—
744C22⋊C4—148no—
745C22⋊C4—284no—
746C22⋊C4—284no—
747C22⋊C4—284no—
748C22⋊C4—284no—
749C42—44no—
750C42—148no—
751C42—284no—
752C42—284no—
753C42—284no—
754C2×C7#229311yescharacteristic
755C2×C7C4×#12111yescharacteristic
756C2×C7#232211yescharacteristic
757C2×C7#234711yescharacteristic
758C2×C7#235211yescharacteristic
759C2×C7#236711yescharacteristic
760C2×C7#237311yescharacteristic
761C2×C7#254311yescharacteristic
762C2×C7#254511yescharacteristic
763C2×C7#255811yescharacteristic
764C2×C7#256011yescharacteristic
765C2×C7#259411yescharacteristic
766C2×C7#259611yescharacteristic
767C2×C7#260211yescharacteristic
768C2×C7#260411yescharacteristic
769D7—82no—
770C23—142no—
771C23—142no—
772C23—142no—
773C23—142no—
774C23—142no—
775C23—142no—
776C23—142no—
777C23—281no—
778C23—281no—
779C23—281no—
780C23—281no—
781C23—281no—
782C23—281no—
783C23—281no—
784C23—281no—
785C23—281no—
786C23—281no—
787C23—281no—
788C23—281no—
789C23—281no—
790C23—281no—
791C23—281no—
792C23—281no—
793C23—281no—
794C23—281no—
795C23—281no—
796C23—281no—
797C23—281no—
798C23—281no—
799C23—281no—
800C23—281no—
801C23—281no—
802C23—281no—
803C23—281no—
804C23—281no—
805C23C22×C4×D711yescharacteristic
806C23C2×#115711yescharacteristic
807C23C2×#115711yescharacteristic
808C23C2×D4×D711yescharacteristic
809C23C2×D4×D711yescharacteristic
810C23#654811yescharacteristic
811C23#654811yescharacteristic
812C23C2×#116111yescharacteristic
813C23C2×#116111yescharacteristic
814C23D7×#4111yescharacteristic
815C23D7×#4111yescharacteristic
816C23D7×#4111yescharacteristic
817C23D7×#4111yescharacteristic
818C23#655411yescharacteristic
819C23#655411yescharacteristic
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—74no—
868C2×C4—74no—
869C2×C4—142no—
870C2×C4—142no—
871C2×C4—142no—
872C2×C4—142no—
873C2×C4—142no—
874C2×C4—142no—
875C2×C4—142no—
876C2×C4—142no—
877C2×C4—142no—
878C2×C4—142no—
879C2×C4—142no—
880C2×C4—142no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—142no—
885C2×C4—142no—
886C2×C4—142no—
887C2×C4—142no—
888C2×C4—142no—
889C2×C4—142no—
890C2×C4—142no—
891C2×C4—142no—
892C2×C4—142no—
893C2×C4—142no—
894C2×C4—142no—
895C2×C4—142no—
896C2×C4—281no—
897C2×C4—281no—
898C2×C4—281no—
899C2×C4—281no—
900C2×C4—281no—
901C2×C4—281no—
902C2×C4—281no—
903C2×C4—281no—
904C2×C4—281no—
905C2×C4—281no—
906C2×C4—281no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4—281no—
912C2×C4—281no—
913C2×C4—281no—
914C2×C4—281no—
915C2×C4—281no—
916C2×C4#643514yes—
917C2×C4#645614yes—
918C7#1407711yescharacteristic, complemented, Sylow
919C22—282no—
920C22—282no—
921C22—282no—
922C22—282no—
923C22—282no—
924C22—282no—
925C22—282no—
926C22—561no—
927C22—561no—
928C22—561no—
929C22—561no—
930C22—561no—
931C22—561no—
932C22—561no—
933C22—561no—
934C22C2×#643511yescharacteristic
935C22#9018111yescharacteristic
936C22C2×#645611yescharacteristic
937C22#9020511yescharacteristic
938C22#9021311yescharacteristic
939C22#9022211yescharacteristic
940C22#9022411yescharacteristic
941C22#9023111yescharacteristic
942C22C4×D4×D711yescharacteristic
943C22#9023711yescharacteristic
944C22#9023711yescharacteristic
945C22#9023911yescharacteristic
946C22#9023911yescharacteristic
947C22#9024311yescharacteristic
948C22#9024911yescharacteristic
949C22C4×#116111yescharacteristic
950C22#9027111yescharacteristic
951C22#9027111yescharacteristic
952C22#9027511yescharacteristic
953C22#9028011yescharacteristic
954C22D7×#12111yescharacteristic
955C22#9030111yescharacteristic
956C22#9031811yescharacteristic
957C22#9032811yescharacteristic
958C22#9033611yescharacteristic
959C22#9033611yescharacteristic
960C22#9033911yescharacteristic
961C22#9035211yescharacteristic
962C22#9035511yescharacteristic
963C22#9036811yescharacteristic
964C22#9038211yescharacteristic
965C22#9038511yescharacteristic
966C22#9039311yescharacteristic
967C22#9039311yescharacteristic
968C22#9041611yescharacteristic
969C4—24no—
970C4—24no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—81no—
975C4—81no—
976C4—144no—
977C4—144no—
978C4—282no—
979C4—282no—
980C4—282no—
981C4—282no—
982C4—282no—
983C2—562no—
984C2#1173090611yescharacteristic
985C2#1173106211yescharacteristic
986C2#1173107911yescharacteristic
987C2#1173182911yescharacteristic
988C2#1173206311yescharacteristic
989C2#1173234711yescharacteristic
990C2#1173241711yescharacteristic
991C2#1173256211yescharacteristic
992C2#1173256711yescharacteristic
993C2#1173257111yescharacteristic
994C2#1173292611yescharacteristic
995C2#1173303811yescharacteristic
996C2#1173340911yescharacteristic
997C2#1173351411yescharacteristic
998C2#1173398511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1436C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1436D7
hypocenterC7#14077
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C2×#89745C2semidirect
2. C2×C4×Dic7⋊C4C2semidirect
6. C7×#1436C2semidirect
10. #11727171C2semidirect
11. #11727165C2semidirect
13. #11727160C2semidirect
14. #11727156C2semidirect
15. Dic7×#95C2semidirect
53. #89442C4semidirect
153. #1436D7semidirect
918. C7#14077semidirect

Maximal subgroups

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

subgroupindex
C2×#897452
C2×C4×Dic7⋊C42
C2×#894422
C2×#894412
C7×#14362
#117293242
#117292912
#117271822
#117271712
#117271652
#117271622
#117271602
#117271562
Dic7×#952
#140777