Finite Group Databasebeta

← #13275367

Subgroups — #13275367

Order 1792.

1778 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89744C211yesmaximal, characteristic
2C2×C4⋊C4×Dic7C211yesmaximal, characteristic
3C2×C4×Dic7⋊C4C211yesmaximal, characteristic
4C2×C4×Dic7⋊C4C211yesmaximal, characteristic
5C2×#89419C211yesmaximal, characteristic
6C2×#89421C211yesmaximal, characteristic
7C2×#89421C211yesmaximal, characteristic
8C7×#1436C211yesmaximal, characteristic
9#11727161C211yesmaximal, characteristic
10#11727160C211yesmaximal, characteristic
11#11727159C211yesmaximal, characteristic
12Dic7⋊#95C211yesmaximal, characteristic
13#11727157C211yesmaximal, characteristic
14#11727155C211yesmaximal, characteristic
15Dic7×#95C211yesmaximal, characteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C22×C4⋊Dic7C2211yescharacteristic
19C22×Dic7⋊C4C2211yescharacteristic
20C22×Dic7⋊C4C2211yescharacteristic
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
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
51C4⋊C4×Dic7—24no—
52#89744C418yescomplemented
53C4×Dic7⋊C4—24no—
54C4×Dic7⋊C4—24no—
55#89421—24no—
56#89421C418yescomplemented
57#89419C418yescomplemented
58#13821—71nomaximal, Sylow
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4C2×C414yes—
77C2×C42×C7—22no—
78C2×C42×C7—22no—
79C2×C42×C7—41no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7C2×C414yes—
83C2×Dic7⋊C4—22no—
84C2×Dic7⋊C4—22no—
85C2×Dic7⋊C4—22no—
86C2×Dic7⋊C4—22no—
87C2×Dic7⋊C4—22no—
88C2×Dic7⋊C4—22no—
89C2×Dic7⋊C4—22no—
90C2×Dic7⋊C4—22no—
91C2×Dic7⋊C4C2×C414yes—
92C2×Dic7⋊C4C2×C414yes—
93C2×Dic7⋊C4C2×C414yes—
94C2×Dic7⋊C4C2×C414yes—
95C2×Dic7⋊C4C2×C414yes—
96C2×Dic7⋊C4C2×C414yes—
97C2×Dic7⋊C4C2×C414yes—
98C2×Dic7⋊C4C2×C414yes—
99C2×Dic7⋊C4D414yes—
100C2×Dic7⋊C4Q814yes—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—22no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—22no—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—22no—
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×Dic7C2×C414yes—
121C2×C4×Dic7C2×C414yes—
122C2×C4×Dic7C2×C414yes—
123C2×C4×Dic7C2×C414yes—
124C2×C4×Dic7C2×C414yes—
125C7×#95—22no—
126C7×#95—22no—
127C7×#95—41no—
128C7×#95C2×C414yes—
129C7×#95C2×C414yes—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—41no—
138C7⋊#95C2×C414yes—
139C7⋊#95C2×C414yes—
140C7⋊#95C2×C414yes—
141C7⋊#95C2×C414yes—
142C7⋊#95D414yes—
143C2×#389—71no—
144C2×#389—71no—
145C2×C4×C4⋊C4—71no—
146C2×C4×C4⋊C4—71no—
147C2×C4×C4⋊C4—71no—
148C2×C4×C4⋊C4—71no—
149C2×C4×C4⋊C4—71no—
150#1436—71no—
151#1436—71no—
152#1436—71no—
153#1436D711yescharacteristic
154C4⋊#95—71no—
155#1434—71no—
156#1434—71no—
157C4×#95—71no—
158C24×C7C2411yescharacteristic
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
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×C7C22×C412yes—
196C22×C4×C7C22×C412yes—
197C22×C4×C7C22×C412yes—
198C22×C4×C7C22×C412yes—
199C22×C4×C7C22×C412yes—
200C22×C4×C7C22×C412yes—
201C22×C4×C7C22×C412yes—
202C22×C4×C7C22×C412yes—
203C22×C4×C7C22×C412yes—
204C22×C4×C7C2×D412yes—
205C22×C4×C7C2×D412yes—
206C22×C4×C7C2×Q812yes—
207C22×C4×C7#4112yes—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
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×Dic7C22×C412yes—
243C22×Dic7C22×C412yes—
244C22×Dic7C22×C412yes—
245C22×Dic7C22×C412yes—
246C22×Dic7C22×C412yes—
247C22×Dic7C22×C412yes—
248C22×Dic7C22×C412yes—
249C22×Dic7C22×C412yes—
250C22×Dic7C22×C412yes—
251C22×Dic7C22×C412yes—
252C22×Dic7C22×C412yes—
253C22×Dic7C22×C412yes—
254C22×Dic7C2×D412yes—
255C22×Dic7C2×D412yes—
256C22×Dic7C2×D412yes—
257C22×Dic7C2×D412yes—
258C22×Dic7C2×Q812yes—
259C22×Dic7C2×Q812yes—
260C22×Dic7#4112yes—
261C22×Dic7#4112yes—
262C22×Dic7#4112yes—
263C22×Dic7#4112yes—
264C7×C4⋊C4—28no—
265C42×C7—44no—
266C4⋊Dic7—28no—
267Dic7⋊C4—28no—
268Dic7⋊C4—28no—
269Dic7⋊C4—28no—
270Dic7⋊C4—28no—
271Dic7⋊C4C42116yescomplemented
272Dic7⋊C4C4⋊C4116yescomplemented
273C4×Dic7—28no—
274C4×Dic7—28no—
275C4×Dic7—28no—
276C4×Dic7—28no—
277C4×Dic7—28no—
278C4×Dic7—44no—
279C4×Dic7—44no—
280C4×Dic7—44no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C4⋊C4—71no—
288C22×C4⋊C4C2×D711yescharacteristic
289C22×C42—71no—
290C22×C42—71no—
291C22×C42—71no—
292C22×C42—71no—
293C22×C42—71no—
294C22×C42—71no—
295C22×C42—71no—
296C22×C42—71no—
297C22×C42C2×D711yescharacteristic
298#389—78no—
299#389—78no—
300C4×C4⋊C4—78no—
301C4×C4⋊C4—144no—
302C4×C4⋊C4—144no—
303C4×C4⋊C4—144no—
304C4×C4⋊C4—144no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
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×#95C2×D711yescharacteristic
319C2×#95C2×D711yescharacteristic
320C2×#95C2×D711yescharacteristic
321C2×#95C2×D711yescharacteristic
322C2×#95C2×D711yescharacteristic
323C23×C7C23×C411yescharacteristic
324C23×C7C23×C411yescharacteristic
325C23×C7C23×C411yescharacteristic
326C23×C7C22×D411yescharacteristic
327C23×C7C22×D411yescharacteristic
328C23×C7C22×Q811yescharacteristic
329C23×C7C2×#4111yescharacteristic
330C23×C7C2×#4111yescharacteristic
331C23×C7C2×#4111yescharacteristic
332C23×C7C2×#4111yescharacteristic
333C23×C7C2×#4111yescharacteristic
334C23×C7H(5,𝔽2)11yescharacteristic
335C23×C72−1+411yescharacteristic
336C23×C72−1+411yescharacteristic
337C23×C72−1+411yescharacteristic
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
383C2×C4×C7—41no—
384C2×C4×C7C2×C4214yes—
385C2×C4×C7C2×C4⋊C414yes—
386C2×C4×C7C4×D414yes—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—41no—
421C2×Dic7—41no—
422C2×Dic7—41no—
423C2×Dic7—41no—
424C2×Dic7—41no—
425C2×Dic7—41no—
426C2×Dic7—41no—
427C2×Dic7—41no—
428C2×Dic7—41no—
429C2×Dic7—41no—
430C2×Dic7—41no—
431C2×Dic7—41no—
432C2×Dic7C2×C4214yes—
433C2×Dic7C2×C4214yes—
434C2×Dic7C2×C4⋊C414yes—
435C2×Dic7C2×C4⋊C414yes—
436C2×Dic7#11714yes—
437C2×Dic7C4×D414yes—
438C2×Dic7C4×D414yes—
439C2×Dic7C4×D414yes—
440C2×Dic7C4×D414yes—
441C2×Dic7C4×Q814yes—
442C2×Dic7C4×Q814yes—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4—71no—
450C23×C4—71no—
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C23×C4C22×D711yescharacteristic
455C23×C4C22×D711yescharacteristic
456C23×C4C22×D711yescharacteristic
457C23×C4C22×D711yescharacteristic
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—74no—
463C2×C4⋊C4—74no—
464C2×C4⋊C4—74no—
465C2×C4⋊C4—74no—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—74no—
468C2×C4⋊C4—74no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—74no—
471C2×C4⋊C4—142no—
472C2×C4⋊C4—142no—
473C2×C4⋊C4—142no—
474C2×C4⋊C4—142no—
475C2×C4⋊C4—142no—
476C2×C4⋊C4—142no—
477C2×C4⋊C4—142no—
478C2×C4⋊C4—142no—
479C2×C4⋊C4—142no—
480C2×C4⋊C4—142no—
481C2×C4⋊C4C4×D714yes—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—41no—
485C2×C42—74no—
486C2×C42—74no—
487C2×C42—74no—
488C2×C42—74no—
489C2×C42—74no—
490C2×C42—142no—
491C2×C42—142no—
492C2×C42—142no—
493C2×C42—142no—
494C2×C42—142no—
495C2×C42—142no—
496C2×C42—142no—
497C2×C42—142no—
498C2×C42—142no—
499C2×C42—142no—
500C2×C42—142no—
501C2×C42—142no—
502C2×C42—142no—
503C2×C42—142no—
504C2×C42—142no—
505C2×C42—142no—
506C2×C42—281no—
507C2×C42—281no—
508C2×C42—281no—
509#95—22no—
510#95—22no—
511#95—41no—
512#95—74no—
513#95—74no—
514#95—74no—
515#95—74no—
516#95—74no—
517#95—142no—
518#95—142no—
519#95—142no—
520#95—142no—
521#95—142no—
522#95—142no—
523#95—142no—
524#95—281no—
525#95C4×D714yes—
526#95C4×D714yes—
527C22×C7C22×C4211yescharacteristic
528C22×C7C22×C4⋊C411yescharacteristic
529C22×C7C2×#11711yescharacteristic
530C22×C7C2×C4×D411yescharacteristic
531C22×C7C2×C4×D411yescharacteristic
532C22×C7C2×C4×D411yescharacteristic
533C22×C7C2×C4×D411yescharacteristic
534C22×C7C2×C4×D411yescharacteristic
535C22×C7C2×C4×Q811yescharacteristic
536C22×C7C2×C4×Q811yescharacteristic
537C22×C7C4×#4111yescharacteristic
538C22×C7C4×#4111yescharacteristic
539C22×C7C4×#4111yescharacteristic
540C22×C7#51911yescharacteristic
541C22×C7#51911yescharacteristic
542C22×C7#51911yescharacteristic
543C22×C7#52011yescharacteristic
544C22×C7#52011yescharacteristic
545C22×C7#52011yescharacteristic
546C22×C7D4211yescharacteristic
547C22×C7#54711yescharacteristic
548C22×C7#54711yescharacteristic
549C22×C7#54711yescharacteristic
550C22×C7#54811yescharacteristic
551C22×C7#54811yescharacteristic
552C22×C7D4×Q811yescharacteristic
553C22×C7#55211yescharacteristic
554C22×C7#55211yescharacteristic
555C22×C7#55311yescharacteristic
556C22×C7#55311yescharacteristic
557C22×C7#55411yescharacteristic
558C22×C7#55611yescharacteristic
559C22×C7#55611yescharacteristic
560C22×C7#55711yescharacteristic
561C22×C7#55711yescharacteristic
562C4×C7—24no—
563C4×C7—24no—
564C4×C7—24no—
565C4×C7—42no—
566C4×C7—42no—
567C4×C7—42no—
568C4×C7—42no—
569Dic7—24no—
570Dic7—24no—
571Dic7—24no—
572Dic7—24no—
573Dic7—42no—
574Dic7—42no—
575Dic7—42no—
576Dic7C4×C4⋊C418yescomplemented
577C24C23×D711yescharacteristic
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—72no—
615C22×C4—72no—
616C22×C4—72no—
617C22×C4—72no—
618C22×C4—72no—
619C22×C4—72no—
620C22×C4—72no—
621C22×C4—72no—
622C22×C4—72no—
623C22×C4—72no—
624C22×C4—72no—
625C22×C4—72no—
626C22×C4—72no—
627C22×C4—72no—
628C22×C4—72no—
629C22×C4—72no—
630C22×C4—72no—
631C22×C4—72no—
632C22×C4—72no—
633C22×C4—72no—
634C22×C4—72no—
635C22×C4—72no—
636C22×C4—141no—
637C22×C4—141no—
638C22×C4—141no—
639C22×C4—141no—
640C22×C4—141no—
641C22×C4—141no—
642C22×C4—141no—
643C22×C4—141no—
644C22×C4—141no—
645C22×C4—141no—
646C22×C4—141no—
647C22×C4—141no—
648C22×C4—141no—
649C22×C4—141no—
650C22×C4—141no—
651C22×C4—141no—
652C22×C4—141no—
653C22×C4—141no—
654C22×C4—141no—
655C22×C4—141no—
656C22×C4—141no—
657C22×C4—141no—
658C22×C4—141no—
659C22×C4—141no—
660C22×C4—141no—
661C22×C4—141no—
662C22×C4—141no—
663C22×C4—141no—
664C22×C4—141no—
665C22×C4—141no—
666C22×C4—141no—
667C22×C4—141no—
668C22×C4—141no—
669C22×C4—141no—
670C22×C4C2×C4×D712yes—
671C22×C4C2×C4×D712yes—
672C22×C4C2×C4×D712yes—
673C22×C4C2×C4×D712yes—
674C22×C4C2×C4×D712yes—
675C22×C4C2×C4×D712yes—
676C22×C4C2×C4×D712yes—
677C22×C4C2×C4×D712yes—
678C22×C4C2×C4×D712yes—
679C22×C4D4×D712yes—
680C22×C4D4×D712yes—
681C22×C4#115912yes—
682C22×C4Q8×D712yes—
683C4⋊C4—28no—
684C4⋊C4—716no—
685C4⋊C4—716no—
686C4⋊C4—148no—
687C4⋊C4—148no—
688C4⋊C4—148no—
689C4⋊C4—148no—
690C4⋊C4—148no—
691C42—44no—
692C42—148no—
693C42—148no—
694C42—148no—
695C42—148no—
696C42—148no—
697C42—284no—
698C42—284no—
699C42—284no—
700C2×C7C2×C4×C4⋊C411yescharacteristic
701C2×C7C42×D411yescharacteristic
702C2×C7#227611yescharacteristic
703C2×C7#234411yescharacteristic
704C2×C7#234711yescharacteristic
705C2×C7D4×C4⋊C411yescharacteristic
706C2×C7#235111yescharacteristic
707C2×C7#236111yescharacteristic
708C2×C7#236111yescharacteristic
709C2×C7#236211yescharacteristic
710C2×C7#236211yescharacteristic
711C2×C7#236511yescharacteristic
712C2×C7#236511yescharacteristic
713C2×C7#237011yescharacteristic
714C2×C7#237011yescharacteristic
715C23C22×C4×D711yescharacteristic
716C23C22×C4×D711yescharacteristic
717C23C22×C4×D711yescharacteristic
718C23C2×D4×D711yescharacteristic
719C23C2×D4×D711yescharacteristic
720C23C2×#115911yescharacteristic
721C23#654811yescharacteristic
722C23C2×Q8×D711yescharacteristic
723C23#655111yescharacteristic
724C23D7×#4111yescharacteristic
725C23D7×#4111yescharacteristic
726C23D7×#4111yescharacteristic
727C23D7×#4111yescharacteristic
728C23#655411yescharacteristic
729C23#655411yescharacteristic
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—74no—
777C2×C4—74no—
778C2×C4—74no—
779C2×C4—74no—
780C2×C4—74no—
781C2×C4—74no—
782C2×C4—74no—
783C2×C4—74no—
784C2×C4—74no—
785C2×C4—74no—
786C2×C4—74no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—142no—
807C2×C4—142no—
808C2×C4—142no—
809C2×C4—142no—
810C2×C4—142no—
811C2×C4—142no—
812C2×C4—142no—
813C2×C4—142no—
814C2×C4—142no—
815C2×C4—142no—
816C2×C4—142no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—281no—
821C2×C4—281no—
822C2×C4—281no—
823C2×C4—281no—
824C2×C4—281no—
825C2×C4—281no—
826C2×C4—281no—
827C2×C4—281no—
828C2×C4—281no—
829C2×C4—281no—
830C2×C4—281no—
831C2×C4—281no—
832C2×C4C42×D714yes—
833C2×C4(C22⋊D7)⋊C414yes—
834C2×C4D7×C4⋊C414yes—
835C7#1382111yescharacteristic, complemented, Sylow
836C22C2×C42×D711yescharacteristic
837C22C2×(C22⋊D7)⋊C411yescharacteristic
838C22C2×D7×C4⋊C411yescharacteristic
839C22#9019511yescharacteristic
840C22#9020711yescharacteristic
841C22D7×#11711yescharacteristic
842C22#9021311yescharacteristic
843C22C4×#115911yescharacteristic
844C22C4×#115911yescharacteristic
845C22C4×D4×D711yescharacteristic
846C22C4×D4×D711yescharacteristic
847C22C4×D4×D711yescharacteristic
848C22C4×D4×D711yescharacteristic
849C22#9023711yescharacteristic
850C22#9023711yescharacteristic
851C22C4×Q8×D711yescharacteristic
852C22C4×Q8×D711yescharacteristic
853C22#9026311yescharacteristic
854C22#9026311yescharacteristic
855C22#9028111yescharacteristic
856C22#9028911yescharacteristic
857C22#9029211yescharacteristic
858C22#9032211yescharacteristic
859C22#9032311yescharacteristic
860C22#9032411yescharacteristic
861C22#9032711yescharacteristic
862C22#9034611yescharacteristic
863C22#9034611yescharacteristic
864C22#9035211yescharacteristic
865C22#9036211yescharacteristic
866C22#9037611yescharacteristic
867C22#9038411yescharacteristic
868C22#9039311yescharacteristic
869C22#9039911yescharacteristic
870C22#9041211yescharacteristic
871C4—24no—
872C4—24no—
873C4—24no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—78no—
879C4—144no—
880C4—144no—
881C4—144no—
882C4—144no—
883C4—282no—
884C4—282no—
885C4—282no—
886C2C4×(C22⋊D7)⋊C411yescharacteristic
887C2#1173106111yescharacteristic
888C2C4×D7×C4⋊C411yescharacteristic
889C2#1173183811yescharacteristic
890C2#1173184211yescharacteristic
891C2#1173212111yescharacteristic
892C2#1173240611yescharacteristic
893C2#1173241111yescharacteristic
894C2#1173241211yescharacteristic
895C2#1173241311yescharacteristic
896C2#1173291911yescharacteristic
897C2#1173292411yescharacteristic
898C2#1173342711yescharacteristic
899C2#1173343511yescharacteristic
900C2#1173393711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC7×#1436C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1436D7
hypocenterC7#13821
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
52. #89744C4semidirect
56. #89421C4semidirect
57. #89419C4semidirect
271. Dic7⋊C4C42semidirect
272. Dic7⋊C4C4⋊C4semidirect
576. Dic7C4×C4⋊C4semidirect
835. C7#13821semidirect

Maximal subgroups

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

subgroupindex
C2×#897442
C2×C4⋊C4×Dic72
C2×C4×Dic7⋊C42
C2×#894192
C2×#894212
C7×#14362
#117271612
#117271602
#117271592
Dic7⋊#952
#117271572
#117271552
Dic7×#952
#138217