Finite Group Databasebeta

← #13276038

Subgroups — #13276038

Order 1792.

2574 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C2×C7×#380C211yesmaximal, characteristic, complemented
3C2×#89984C211yesmaximal, characteristic, complemented
4C2×#89759C211yesmaximal, characteristic, complemented
5C2×#89759C211yesmaximal, characteristic, complemented
6C2×#89748C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
8C2×#89729C212yesmaximal
9#11729301C212yesmaximal, complemented
10#11727182C212yesmaximal, complemented
11Dic7⋊#95C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2211yescharacteristic
14C23×C4×D7C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2212yes—
18C22×C22⋊Dic7C2212yes—
19C22×C22⋊Dic7C2211yescharacteristic
20C2×C4×C22⋊D7—24no—
21C2×C4×C22⋊D7—24no—
22C2×C4×C22⋊D7C418yescomplemented
23C22×(C2×D7)⋊C4C2212yes—
24C22×(C2×D7)⋊C4C2212yes—
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×Dic7⋊C4C2212yes—
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2212yes—
31C22×C4×Dic7C2212yes—
32C22×C4×Dic7C2211yescharacteristic
33C7×#380—24no—
34C2×C7×#95C2212yes—
35#89984—24no—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40#89759—24no—
41#89759—24no—
42#89748—24no—
43C4⋊C4×Dic7—24no—
44#89729—28no—
45#13906—71nomaximal, Sylow
46C25×C7C2311yescharacteristic
47C24×D7C2311yescharacteristic
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—22no—
51C23×C4×C7—22no—
52C23×C4×C7—22no—
53C23×C4×C7—22no—
54C23×C4×C7C2×C414yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2312yes—
58C23×C4×C7C2311yescharacteristic
59C22×C22⋊D7—22no—
60C22×C22⋊D7—22no—
61C22×C22⋊D7—22no—
62C22×C22⋊D7—22no—
63C22×C22⋊D7C2×C414yes—
64C22×C22⋊D7D414yes—
65C22×C22⋊D7Q814yes—
66C23×Dic7C2312yes—
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2312yes—
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C22×C4×D7—22no—
72C22×C4×D7—22no—
73C22×C4×D7—22no—
74C22×C4×D7—22no—
75C22×C4×D7—22no—
76C22×C4×D7—22no—
77C22×C4×D7C2×C414yes—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4D414yescomplemented
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—42no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—24no—
90C2×C22⋊Dic7—24no—
91C2×C22⋊Dic7—42no—
92C2×C22⋊Dic7C2×C414yes—
93C4×C22⋊D7—232no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—22no—
96C2×(C2×D7)⋊C4—24no—
97C2×(C2×D7)⋊C4—24no—
98C2×(C2×D7)⋊C4—24no—
99C2×(C2×D7)⋊C4—24no—
100C2×(C2×D7)⋊C4—42no—
101C2×(C2×D7)⋊C4—42no—
102C2×(C2×D7)⋊C4C2×C414yes—
103C2×C4⋊Dic7—22no—
104C2×C4⋊Dic7—22no—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—22no—
107C2×C4⋊Dic7—22no—
108C2×C4⋊Dic7D414yescomplemented
109C2×Dic7⋊C4—22no—
110C2×Dic7⋊C4—22no—
111C2×Dic7⋊C4—24no—
112C2×Dic7⋊C4—24no—
113C2×Dic7⋊C4—24no—
114C2×Dic7⋊C4—24no—
115C2×Dic7⋊C4—42no—
116C2×Dic7⋊C4—42no—
117C2×Dic7⋊C4C2×C414yes—
118C2×C4×Dic7—24no—
119C2×C4×Dic7—24no—
120C2×C4×Dic7—24no—
121C2×C4×Dic7C2×C414yes—
122C2×C4×Dic7D414yes—
123C2×C4×Dic7D414yes—
124C7×#95—24no—
125C7⋊#95—24no—
126C7⋊#95—24no—
127C7⋊#95—24no—
128C7⋊#95—24no—
129C22×C4×D4—71no—
130C2×#390—72no—
131C2×#384—71no—
132C2×#380—71no—
133C2×#380—71no—
134C2×#380—71no—
135C2×#380D711yescharacteristic, complemented
136C2×C4×C4⋊C4—71no—
137#1439—72no—
138#1439—72no—
139C4⋊#95—72no—
140C24×C7—21no—
141C24×C7—21no—
142C24×C7—21no—
143C24×C7—21no—
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—21no—
148C24×C7—21no—
149C24×C7—21no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7C22×C412yes—
153C24×C7C2×D412yes—
154C24×C7C2×Q812yes—
155C24×C7C2411yescharacteristic
156C23×D7—21no—
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×D7C22×C412yes—
169C23×D7C2×D412yes—
170C23×D7C2×Q812yes—
171C22×C4×C7—21no—
172C22×C4×C7—22no—
173C22×C4×C7—21no—
174C22×C4×C7—22no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—28no—
184C22×C4×C7—28no—
185C22×C4×C7—28no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—44no—
194C22×C4×C7—44no—
195C22×C4×C7—44no—
196C22×C4×C7—44no—
197C22×C4×C7C22×C412yes—
198C22×C4×C7C22×C412yes—
199C22×C4×C7C2×D414yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D412yes—
203C22×C4×C7C2×D412yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
206C2×C22⋊D7—28no—
207C2×C22⋊D7—28no—
208C2×C22⋊D7—28no—
209C2×C22⋊D7—28no—
210C2×C22⋊D7—28no—
211C2×C22⋊D7—28no—
212C2×C22⋊D7C4⋊C4116yescomplemented
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7C22×C412yes—
237C22×Dic7C22×C412yes—
238C22×Dic7C22×C412yes—
239C22×Dic7C2×D414yes—
240C22×Dic7C2×D412yes—
241C22×Dic7C2×D412yes—
242C22×Dic7C2×D412yes—
243C22×Dic7C2×D412yes—
244C22×Dic7C2×D412yes—
245C22×Dic7C2×Q812yes—
246C22×Dic7#4112yes—
247C22×Dic7#4112yes—
248C2×C4×D7—28no—
249C2×C4×D7—28no—
250C2×C4×D7—28no—
251C2×C4×D7—44no—
252C2×C4×D7—44no—
253C2×C4×D7—44no—
254C2×C4×D7—44no—
255C7×C4⋊C4—28no—
256C7×C4⋊C4—44no—
257C7×C22⋊C4—48no—
258C22⋊Dic7—28no—
259C22⋊Dic7—48no—
260(C2×D7)⋊C4—28no—
261(C2×D7)⋊C4—48no—
262(C2×D7)⋊C4—48no—
263C4⋊Dic7—28no—
264C4⋊Dic7—44no—
265Dic7⋊C4—28no—
266Dic7⋊C4—48no—
267Dic7⋊C4—48no—
268C4×Dic7—48no—
269C4×Dic7C22⋊C4116yescomplemented
270C23×D4—71no—
271C24×C4—71no—
272C24×C4C2×D711yescharacteristic
273C2×C4×D4—78no—
274C2×C4×D4—144no—
275C2×C4×D4—144no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—72no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—72no—
281C22×C4⋊C4C2×D711yescharacteristic
282C22×C4⋊C4C2×D711yescharacteristic
283C22×C22⋊C4—71no—
284C22×C22⋊C4—71no—
285C22×C22⋊C4—72no—
286C22×C22⋊C4—72no—
287C22×C22⋊C4—72no—
288C22×C22⋊C4C2×D712yes—
289C22×C42—71no—
290C22×C42—72no—
291#390—148no—
292#384—144no—
293#380—24no—
294#380—144no—
295#380—144no—
296#380—144no—
297C4×C4⋊C4—144no—
298C2×#95—72no—
299C2×#95—72no—
300C2×#95—72no—
301C2×#95—72no—
302C2×#95C2×D712yes—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—22no—
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—41no—
331C23×C7—41no—
332C23×C7—41no—
333C23×C7—41no—
334C23×C7—41no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7C2×C4⋊C414yes—
338C23×C7C23×C411yescharacteristic
339C23×C7C22×D411yescharacteristic
340C23×C7C22×D411yescharacteristic
341C23×C7C22×D411yescharacteristic
342C23×C7C22×D411yescharacteristic
343C23×C7C22×D411yescharacteristic
344C23×C7C22×Q811yescharacteristic
345C23×C7C2×#4111yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7C2×#4111yescharacteristic
349C23×C7H(5,𝔽2)11yescharacteristic
350C23×C7H(5,𝔽2)11yescharacteristic
351C23×C72−1+411yescharacteristic
352C23×C72−1+411yescharacteristic
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—41no—
372C22×D7—41no—
373C22×D7—41no—
374C22×D7—41no—
375C22×D7—41no—
376C22×D7—41no—
377C22×D7—41no—
378C22×D7—41no—
379C22×D7—41no—
380C22×D7—41no—
381C22×D7—41no—
382C22×D7—41no—
383C22×D7—41no—
384C22×D7—41no—
385C22×D7—41no—
386C22×D7—41no—
387C22×D7C2×C4⋊C414yes—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—24no—
392C2×C4×C7—24no—
393C2×C4×C7—24no—
394C2×C4×C7—42no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—42no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7—416no—
403C2×C4×C7—42no—
404C2×C4×C7—42no—
405C2×C4×C7—42no—
406C2×C4×C7—42no—
407C2×C4×C7—42no—
408C2×C4×C7—42no—
409C2×C4×C7—42no—
410C2×C4×C7C2×C22⋊C414yes—
411C2×C4×C7C4×D414yes—
412C2×C4×C7C4×D414yes—
413C2×C4×C7#12114yes—
414C2×C4×C7#12114yes—
415C2×C4×C7#12414yes—
416C2×C4×C7#12714yes—
417C22⋊D7—232no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—24no—
428C2×Dic7—24no—
429C2×Dic7—24no—
430C2×Dic7—42no—
431C2×Dic7—41no—
432C2×Dic7—41no—
433C2×Dic7—41no—
434C2×Dic7—41no—
435C2×Dic7—42no—
436C2×Dic7—42no—
437C2×Dic7—42no—
438C2×Dic7—42no—
439C2×Dic7—42no—
440C2×Dic7—42no—
441C2×Dic7—42no—
442C2×Dic7—42no—
443C2×Dic7—42no—
444C2×Dic7—42no—
445C2×Dic7C2×C22⋊C414yes—
446C2×Dic7C2×C22⋊C414yes—
447C2×Dic7C2×C4⋊C414yes—
448C2×Dic7#11714yes—
449C2×Dic7#12114yes—
450C2×Dic7#12114yes—
451C2×Dic7C22⋊Q814yes—
452C2×Dic7C22⋊Q814yes—
453C4×D7—416no—
454C25—71no—
455C25C22×D711yescharacteristic
456C22×D4—74no—
457C22×D4—74no—
458C22×D4—74no—
459C22×D4—142no—
460C22×D4—142no—
461C22×D4—142no—
462C22×D4—142no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—72no—
472C23×C4—71no—
473C23×C4—74no—
474C23×C4—72no—
475C23×C4—142no—
476C23×C4—142no—
477C23×C4—142no—
478C23×C4—142no—
479C23×C4—142no—
480C23×C4—142no—
481C23×C4C4×D714yes—
482C23×C4C22×D712yes—
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D712yes—
485C23×C4C22×D711yescharacteristic
486C4×D4—1432no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—74no—
493C2×C4⋊C4—74no—
494C2×C4⋊C4—142no—
495C2×C4⋊C4—142no—
496C2×C4⋊C4—142no—
497C2×C4⋊C4—142no—
498C2×C4⋊C4—144no—
499C2×C4⋊C4—144no—
500C2×C4⋊C4—144no—
501C2×C4⋊C4—144no—
502C2×C4⋊C4—142no—
503C2×C4⋊C4—142no—
504C2×C4⋊C4—142no—
505C2×C4⋊C4—282no—
506C2×C4⋊C4—282no—
507C2×C4⋊C4C22⋊D714yescomplemented
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—74no—
512C2×C22⋊C4—74no—
513C2×C22⋊C4—142no—
514C2×C22⋊C4—142no—
515C2×C22⋊C4—142no—
516C2×C22⋊C4—142no—
517C2×C22⋊C4—144no—
518C2×C22⋊C4—144no—
519C2×C22⋊C4—144no—
520C2×C22⋊C4—144no—
521C2×C22⋊C4—144no—
522C2×C22⋊C4—144no—
523C2×C22⋊C4—282no—
524C2×C22⋊C4—282no—
525C2×C22⋊C4—282no—
526C2×C42—74no—
527C2×C42—74no—
528C2×C42—74no—
529C2×C42—144no—
530C2×C42—144no—
531C2×C42—144no—
532#95—24no—
533#95—144no—
534#95—144no—
535#95—144no—
536#95—144no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—24no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7C22×C22⋊C411yescharacteristic
553C22×C7C22×C4⋊C411yescharacteristic
554C22×C7C2×#11711yescharacteristic
555C22×C7C2×C4×D411yescharacteristic
556C22×C7C2×C4×D411yescharacteristic
557C22×C7#52011yescharacteristic
558C22×C7#52011yescharacteristic
559C22×C7C2×#12111yescharacteristic
560C22×C7C2×#12111yescharacteristic
561C22×C7C2×#12111yescharacteristic
562C22×C7C2×#12111yescharacteristic
563C22×C7C2×C22⋊Q811yescharacteristic
564C22×C7C2×C22⋊Q811yescharacteristic
565C22×C7C2×#12411yescharacteristic
566C22×C7C2×#12711yescharacteristic
567C22×C7#53511yescharacteristic
568C22×C7#53611yescharacteristic
569C22×C7#53711yescharacteristic
570C22×C7#53711yescharacteristic
571C22×C7D4211yescharacteristic
572C22×C7D4211yescharacteristic
573C22×C7#54711yescharacteristic
574C22×C7#54711yescharacteristic
575C22×C7#54711yescharacteristic
576C22×C7#54711yescharacteristic
577C22×C7D4×Q811yescharacteristic
578C22×C7D4×Q811yescharacteristic
579C22×C7#55011yescharacteristic
580C22×C7#55011yescharacteristic
581C22×C7#55411yescharacteristic
582C22×C7#55411yescharacteristic
583C22×C7#55511yescharacteristic
584C22×C7#55511yescharacteristic
585C22×C7#55611yescharacteristic
586C22×C7#55611yescharacteristic
587C2×D7—24no—
588C2×D7—24no—
589C2×D7—24no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—42no—
594C2×D7—42no—
595C2×D7—42no—
596C2×D7—42no—
597C2×D7—42no—
598C2×D7—42no—
599C2×D7—42no—
600C2×D7—42no—
601C2×D7—42no—
602C4×C7—44no—
603C4×C7—42no—
604C4×C7—82no—
605C4×C7#39018yescomplemented
606Dic7—24no—
607Dic7—44no—
608Dic7—42no—
609Dic7—82no—
610Dic7#38018yescomplemented
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—72no—
624C24—72no—
625C24—72no—
626C24—141no—
627C24—141no—
628C24—141no—
629C24—141no—
630C24—141no—
631C24—141no—
632C24—141no—
633C24—141no—
634C24—141no—
635C24—141no—
636C24—141no—
637C24—141no—
638C24C2×C4×D712yes—
639C24D4×D712yes—
640C24Q8×D712yes—
641C24C23×D711yescharacteristic
642C2×D4—716no—
643C2×D4—148no—
644C2×D4—148no—
645C2×D4—148no—
646C2×D4—148no—
647C2×D4—148no—
648C2×D4—148no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—28no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—72no—
676C22×C4—72no—
677C22×C4—72no—
678C22×C4—72no—
679C22×C4—72no—
680C22×C4—72no—
681C22×C4—72no—
682C22×C4—72no—
683C22×C4—72no—
684C22×C4—72no—
685C22×C4—72no—
686C22×C4—74no—
687C22×C4—141no—
688C22×C4—141no—
689C22×C4—141no—
690C22×C4—141no—
691C22×C4—142no—
692C22×C4—141no—
693C22×C4—141no—
694C22×C4—142no—
695C22×C4—142no—
696C22×C4—141no—
697C22×C4—141no—
698C22×C4—141no—
699C22×C4—142no—
700C22×C4—142no—
701C22×C4—142no—
702C22×C4—141no—
703C22×C4—148no—
704C22×C4—148no—
705C22×C4—148no—
706C22×C4—142no—
707C22×C4—142no—
708C22×C4—142no—
709C22×C4—142no—
710C22×C4—142no—
711C22×C4—142no—
712C22×C4—142no—
713C22×C4—284no—
714C22×C4—284no—
715C22×C4—284no—
716C22×C4—284no—
717C22×C4C2×C4×D712yes—
718C22×C4C2×C4×D712yes—
719C22×C4#115712yes—
720C22×C4D4×D712yes—
721C22×C4D4×D712yes—
722C22×C4D4×D712yes—
723C22×C4#115912yes—
724C22×C4C2×C22⋊D714yes—
725C22×C4C2×C22⋊D712yes—
726C4⋊C4—28no—
727C4⋊C4—44no—
728C4⋊C4—148no—
729C4⋊C4—148no—
730C4⋊C4—288no—
731C4⋊C4—288no—
732C4⋊C4—284no—
733C22⋊C4—48no—
734C22⋊C4—148no—
735C22⋊C4—148no—
736C22⋊C4—288no—
737C22⋊C4—288no—
738C22⋊C4—288no—
739C42—716no—
740C42—288no—
741C2×C7—44no—
742C2×C7C2×#38011yescharacteristic
743C2×C7C2×#39011yescharacteristic
744C2×C7#231111yescharacteristic
745C2×C7D4×C4⋊C411yescharacteristic
746C2×C7D4×C4⋊C411yescharacteristic
747C2×C7#235411yescharacteristic
748C2×C7#235411yescharacteristic
749C2×C7#253711yescharacteristic
750C2×C7#253711yescharacteristic
751C2×C7#253811yescharacteristic
752C2×C7#253811yescharacteristic
753C2×C7#254111yescharacteristic
754C2×C7#254211yescharacteristic
755C2×C7#254711yescharacteristic
756C2×C7#256311yescharacteristic
757D7—44no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—74no—
793C23—142no—
794C23—142no—
795C23—142no—
796C23—142no—
797C23—142no—
798C23—142no—
799C23—142no—
800C23—142no—
801C23—142no—
802C23—142no—
803C23—142no—
804C23—142no—
805C23—142no—
806C23—142no—
807C23—142no—
808C23—142no—
809C23—142no—
810C23—142no—
811C23—281no—
812C23—281no—
813C23—281no—
814C23—281no—
815C23—281no—
816C23—281no—
817C23—281no—
818C23—281no—
819C23—281no—
820C23—281no—
821C23—281no—
822C23—281no—
823C23—281no—
824C23—281no—
825C23—281no—
826C23—281no—
827C23D7×C4⋊C414yes—
828C23C22×C4×D711yescharacteristic
829C23C2×#115711yescharacteristic
830C23C2×D4×D711yescharacteristic
831C23C2×D4×D711yescharacteristic
832C23C2×D4×D711yescharacteristic
833C23C2×D4×D711yescharacteristic
834C23C2×#115911yescharacteristic
835C23#654811yescharacteristic
836C23C2×Q8×D711yescharacteristic
837C23#655111yescharacteristic
838C23D7×#4111yescharacteristic
839C23D7×#4111yescharacteristic
840C23#655311yescharacteristic
841C23#655411yescharacteristic
842C23C22×C22⋊D711yescharacteristic
843D4—1432no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—416no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—74no—
867C2×C4—74no—
868C2×C4—74no—
869C2×C4—74no—
870C2×C4—74no—
871C2×C4—74no—
872C2×C4—74no—
873C2×C4—74no—
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—144no—
883C2×C4—142no—
884C2×C4—144no—
885C2×C4—144no—
886C2×C4—281no—
887C2×C4—281no—
888C2×C4—282no—
889C2×C4—282no—
890C2×C4—281no—
891C2×C4—281no—
892C2×C4—282no—
893C2×C4—282no—
894C2×C4—2816no—
895C2×C4—282no—
896C2×C4—282no—
897C2×C4—282no—
898C2×C4—282no—
899C2×C4—282no—
900C2×C4—282no—
901C2×C4—282no—
902C2×C4D7×C22⋊C414yes—
903C2×C4(C22⋊D7)⋊C414yes—
904C2×C4#644714yes—
905C2×C4#644814yes—
906C2×C4C4×C22⋊D714yes—
907C2×C4#650214yes—
908C2×C4#650314yes—
909C7#1390611yescharacteristic, complemented, Sylow
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—144no—
926C22—144no—
927C22—144no—
928C22—282no—
929C22—282no—
930C22—282no—
931C22—282no—
932C22—282no—
933C22—282no—
934C22—282no—
935C22—282no—
936C22—282no—
937C22—282no—
938C22—282no—
939C22—282no—
940C22C2×D7×C22⋊C411yescharacteristic
941C22C2×(C22⋊D7)⋊C411yescharacteristic
942C22C2×#644711yescharacteristic
943C22C2×#644811yescharacteristic
944C22C2×D7×C4⋊C411yescharacteristic
945C22#9019511yescharacteristic
946C22#9019811yescharacteristic
947C22#9020211yescharacteristic
948C22D7×#11711yescharacteristic
949C22#9021411yescharacteristic
950C22#9022311yescharacteristic
951C22#9022411yescharacteristic
952C22#9029011yescharacteristic
953C22D7×#12111yescharacteristic
954C22D7×#12111yescharacteristic
955C22#9029811yescharacteristic
956C22#9029911yescharacteristic
957C22#9030011yescharacteristic
958C22#9030211yescharacteristic
959C22#9030711yescharacteristic
960C22D7×C22⋊Q811yescharacteristic
961C22D7×C22⋊Q811yescharacteristic
962C22#9031911yescharacteristic
963C22#9032011yescharacteristic
964C22#9032211yescharacteristic
965C22#9032311yescharacteristic
966C22#9032611yescharacteristic
967C22#9033211yescharacteristic
968C22C2×C4×C22⋊D711yescharacteristic
969C22D4×C22⋊D711yescharacteristic
970C22C2×#650211yescharacteristic
971C22C2×#650311yescharacteristic
972C22Q8×C22⋊D711yescharacteristic
973C22#9051511yescharacteristic
974C22#9052511yescharacteristic
975C4—42no—
976C4—44no—
977C4—78no—
978C4—82no—
979C4—144no—
980C4—282no—
981C4—284no—
982C4—562no—
983C4#8972918yescomplemented
984C2—44no—
985C2—284no—
986C2#1173133011yescharacteristic
987C2#1173138011yescharacteristic
988C2#1173138111yescharacteristic
989C2#1173138211yescharacteristic
990C2#1173138711yescharacteristic
991C2D7×#38011yescharacteristic
992C2#1173144811yescharacteristic
993C2#1173145511yescharacteristic
994C2C2×#8972911yescharacteristic
995C2C4⋊C4×C22⋊D711yescharacteristic
996C2#1173968611yescharacteristic
997C2#1174011211yescharacteristic
998C2#1174011411yescharacteristic
999C2#1174022311yescharacteristic
1000C2#1174022511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#380C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#380D7
hypocenterC7#13906
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×C7×#380C2semidirect
3. C2×#89984C2semidirect
4. C2×#89759C2semidirect
5. C2×#89759C2semidirect
6. C2×#89748C2semidirect
7. C2×C4⋊C4×Dic7C2semidirect
9. #11729301C2semidirect
10. #11727182C2semidirect
11. Dic7⋊#95C2semidirect
22. C2×C4×C22⋊D7C4semidirect
83. C2×C7×C4⋊C4D4semidirect
108. C2×C4⋊Dic7D4semidirect
135. C2×#380D7semidirect
212. C2×C22⋊D7C4⋊C4semidirect
269. C4×Dic7C22⋊C4semidirect
507. C2×C4⋊C4C22⋊D7semidirect
605. C4×C7#390semidirect
610. Dic7#380semidirect
909. C7#13906semidirect
983. C4#89729semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C2×C7×#3802
C2×#899842
C2×#897592
C2×#897482
C2×C4⋊C4×Dic72
C2×#897292
#117293012
#117271822
Dic7⋊#952
#139067