Finite Group Databasebeta

← C2×#11740412 #13522893

Subgroups — C2×#11740412 #13522893

Order 1792.

3678 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#124C211yesmaximal, characteristic, complemented
2C22×#6507C211yesmaximal, characteristic, complemented
3C22×#6502C211yesmaximal, characteristic
4C22×#6448C211yesmaximal, characteristic, complemented
5C2×#90003C211yesmaximal, characteristic, complemented
6C2×#89994C211yesmaximal, characteristic, complemented
7#11740412C2116yesmaximal, direct product factor
8C2×#89731C211yesmaximal, characteristic, complemented
9C2×#89719C211yesmaximal, characteristic, complemented
10C2×#89729C211yesmaximal, characteristic, complemented
11C2×#89729C211yesmaximal, characteristic, complemented
12C2×#89716C211yesmaximal, characteristic, complemented
13C2×#89714C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
15C2×#89712C211yesmaximal, characteristic, complemented
16C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×Dic14C2211yescharacteristic
23C2×C7×#124—28no—
24C2×C7×#124C2218yescomplemented
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C42×C7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C2×#6507—28no—
36C2×#6507C2218yescomplemented
37C2×#6502—28no—
38C2×#6502C2218yes—
39C22×(C2×D7)⋊C4C2211yescharacteristic
40C22×(C2×D7)⋊C4C2211yescharacteristic
41C22×(C2×D7)⋊C4C2211yescharacteristic
42C22×(C2×D7)⋊C4C2211yescharacteristic
43C22×(C2×D7)⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×Dic7⋊C4C2211yescharacteristic
48C22×Dic7⋊C4C2211yescharacteristic
49C22×C4×Dic7C2211yescharacteristic
50C22×C4×Dic7C2211yescharacteristic
51C22×C4×Dic7C2211yescharacteristic
52C2×#6448—28no—
53C2×#6448C2218yescomplemented
54#90003C2218yescomplemented
55#89994C2218yescomplemented
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62#89731C2218yescomplemented
63#89729C2218yescomplemented
64#89729C2218yescomplemented
65#89719C2218yescomplemented
66#89716C2218yescomplemented
67#89714C2218yescomplemented
68C22⋊C4×Dic7C2218yescomplemented
69#89712C2218yescomplemented
70C4×Dic7⋊C4C2218yescomplemented
71C2×#2491—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C22×C7×Q8—24no—
76C22×C7×Q8—24no—
77C22×C7×Q8—42no—
78C22×C7×Q8C2314yes—
79C22×C7×D4—24no—
80C22×C7×D4—24no—
81C22×C7×D4—42no—
82C22×C7×D4C2314yes—
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—24no—
89C22×C22⋊D7—24no—
90C22×C22⋊D7—24no—
91C22×C22⋊D7—24no—
92C22×C22⋊D7—24no—
93C22×C22⋊D7—42no—
94C22×C22⋊D7C2314yes—
95C22×C22⋊D7C2314yes—
96C23×Dic7—24no—
97C23×Dic7—24no—
98C23×Dic7—24no—
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2314yes—
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C22×Dic14—24no—
108C22×Dic14—24no—
109C22×Dic14—42no—
110C22×Dic14C2314yes—
111C7×#124—232no—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4—24no—
114C2×C7×C22⋊C4—24no—
115C2×C7×C22⋊C4D418yescomplemented
116C2×C7×C22⋊C4C2314yes—
117C2×C7×C22⋊C4C2314yes—
118C2×C7×C22⋊C4C2314yes—
119C2×C7×C22⋊C4C2314yes—
120C2×C42×C7—24no—
121C2×C42×C7C2314yes—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—24no—
124C2×C22⋊Dic7—24no—
125C2×C22⋊Dic7—24no—
126C2×C22⋊Dic7—42no—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132#6507—232no—
133#6502—232no—
134C2×(C2×D7)⋊C4—24no—
135C2×(C2×D7)⋊C4—24no—
136C2×(C2×D7)⋊C4—24no—
137C2×(C2×D7)⋊C4—24no—
138C2×(C2×D7)⋊C4—42no—
139C2×(C2×D7)⋊C4C2314yes—
140C2×(C2×D7)⋊C4C2314yes—
141C2×(C2×D7)⋊C4C2314yes—
142C2×(C2×D7)⋊C4C2314yes—
143C2×(C2×D7)⋊C4C2314yes—
144C2×Dic7⋊C4—24no—
145C2×Dic7⋊C4—24no—
146C2×Dic7⋊C4—24no—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4D418yes—
149C2×Dic7⋊C4C2314yes—
150C2×Dic7⋊C4C2314yes—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×C4×Dic7—24no—
155C2×C4×Dic7—24no—
156C2×C4×Dic7—24no—
157C2×C4×Dic7C2314yes—
158C2×C4×Dic7C2314yes—
159C2×C4×Dic7C2314yes—
160#6448—232no—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×C4⋊Q8—71no—
168C22×#124—71no—
169C22×#124D711yescharacteristic, complemented
170C22×#121—71no—
171#2491—716no—
172C2×#394—71no—
173C2×#394—71no—
174C2×#393—71no—
175C2×#393—71no—
176C2×#390—71no—
177C2×#390—71no—
178C2×#388—71no—
179C2×#388—71no—
180C2×#380—71no—
181C2×C4×C4⋊C4—71no—
182C2×C4×C22⋊C4—71no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7—22no—
195C24×C7—22no—
196C24×C7C2×D414yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7—22no—
205C23×D7—22no—
206C23×D7—22no—
207C23×D7C2412yes—
208C2×C7×Q8—28no—
209C2×C7×Q8—28no—
210C2×C7×Q8—44no—
211C2×C7×Q8—416no—
212C2×C7×D4—28no—
213C2×C7×D4—28no—
214C2×C7×D4—44no—
215C2×C7×D4—416no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7C2×D414yes—
229C22×C4×C7C2×D414yes—
230C22×C4×C7C2×D414yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2412yes—
236C2×C22⋊D7—28no—
237C2×C22⋊D7—28no—
238C2×C22⋊D7—28no—
239C2×C22⋊D7—28no—
240C2×C22⋊D7—28no—
241C2×C22⋊D7—44no—
242C2×C22⋊D7—416no—
243C2×C22⋊D7—416no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7—28no—
261C22×Dic7—28no—
262C22×Dic7—28no—
263C22×Dic7—416no—
264C22×Dic7C2×D414yes—
265C22×Dic7C2×D414yes—
266C22×Dic7#4114yes—
267C22×Dic7#4114yes—
268C22×Dic7#4114yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C22×Dic7C2412yes—
273C22×Dic7C2412yes—
274C22×Dic7C2412yes—
275C22×Dic7C2412yes—
276C2×Dic14—28no—
277C2×Dic14—28no—
278C2×Dic14—44no—
279C2×Dic14—416no—
280C7×C22⋊C4—28no—
281C7×C22⋊C4—28no—
282C7×C22⋊C4—28no—
283C7×C22⋊C4C2×D4116yescomplemented
284C42×C7—28no—
285C22⋊Dic7—28no—
286C22⋊Dic7—28no—
287C22⋊Dic7—28no—
288C22⋊Dic7—28no—
289C22⋊Dic7—44no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—28no—
294(C2×D7)⋊C4—44no—
295Dic7⋊C4—28no—
296Dic7⋊C4—28no—
297Dic7⋊C4—28no—
298Dic7⋊C4—28no—
299Dic7⋊C4C2×D4116yes—
300C4×Dic7—28no—
301C4×Dic7—28no—
302C4×Dic7—28no—
303C23×Q8—71no—
304C23×Q8C2×D711yescharacteristic
305C23×D4—71no—
306C23×D4—71no—
307C23×D4C2×D711yescharacteristic
308C24×C4—71no—
309C2×C4⋊Q8—78no—
310C2×C4⋊Q8—148no—
311C2×#124—28no—
312C2×#124—78no—
313C2×#124—148no—
314C2×#124C2×D718yescomplemented
315C2×#121—78no—
316C2×#121—148no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C22⋊C4—71no—
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4C2×D711yescharacteristic
333C22×C22⋊C4C2×D711yescharacteristic
334C22×C22⋊C4C2×D711yescharacteristic
335C22×C22⋊C4C2×D711yescharacteristic
336C22×C42—71no—
337C22×C42—71no—
338C22×C42—71no—
339C22×C42C2×D711yescharacteristic
340#394—78no—
341#394—78no—
342#393—78no—
343#393—78no—
344#390—78no—
345#390—78no—
346#388—78no—
347#388—78no—
348#380—78no—
349C4×C4⋊C4—78no—
350C4×C22⋊C4—78no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95—71no—
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—44no—
374C23×C7—44no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7—44no—
382C23×C7—44no—
383C23×C7—44no—
384C23×C7C22×D412yes—
385C23×C7C22×D414yes—
386C23×C7C22×D412yes—
387C23×C7C2×#4112yes—
388C23×C7C2×#4112yes—
389C23×C7C2×#4112yes—
390C23×C7H(5,𝔽2)12yes—
391C23×C72−1+412yes—
392C23×C7C2511yescharacteristic
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—44no—
401C22×D7—44no—
402C22×D7—44no—
403C22×D7—44no—
404C22×D7—44no—
405C22×D7—44no—
406C22×D7—44no—
407C7×Q8—416no—
408C7×D4—416no—
409C2×C4×C7—28no—
410C2×C4×C7—28no—
411C2×C4×C7—28no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—44no—
425C2×C4×C7—44no—
426C2×C4×C7C22×D414yes—
427C2×C4×C7C22×D414yes—
428C2×C4×C7C22×D414yes—
429C22⋊D7—416no—
430C22⋊D7—416no—
431C2×Dic7—28no—
432C2×Dic7—28no—
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—44no—
450C2×Dic7—44no—
451C2×Dic7—44no—
452C2×Dic7—44no—
453C2×Dic7—416no—
454C2×Dic7#124116yescomplemented
455C2×Dic7C22×D414yes—
456C2×Dic7C22×D414yes—
457C2×Dic7C2×#4114yes—
458C2×Dic7C2×#4114yes—
459C2×Dic7C2×#4114yes—
460Dic14—416no—
461C25—71no—
462C25C22×D711yescharacteristic
463C25C22×D711yescharacteristic
464C22×Q8—24no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8—74no—
468C22×Q8—144no—
469C22×Q8—144no—
470C22×Q8—282no—
471C22×Q8C22×D714yes—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4—42no—
475C22×D4—74no—
476C22×D4—74no—
477C22×D4—144no—
478C22×D4—144no—
479C22×D4—144no—
480C22×D4—144no—
481C22×D4—144no—
482C22×D4—282no—
483C22×D4C22×D714yes—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—74no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—144no—
493C23×C4—144no—
494C23×C4—144no—
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500C4⋊Q8—1432no—
501#124—232no—
502#124—1432no—
503#121—1432no—
504C2×C4⋊C4—78no—
505C2×C4⋊C4—74no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—74no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—144no—
511C2×C4⋊C4—144no—
512C2×C4⋊C4—144no—
513C2×C4⋊C4—144no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—74no—
518C2×C22⋊C4—74no—
519C2×C22⋊C4—74no—
520C2×C22⋊C4—74no—
521C2×C22⋊C4—74no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—144no—
528C2×C22⋊C4—144no—
529C2×C22⋊C4—144no—
530C2×C22⋊C4—144no—
531C2×C22⋊C4—144no—
532C2×C22⋊C4—144no—
533C2×C22⋊C4—144no—
534C2×C22⋊C4—144no—
535C2×C22⋊C4—282no—
536C2×C22⋊C4—282no—
537C2×C22⋊C4C22⋊D718yescomplemented
538C2×C22⋊C4C22×D714yes—
539C2×C22⋊C4C22×D714yes—
540C2×C22⋊C4C22×D714yes—
541C2×C22⋊C4C22×D714yes—
542C2×C42—24no—
543C2×C42—74no—
544C2×C42—74no—
545C2×C42—74no—
546C2×C42—144no—
547C2×C42—144no—
548C2×C42—144no—
549C2×C42C22×D714yes—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95—74no—
555#95—74no—
556C22×C7—24no—
557C22×C7—24no—
558C22×C7—24no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—416no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—88no—
572C22×C7C2×#12414yes—
573C22×C7#53214yes—
574C22×C7#54214yes—
575C22×C7D4214yes—
576C22×C7#54714yes—
577C22×C7#54814yes—
578C22×C7#55514yes—
579C22×C7C23×D411yescharacteristic
580C22×C7C23×D411yescharacteristic
581C22×C7C22×#4111yescharacteristic
582C22×C7C22×#4111yescharacteristic
583C22×C7C22×#4111yescharacteristic
584C22×C7C2×H(5,𝔽2)11yescharacteristic
585C22×C7C2×2−1+411yescharacteristic
586C2×D7—42no—
587C2×D7—42no—
588C2×D7—42no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—88no—
594C4×C7—24no—
595C4×C7—24no—
596C4×C7—24no—
597C4×C7—42no—
598C4×C7—42no—
599Dic7—24no—
600Dic7—24no—
601Dic7—42no—
602Dic7—42no—
603Dic7—42no—
604Dic7—42no—
605Dic7C2×#12418yescomplemented
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—72no—
620C24—142no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24—142no—
625C24—142no—
626C24—142no—
627C24C2×C22⋊D714yes—
628C24C23×D712yes—
629C24C23×D712yes—
630C24C23×D711yescharacteristic
631C2×Q8—28no—
632C2×Q8—28no—
633C2×Q8—44no—
634C2×Q8—416no—
635C2×Q8—148no—
636C2×Q8—148no—
637C2×Q8—284no—
638C2×Q8—2816no—
639C2×D4—28no—
640C2×D4—28no—
641C2×D4—44no—
642C2×D4—416no—
643C2×D4—148no—
644C2×D4—148no—
645C2×D4—148no—
646C2×D4—148no—
647C2×D4—148no—
648C2×D4—2816no—
649C2×D4—284no—
650C2×D4—2816no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—74no—
664C22×C4—74no—
665C22×C4—74no—
666C22×C4—72no—
667C22×C4—74no—
668C22×C4—74no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—72no—
672C22×C4—72no—
673C22×C4—72no—
674C22×C4—72no—
675C22×C4—148no—
676C22×C4—148no—
677C22×C4—148no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—142no—
692C22×C4—142no—
693C22×C4—142no—
694C22×C4—2816no—
695C22×C4D4×D714yes—
696C22×C4C2×C22⋊D714yes—
697C22×C4C2×C22⋊D714yes—
698C22×C4C23×D712yes—
699C22×C4C23×D712yes—
700C22×C4C23×D712yes—
701C22×C4C23×D712yes—
702C22×C4C23×D712yes—
703C4⋊C4—716no—
704C4⋊C4—148no—
705C4⋊C4—148no—
706C4⋊C4—148no—
707C4⋊C4—148no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—148no—
712C22⋊C4—148no—
713C22⋊C4—148no—
714C22⋊C4—148no—
715C22⋊C4—148no—
716C22⋊C4—148no—
717C22⋊C4—148no—
718C22⋊C4—148no—
719C22⋊C4—284no—
720C22⋊C4—284no—
721C22⋊C4C2×C22⋊D7116yescomplemented
722C42—28no—
723C42—148no—
724C42—148no—
725C42—148no—
726C2×C7—44no—
727C2×C7—82no—
728C2×C7#249118yescomplemented
729C2×C7C22×#12411yescharacteristic
730C2×C7C2×#53211yescharacteristic
731C2×C7C2×#54211yescharacteristic
732C2×C7C2×D4211yescharacteristic
733C2×C7C2×#54711yescharacteristic
734C2×C7C2×#54811yescharacteristic
735C2×C7C2×#55511yescharacteristic
736D7—82no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—142no—
765C23—142no—
766C23—142no—
767C23—142no—
768C23—142no—
769C23—142no—
770C23—142no—
771C23—284no—
772C23—284no—
773C23—284no—
774C23—284no—
775C23—284no—
776C23—284no—
777C23—284no—
778C23C2×D4×D712yes—
779C23#654812yes—
780C23D7×#4112yes—
781C23D7×#4112yes—
782C23D7×#4112yes—
783C23#655412yes—
784C23C22×C22⋊D714yes—
785C23C22×C22⋊D712yes—
786C23C24×D711yescharacteristic
787Q8—416no—
788Q8—2816no—
789D4—416no—
790D4—2816no—
791D4—2816no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—74no—
810C2×C4—74no—
811C2×C4—74no—
812C2×C4—716no—
813C2×C4—74no—
814C2×C4—74no—
815C2×C4—148no—
816C2×C4—148no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—142no—
832C2×C4—142no—
833C2×C4—2816no—
834C2×C4—284no—
835C2×C4—284no—
836C2×C4—284no—
837C2×C4—284no—
838C2×C4C2×D4×D714yes—
839C2×C4C22×C22⋊D714yes—
840C2×C4C22×C22⋊D714yes—
841C7C2×#249111yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—416no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—88no—
858C22—282no—
859C22—282no—
860C22—282no—
861C22—282no—
862C22—282no—
863C22—282no—
864C22—282no—
865C22—568no—
866C22#9036014yes—
867C22#9036114yes—
868C22D7×#12414yes—
869C22#9036814yes—
870C22D4×C22⋊D714yes—
871C22#9051514yes—
872C22#9052314yes—
873C22C22×D4×D711yescharacteristic
874C22C2×#654811yescharacteristic
875C22C2×D7×#4111yescharacteristic
876C22C2×D7×#4111yescharacteristic
877C22C2×D7×#4111yescharacteristic
878C22C2×#655411yescharacteristic
879C22C23×C22⋊D711yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—42no—
884C4—42no—
885C4—78no—
886C4—144no—
887C4—144no—
888C4—282no—
889C4—282no—
890C4—282no—
891C4—282no—
892C2—44no—
893C2—82no—
894C2—562no—
895C2#1174041218yesdirect product factor
896C2C2×#9036011yescharacteristic
897C2C2×#9036111yescharacteristic
898C2C2×D7×#12411yescharacteristic
899C2C2×#9036811yescharacteristic
900C2C2×D4×C22⋊D711yescharacteristic
901C2C2×#9052311yescharacteristic
902C2C2×#9051511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#124C2
socleC24×C7C24
prime radicalC22×#6502C2
hypercenterC22×#124D7
hypocenterC7C2×#2491
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×C7×#124C2semidirect
2. C22×#6507C2semidirect
4. C22×#6448C2semidirect
5. C2×#90003C2semidirect
6. C2×#89994C2semidirect
7. #11740412C2direct (N × H)
8. C2×#89731C2semidirect
9. C2×#89719C2semidirect
10. C2×#89729C2semidirect
11. C2×#89729C2semidirect
12. C2×#89716C2semidirect
13. C2×#89714C2semidirect
14. C2×C22⋊C4×Dic7C2semidirect
15. C2×#89712C2semidirect
16. C2×C4×Dic7⋊C4C2semidirect
24. C2×C7×#124C22semidirect
36. C2×#6507C22semidirect
53. C2×#6448C22semidirect
54. #90003C22semidirect
55. #89994C22semidirect
62. #89731C22semidirect
63. #89729C22semidirect
64. #89729C22semidirect
65. #89719C22semidirect
66. #89716C22semidirect
67. #89714C22semidirect
68. C22⋊C4×Dic7C22semidirect
69. #89712C22semidirect
70. C4×Dic7⋊C4C22semidirect
115. C2×C7×C22⋊C4D4semidirect
169. C22×#124D7semidirect
283. C7×C22⋊C4C2×D4semidirect
314. C2×#124C2×D7semidirect
454. C2×Dic7#124semidirect
537. C2×C22⋊C4C22⋊D7semidirect
605. Dic7C2×#124semidirect
721. C22⋊C4C2×C22⋊D7semidirect
728. C2×C7#2491semidirect
841. C7C2×#2491semidirect
895. C2#11740412direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1242
C22×#65072
C22×#65022
C22×#64482
C2×#900032
C2×#899942
#117404122
C2×#897312
C2×#897192
C2×#897292
C2×#897162
C2×#897142
C2×C22⋊C4×Dic72
C2×#897122
C2×C4×Dic7⋊C42
C2×#24917